The value of the function as x increases comes closer to 6 and at limit x→∝ the value is 6.
In mathematics, a limit is the value that such a function (or sequence) gains as the input (or index) gets closer to a particular value.
Without limits, it is impossible to perform calculus or mathematical analysis; limits are also necessary to compute continuity, derivatives, and integrals.The concept of a limit of a series is further generalized to encompass the concept of such a limit of a topological net, in addition to being strongly related to limit and indirect limit in category theory.Several different converging ideas can be defined on function spaces. This sometimes relies on how frequently the area is set up. Two well-known examples of function spaces having a notion of convergence are Lp spaces and Sobolev space.Given the function is [tex]f(x) = 6-\frac{1}{x-4}[/tex]
Now we put the limit to the function as [tex]lim_{x\rightarrow \infty} f(x)[/tex]
Therefore :
[tex]lim_{x\rightarrow \infty} (6-\frac{1}{x-4})\\=lim_{x\rightarrow \infty} 6 - lim_{x\rightarrow \infty}\frac{1}{x-4}\\=6 - 0\\=6[/tex]
Hence the value of the function is 6.
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you can drive around a NASCAR speedway 40 times for $10 how many times can you go around the track for eight dollars?
If x = a/b (with a ≠ b and b ≠ 0), then express a+b/a-b in terms of x.
Using the properties of ratio and proportion we can find the value as [tex]\frac{x+1}{x-1}[/tex] .
A theorem built on the idea of proportions enables a computation procedure that is speedier and requires fewer expansions.
When working with rational functions or fractional equations, it is helpful. Use the componendo and dividendo rule to study ratios and proportions. If the ratio of any two provided numbers is the same as the ratio of the other two numbers, then the ratios of the sum of the denominator and numerator to the difference of the denominator and numerator of the two rational numbers are comparable in nature.The given ratio is of the form x = a /b
This can be written in the form of
[tex]\frac{x}{1} = \frac{a}{b}[/tex]
Now we have to find the value of [tex]\frac{a+b}{a-b}[/tex].
Using the componendo and dividendo rule we get:
Adding the denominator to the numerator to get the new numerator and subtracting the denominator from the numerator to get the new denominator.
Mathematically:
[tex]\frac{a+b}{a-b} = \frac{x+1}{x-1}[/tex]
Therefore this is the required result.
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All sixth grade students are asked to bring something for the fall dance. One student brought 1 ½ gallon of apple juice and another student brought 3 ½ gallon of apple juice. Each serving is ⅓ cup. Given this amount, how many students would be able to have some apple juice ?
Based on the gallons of apple juice brought by the students, and the serving per gallon, the number of students that would have some apple juice is 15 students
How to find the number of students?First, find the total amount of juice that the students brought of apple juice:
= 1 ½ + 3 ½
= 3/2 + 7/2
= 10 / 2
= 5 gallons
If each serving is in a 1/2 cup, then the number of students that would be able to get some apple juice is:
= Number of gallons of juice / Number of cups per serving
= 5 ÷ ⅓
= 5 x 3/1
= 15 / 1
= 15 students
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G=30 and h=6 and g/5-h
Composition Functions
Composition functions are functions that combine to make a new function. We use the notation ◦ to denote a composition.
f ◦ g is the composition function that has f composed with g. Be aware though, f ◦ g is not
the same as g ◦ f. (This means that composition is not commutative).
f ◦ g ◦ h is the composition that composes f with g with h.
Since when we combine functions in composition to make a new function, sometimes we
define a function to be the composition of two smaller function. For instance,
h = f ◦ g (1)
h is the function that is made from f composed with g.
