In mathematics, a limit is the value that a function (or sequence) approaches as the input (or index) approaches some value.
g(x) , one may look at how big f(x) and g(x) are. For example: If f(x) is close to some positive number and g(x) is close to 0 and positive, then the limit will be ∞. If f(x) is close to some positive number and g(x) is close to 0 and negative, then the limit will be −∞.
A forest has 800 pine trees, but a disease is introduced that kills a fourth of the pine trees in the forest
every year.
Which graph shows the number y of pine trees remaining in the forest 2 years after the disease is
introduced?
In a graph
The exponential function that models the number of trees after t years is given by:
[tex]A(t) = 800\left(\frac{3}{4}\right)^t[/tex]
Hence, after 2 years, 450 trees will be remaining, as the graph at the end of this answer shows.
What is an exponential function?A decaying exponential function is modeled by:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem:
The forest has 800 pine trees, hence A(0) = 800.Each year, a disease is introduced that kills a fourth of the pine trees in the forest every year, hence [tex]r = \frac{1}{4}[/tex].Then, the equation is:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]A(t) = 800(1 - \frac{1}{4})^t[/tex]
[tex]A(t) = 800\left(\frac{3}{4}\right)^t[/tex]
After 2 years:
[tex]A(2) = 800\left(\frac{3}{4}\right)^2 = 450[/tex]
450 trees will be remaining.
You can learn more about exponential functions at https://brainly.com/question/25537936
A student answers 20 out of the first 32 questions correctly, but gets three-quarters of remaining questions wrong. all the questions are equal value. if the students' score is 40%, how many questions were there is exam?
Answer:
80 Questions
Step-by-step explanation:
First 20/32
then 3/4 questions wrong
so let's say he got there were 48 remaining questions
then he would have 36 wrong and and 12 correct
therefore it would be..
20 + 12/32 + 48
32/80
__________________________________________
so let's check the answer
it says he got 40%
so let's do 32/80
= 0.4
to convert it into percentage times by 100
= 0.4 x 100
= 40%
Answer:
There are [tex]80[/tex] questions on this exam.
Step-by-step explanation:
Let [tex]x[/tex] denote the number of questions on this exam in total (including the first [tex]32[/tex] questions.)
There would be [tex](x - 32)[/tex] questions after the first [tex]32[/tex].
Since the student got three-quarters of these wrong, only one-quarter ([tex]1 - (3/4) = (1/4)[/tex]) of these [tex](x - 32)[/tex] questions are correct. That would be another [tex](1/4) \cdot (x - 32)[/tex] right answers.
In total, the number of questions that the student got correct would be:
[tex]\begin{aligned} & 20 + \frac{1}{4} \cdot (x - 32) \\ =\; & 20 + \frac{x}{4} - 8 \\ =\; & 12 + \frac{x}{4}\end{aligned}[/tex].
On the other hand, it is given that the student got [tex]40\%[/tex] of the [tex]x[/tex] questions right. Hence, the number of correct answers may also be expressed as:
[tex]\begin{aligned} & (40\%) \, x\\ =\; & \frac{2\, x}{5} \end{aligned}[/tex].
Both expressions give the number of correct answers. Equate the two expressions and solve for [tex]x[/tex]:
[tex]\displaystyle 12 + \frac{x}{4} = \frac{2\, x}{5}[/tex].
[tex]\displaystyle \left(\frac{2}{5} - \frac{1}{4}\right)\, x = 12[/tex].
[tex]\displaystyle \frac{8 - 5}{20}\, x = 12[/tex].
[tex]\displaystyle \frac{3}{20}\, x = 12[/tex].
[tex]\begin{aligned} x &= 12 \times \frac{20}{3} \\ &= 80\end{aligned}[/tex].
In other words, there are [tex]80[/tex] questions on this exam in total.
A grocery store owner asked the first 20 children who visited the store one day about their favorite snack. This is what type of sampling
Answer:
Non-probability sampling: In non-probability sampling, the researcher chooses members for research at random. This sampling method is not a fixed or predefined selection process. This makes it difficult for all elements of a population to have equal opportunities to be included in a sample.