For regular functions such as, say:
f(x) = 3x
2 + 2x + 1 (2)
What do we end up doing with this function? All we do is plug in various values of x into
the function because that’s what the function accepts as inputs. So we would have different
outputs for each input:
f(−2) = 3(−2)2 + 2(−2) + 1 = 12 − 4 + 1 = 9 (3)
f(0) = 3(0)2 + 2(0) + 1 = 1 (4)
f(2) = 3(2)2 + 2(2) + 1 = 12 + 4 + 1 = 17 (5)
When composing functions we do the same thing but instead of plugging in numbers we are
plugging in whole functions. For example let’s look at the following problems below:
Examples
• Find (f ◦ g)(x) for f and g below.
f(x) = 3x + 4 (6)
g(x) = x
2 +
1
x
(7)
When composing functions we always read from right to left. So, first, we will plug x
into g (which is already done) and then g into f. What this means, is that wherever we
see an x in f we will plug in g. That is, g acts as our new variable and we have f(g(x)).
find the first 5 terms and the 25th term of 6n-3n^2
The fifth and the twenty fifth terms of the arithmetic sequence are a5 = - 45 and a25 = - 1725
What is an arithmetic sequence ?A group of integers that are arranged in a particular order and share a difference between each term is known as an arithmetic sequence. For instance, the common difference between the numbers 3, 9, 15, 21, and 27 in mathematics is 6. The term "arithmetic progression" can refer to an arithmetic sequence..
The given expression is [tex]6n - 3n^2[/tex]
The 5th term that is n = 5
thus the given expression will become
[tex]6n-3n^2[/tex]
which is equal 6×5 - 3 (5)²
= 30 - 3 × 25
= 30 - 75
= - 45
The 25th term is n = 25
Thus the given expression that is [tex]6n-3n^2[/tex]
= 6 × 25 - 3× ( 25) ²
= 150 - 3 × 625
= - 1725
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1. Find the product: 82 •123. Solve using either the partial products or the box method.
a researcher attempts to study the effects of alcohol on task performance. one factor is alcohol (alcohol treatment, placebo control), and the other factor is task difficulty (easy, difficult. if the researcher uses a repeated measures design with 15 participants per condition, how many participants will he need for the study?
If the researcher employs a repeated measures design with 15 participants per condition, the study will require 15 participants
What is repeated measures?A repeated-measures design takes multiple, or repeated, measurements on each experimental unit. We call an experiment with repeated measures one in which all participants participate in all conditions. For example, you might want to learn whether taking vitamin supplements before an exam improves recall. So, in the first condition, you give a vitamin tablet to each participant. A repeated measures design is a type of research design in which multiple measures of the same variable are taken on the same or matched subjects under different conditions or over two or more time periods. In a longitudinal study, for example, repeated measurements are collected to assess change over time.To learn more about repeated measures, refer to:
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Poker is a common game in which players are dealt five cards from a deck of cards. It can be shown that there are 2,598,960 different possible poker hands. The winning hands (from highest to lowest) are shown in the table below. Find the requested probability. Use a calculator. (Show your answer to nine decimal places.)
P(royal flush)
The requested probability is 0.99974
What is probability ?The likelihood of an event happening is gauged by probability. Many things are impossible to completely predict in advance. Only the likelihood of an event occurring, or how probable it is to happen, can be predicted using probability. Tossing a coin, for instance, has a chance of coming up heads or tails.
TOTAL NUMBER OF POSSIBLE HANDS..
WE HAVE 52 CARDS WITH 4 SUITS AND 13 CARDS PER SUITE.
WHEN WE ARE DEALT A 5 CARDER, DISREGARDING THE ORDER OF DEAL,WE HAVE
C[52,5] TOTAL NUMBER OF POSSIBLE HANDS =52!/[47!×5!]=[52× 51 × 50 ×49× 48× (47!) ]/[5! ×47!]=
=[52× 51× 50× 49×48]/ [5!] = 2598960
ROYAL FLUSH
THIS COULD BE OF ANY SUIT ...
SO WE HAVE 4 POSSIBILITIES
ONCE A SUIT IS CHOSEN THE THEN THE OTHER POSSIBILITY IS TO ONLY GET
A,K,Q,J,10 IN THAT SUIT, OF EACH OF WHICH, THERE IS ONLY ONE CARD IN THE PACK
SO THERE IS ONLY 1*1*1*1*1=1 WAY
SO TOAL NUMBER OF POSSIBILITIES ARE 4^ * 1 = 4 WAYS
SO PROBABILITY = 4/2598960 = 0.00000154 ..........ANSWER
PROBABILITY = 0.00000 ...ANSWER
TWO PAIR OR BETTER
THERE ARE ...4+36+624+3744+5108+10200+54912+123552-198180
HENCE PROBABILITY = 198180/2598960=0.0762536
-0.07625...........ANSWER
WE CAN GET 4 OF A KIND OR BETTER IN 4+36+624= 664 WAYS
SO LOSING HANDS TO 4 OF A KIND ARE =2598960-664-2598296
SO PROBABILITY = 2598296/2598960-0.9997445
=0.99974...........ANSWER
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1. 2x+8=15 2. 35=3x+14 3. 2x+7+2x=19
Answer:
2x+8=15
2x=15-8
2x=7
divide both sides by the coefficient of x
x=7/2
x=3.5
86.177 Rounded to the nearest hundredth.
if angle ab is a right triangle then ab is perpendicular to bc
Answer:
it should be a 90-degree angle or right triangle
Step-by-step explanation:
A linear function has a y-intercept of -12 and a slope of 3/2. What is the
equation of the line?
Answer:
y = (3/2)x - 12
Step-by-step explanation:
The equation of a line is expressed in the form y = mx + c, where m is the gradient (slope) and c is the y-intercept. Simply substitute your values into this form:
y = (3/2)x - 12
The scale from a garden to drawing is 8 ft to 1 cm the scale from the same garden to another drawing is 2 ft to 1 cm what are the lengtgs of the base snd height of the garden in the other scale drawing?
The lengths of the base and height of the garden in the other scale drawing is 9.6 cm and 14.4 cm
How to calculate the value?The scale from a garden to the illustration is stated as 8 feet to 1 centimeter in the question. The drawing's base and height are each 2.4 cm long and 3.6 cm tall, respectively.
As a result, the lengths of the garden's base and height are, respectively, 2.4*8 ft (19.2 ft) and 3.6*8 ft (28.8 ft).
We now know that the scale is 2 feet to 1 centimeter between the same garden and another drawing.
Thus, the lengths of the base and the height of the other drawing are 19.2/2 cm. = 9.6 cm. and 28.8/2 cm. = 14.4 cm. respectively.
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I really need help please and thx
worth about 14 points
Answer:
The answer is -71.124
Step-by-step explanation:
Since there is a subtraction sign next to a negative it becomes addition.
so the equation becomes -95.004 + 23.88 which were going to flip around to 23.88 - 95.004
So,
23.880
- 95.004
-------------------
-71 .124
Brooklyn line‘s upright retanglar prisms like the one shown. She aligns each prism behind the previous prism to make a larger prism. The larger prism has a surface area of 1288 and squared. How many prisms does Brooklyn align? Show your work
Answer:
if there are 12 cubes, there must be 3 rows of 4 since its a prism. 1288 square root is 35. something
Step-by-step explanation:
Suppose the probability of event A is P(A) = 7/10. What is the probability of event Anot happening P(A')? (You can give your answer as a fraction, decimal or percent)P(A') = ?
Solution
Given the probability of event A happening is P(A) = 7/10
the probability of event A not happening P(A') = 1 - 7/10 = 3/10
The answer is 3/10
how much less than 6 is the sum of 2 3/4 and 2 4/5
Answer:
0.45
Step-by-step explanation:
2.75+ 2.80= 5.55
6-5.55= 0.45
I hope this helps! :) If it does could you please mark me brainliest?
Answer:
Step-by-step explanation:
answer: 9/20
formulate 2 3/4 + 2 4/5 - 6
sorry if im wrong.
please help ME !!!!!I need help !!!!!!!
From the given figure a pair of lines that appear to parallel are AG and CJ.
The line segments AG, BH and CJ and DF is transversal.
What are parallel lines?Parallel lines are those lines that are equidistant from each other and never meet, no matter how much they may be extended in either directions.
12. A pair of lines that appear to parallel are AG and CJ.
13. A perpendicular is a straight line that makes an angle of 90° with another line.
Here, the perpendicular lines are DF and BH.