Step-by-step explanation:
Uses of non-probability sampling
Non-probability sampling is used for the following:
Create a hypothesis: Researchers use the non-probability sampling method to create an assumption when limited to no prior information is available. This method helps with the immediate return of data and builds a base for further research.
Exploratory research: Researchers use this sampling technique widely when conducting qualitative research, pilot studies, or exploratory research.
Budget and time constraints: The non-probability method when there are budget and time constraints, and some preliminary data must be collected. Since the survey design is not rigid, it is easier to pick respondents at random and have them take the survey or questionnaire.
How do you decide on the type of sampling to use?
For any research, it is essential to choose a sampling method accurately to meet the goals of your study. The effectiveness of your sampling relies on various factors. Here are some steps expert researchers follow to decide the best sampling method.
Jot down the research goals. Generally, it must be a combination of cost, precision, or accuracy.
Identify the effective sampling techniques that might potentially achieve the research goals.
Test each of these methods and examine whether they help in achieving your goal.
Select the method that works best for the research.
Select your respondents
Difference between probability sampling and non-probability sampling methods
We have looked at the different types of sampling methods above and their subtypes. To encapsulate the whole discussion, though, the significant differences between probability sampling methods and non-probability sampling methods are as below:
Probability Sampling Methods Non-Probability Sampling Methods
Definition Probability Sampling is a sampling technique in which samples from a larger population are chosen using a method based on the theory of probability. Non-probability sampling is a sampling technique in which the researcher selects samples based on the researcher’s subjective judgment rather than random selection.
Alternatively Known as Random sampling method. Non-random sampling method
Population selection The population is selected randomly. The population is selected arbitrarily.
Nature The research is conclusive. The research is exploratory.
Sample Since there is a method for deciding the sample, the population demographics are conclusively represented. Since the sampling method is arbitrary, the population demographics representation is almost always skewed.
Time Taken Takes longer to conduct since the research design defines the selection parameters before the market research study begins. This type of sampling method is quick since neither the sample or selection criteria of the sample are undefined.
Results This type of sampling is entirely unbiased and hence the results are unbiased too and conclusive. This type of sampling is entirely biased and hence the results are biased too, rendering the research speculative.
Hypothesis In probability sampling, there is an underlying hypothesis before the study begins and the objective of this method is to prove the hypothesis. In non-probability sampling, the hypothesis is derived after conducting the research study.
Given that for the water leakage n=100 Σx=31,353 and Σx^2 = 10687041 calculate the simple mean.
Answer:
[tex] \bar x = \frac{ \sum x}{n} \\ \\ \bar x = \frac{31353}{100} \\ \\ \bar x = 313.53[/tex]
Answer:
Hello,
Step-by-step explanation:
[tex]n=100\\\\\displaystyle \sum_{i=1}^{100}x_i=31.353\\\\\\\overline{x}=\dfrac{\displaystyle \sum_{i=1}^{100}x_i}{n} =\dfrac{31.353}{100} =\boxed{0.31353}\\\\[/tex]
What is the value of x in |6| = x?
Answer:
6
Step-by-step explanation:
the | | are for absolute value, which means
|-6|=|6|= 6
Pamela is 8 years older that Jiri. The sum of their age is 102. What is Jiri's age?
Answer:
Step-by-step explanation:
102-8= 94
94/2= 47
Jiri is 47 years old.
allowing 20% discount on the marked price of a watch, the value of the watch will be rs 6328, when a VAT of 13% is added find it's marked price
Step-by-step explanation:
let , MP =x
then,
discount amount =D% of MP
= (20/100)× x
= 0.2x
now,Sp without VAT = MP-D
=x - 0.2x
= 0.8x
NoW, SP with VAT = Sp without VAT+ VAT %of SP
or ,6328 = 0.8x + 13% of 0.8x
or, 6328 = 0.8x + (13/100) × 0.8x
or, 6328= 0.8x + 0.104x
or,. 6328= 0.904x
or, X= 6328/0.904
X= 7000 Rs.