14. When two or more lines meet at a common point, they are known as intersecting lines. The point at which they cross each other is known as the point of intersection.
Here, AG and DF, BH and DF, CJ and DF are intersecting lines.
Therefore, from the given figure a pair of lines that appear to parallel are AG and CJ.
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a-software company is hiring an engineer and a manager. How many ways can these positions be filled if 17 people apply for the position of an engineer and 22 people apply for the position of a manager question
Given:
17 people apply for the position of an engineer.
22 people apply for the position of a manager.
[tex]\begin{gathered} \text{Total number of ways to fill the positions=17}\times22 \\ \text{Total number of ways to fill the positions=}374 \end{gathered}[/tex]Number of ways to fill the positions is 374.
Use the iterative rule to find the 5th term in the sequence:
an = 4x3n-1
972
243
324
81
Answer:
324
Step-by-step explanation:
1) substitute the 5 into the formula
n=5 [tex]a_{n}=4[/tex]×[tex]3^{5-1}[/tex]
2) simplify
5-1 = 4
[tex]3^4[/tex] = 81
4×81 = 324
Hope this helps, have a great day!
Answer:
5th term = 324
Step-by-step explanation:
[tex]a_n \: = \: 4 \: \cdot \: {3}^{n - 1} [/tex]
Where, n = 5
[tex]a_5 \: = \: 4 \: \cdot \: {3}^{5 - 1} [/tex]
[tex]a_5 \: = 4 \: \cdot \: {3}^{4} [/tex]
[tex]a_5 \: = 4 \: \cdot \: 81[/tex]
[tex]a_5 \: = \: 324[/tex]
How many two digit numbers have an odd number of factors?
There will be 6 two-digit numbers having an odd number of factors.
According to the question,
We have the following information:
There are two-digit numbers.
It means that the list of numbers is from 10 to 99.
Now, we have to find the numbers with the odd number of factors.
We know that odd numbers are the numbers which are not divisible by 2. For example, 1, 3, 5, etc. are odd numbers.
Note that 1 is also included as a factor.
Now, the numbers with odd number of factors will be the perfect squares as 1 will be added to them and the numbers will become odd.
So, the perfect two-digit square numbers are 16, 25, 36, 49, 64 and 81.
Now, we can prove that these numbers satisfy the given conditions by taking factor of any one number.
Let's take 25. The factors of 25 are 1, 5, and 5. So, in total there are 3 factors.
Hence, there are 6 two-digit numbers having an odd number of factors.
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HELP URGENT!!!!! WILL MARK BRAINLIEST!!!! SHOW WORK!!!!!!
Consider P(x) = x^3+3x^2-4, and c=-2. Show the given value of c is a zero of P(x) (this could be done through synthetic division), find all zeros of P(x), and write P(x) in factored form.
Zeros:
Factored form: P(x)=
Answers:
Zeros: -2 and 1
Factored form: P(x) = (x+2)(x+2)(x-1)
====================================================
Explanation:
One way to show that c = -2 is a zero or root of P(x) is to plug it in as the x value and simplify. If we get P(x) = 0, then that input is a root.
P(x) = x^3+3x^2-4
P(-2) = (-2)^3+3(-2)^2-4
P(-2) = -8+3(4)-4
P(-2) = -8+12-4
P(-2) = 4-4
P(-2) = 0
In short, the input x = -2 leads to the output P(x) = 0.
This confirms -2 is a root of P(x). By extension, this tells us that (x+2) is a factor of P(x).
We can determine the other factor using synthetic division as shown in figure 1. See the image below.
The synthetic division table shows us getting a remainder of 0, as highlighted in yellow.
The other stuff in pink represents the coefficients of the quotient.
We have the coefficients 1, 1, -2 which forms 1x^2+1x-2 and that simplifies to x^2+x-2
This further factors to (x-1)(x+2) because we're looking for two numbers that a) multiply to -2 and b) add to 1. Use the FOIL rule to expand (x-1)(x+2) and you should get x^2+x-2 again. This helps confirm the factorization was done correctly.
---------------------
In short, we found that P(x) = (x+2)(x^2+x-2) and it fully factors to P(x) = (x+2)(x+2)(x-1)
Each factor leads to a root.
x+2 = 0 leads to the root x = -2
x-1 = 0 leads to the root x = 1
Visually, each root is an x intercept where the curve either crosses the x axis or touches it before bouncing away. See figure 2 below.
The maximum speed of a car on a trip is 60 miles per hour. Write and solve an inequality that represents the number of hours the car takes to travel 180 miles.
Noa contributes 16% of her $66,400 annual salary to her 401(k) plan. What is
her pre-tax income?
O A. $57,241
OB. $66,400
C. $79,048
OD. $55,776
Please please help me!!!
answer the question in the photo
( I will mark Brainliest )
Step-by-step explanation:
7. the additive property of equality. we can add the same thing to both sides, and the equality stays true. it is like a balance with 2 cups. it is balanced, and we add the same weight to both sides. it remains balanced.
8. the commutative property of equality.
a = b, therefore b = a.
the simplest of all principles and properties.
imagine what would be the consequence, if that
were not true.
it would mean for example that you give the cashier in a store some money to pay for something, but the amount the cashier receives is not the same amount you have given the cashier. booom !
Suppose you have health insurance that is partially funded by the company you work for. They have agreed to pay 85% of your coverage. What percent of your insurance coverage will you be paying? Show your work.
The Solution.
Your company partially funds 85% of the total coverage. That gives
[tex]85\text{ \%}[/tex]The percent of the insurance coverage that will be paid by you is
[tex]100-85=15\text{ \%}[/tex]Thus, the correct answer is 15%.
draw a picture to solve. Mandi has 8 dog biscuits. She has 7 dog bowls. Each dog bowl gets the same number of dog biscuits. How many dog biscuits are in each bowl?
If Mandi has 8 dog biscuits, she has 7 dog bowls and each dog bowl gets the same number of dog biscuits, then the number of dog biscuits in each bowl is 1.14 biscuits
Number of dog biscuits that Mandi has = 8 dog biscuits
Number of dog bowls that Mandi has = 7 dog bowls
Each dog bowl get the same number of dog biscuits.
To find the number of dog biscuits in each bowl we have to do the division
Number of dog biscuits in each bowl = Number of dog biscuits that Mandi has ÷ Number of dog bowls that Mandi has
Substitute the values in the equation
= 8/7
= 1.14 biscuits
Hence, if Mandi has 8 dog biscuits, she has 7 dog bowls and each dog bowl gets the same number of dog biscuits, then the number of dog biscuits in each bowl is 1.14 biscuits
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A construction company charges $15 per hour for debris removal, plus a one-time fee for the use of a trash dumpster. The total fee for 9 hours of service is $195
The trash dumpster fee was 60 dollars.
Which list shows the numbers in order from greatest to least?
A 4.232, 4.2, 4.142, 4.1
B 4.1, 4.142, 4.2, 4.232
C 4.232, 4.142, 4.2, 4.1
D 4.2, 4.232, 4.142, 4.1
Answer:
ignoring the decimal. The order from greatest to least is 2, 4, 5, 6, and 8
TEXT ANSWER
Question 8
Point M is the midpoint of PQ. The coordinates of P and M are given below.
M(5,-2) and P(11, - 10)
Based on this information, what are the coordinates of ?
Show all work and provide any necessary descriptions.
Answer:
Q (- 1, 6 )
Step-by-step explanation:
use the midpoint formula to find the coordinates of M then equate the x and y coordinates with the actual coordinates of M
P (11, - 10) and let Q = (x, y ) , then
[tex]\frac{11+x}{2}[/tex] = 5 ( multiply both sides by 2 )
11 + x = 10 ( subtract 11 from both sides )
x = - 1
and
[tex]\frac{-10+y}{2}[/tex] = - 2 ( multiply both sides by 2 )
- 10 + y = - 4 ( add 10 to both sides )
y = 6
coordinates of Q = (- 1, 6 )