Hence ,MP is Rs.7000
A computer parts company wants to make a rectangular memory board that has a perimeter of 14 cm and a diagonal of length 5 cm. What are the dimensions of the board?
Answer:
A computer parts company wants to make a rectangular memory board that has a perimeter of 28 centimeters and a diagonal length of 10 centimeters. Find the dimensions of the board. Consider the length to be the longer side.: Call the two sides L & W: the perimeter 2L + 2W = 28 Simplify, divide by 2 L + W = 14 L = (14-W); use this form for substitution
Step-by-step explanation:
==========================================================
Explanation:
x = width
y = length
both x and y are positive real numbers, and the units of which are in cm.
The perimeter of any rectangle is found by saying
P = 2*(length+width)
P = 2*(x+y)
Plugging in P = 14 leads us to
P = 2*(x+y)
14 = 2*(x+y)
14/2 = x+y
7 = x+y
Solve for one of the variables. Let's say we solve for y. That should get us y = 7-x which we'll use a bit later.
--------------
Notice how the diagonal forms two identical right triangles. The legs of which are x and y as defined earlier. The hypotenuse is 5, which is the diagonal length.
Use the pythagorean theorem to help solve for x
a^2 + b^2 = c^2
x^2 + y^2 = 5^2
x^2 + (7-x)^2 = 25 ... plug in y = 7-x
x^2 + 49 - 14x + x^2 = 25 ... use FOIL rule
2x^2-14x+49 = 25
2x^2-14x+49-25 = 0
2x^2-14x+24 = 0
2(x^2-7x+12) = 0
x^2-7x+12 = 0
(x-3)(x-4) = 0
x-3 = 0 or x-4 = 0
x = 3 or x = 4
If x = 3, then y = 7-x = 7-3 = 4
If x = 4, then y = 7-x = 7-4 = 3
We have this symmetry going on. If x is one of 3 or 4, then y is the other of those values. Because x = 3 and y = 4, or vice versa, this means we have a 3-4-5 right triangle (well to be fair we have two identical copies of such a triangle to form the rectangle).
Therefore, the dimensions of the rectangular board is 3 cm by 4 cm. The order doesn't matter so you could easily say "4 cm by 3 cm" to mean the same thing.
--------------
Check:
P = perimeter
P = 2*(length+width)
P = 2*(x+y)
P = 2*(3+4)
P = 2*7
P = 14
That helps confirm the answer.
1. Look at the figure. Which construction is illustrated?
N
IR
H
a line perpendicular to
H3
through point N
a line parallel to
HU
through pointly
The construction illustrated in the figure is that of a line parallel to [tex]\overrightarrow{HJ}[/tex] through point N.
Given: Figure containing illustration of the construction
To find: The construction illustrated in the figure
It can be seen that the figure contains a straight line passing through H and J, a straight line passing through H and N, and a straight line passing through N which seems to be parallel to [tex]\overrightarrow{HJ}[/tex].
The figure also contains arcs made by a compass that measures the angle between [tex]\overrightarrow{HJ}[/tex] and [tex]\overrightarrow{HN}[/tex]. These arcs have been replicated at the point N on the straight line [tex]\overrightarrow{HN}[/tex].
This implies that the straight line through N has been constructed in such a way, so that the angle between that straight line and [tex]\overrightarrow{HN}[/tex] is equal to the angle between [tex]\overrightarrow{HJ}[/tex] and [tex]\overrightarrow{HN}[/tex]. This makes these angles, corresponding angles and [tex]\overrightarrow{HN}[/tex] as the transversal. Thus, the new straight line is constructed parallel to [tex]\overrightarrow{HJ}[/tex].
A strong counterargument that this illustration is not that of a line perpendicular to [tex]\overrightarrow{HJ}[/tex] through point N is that the figure does not contain any straight line perpendicular to [tex]\overrightarrow{HJ}[/tex].
Thus, the construction illustrated in the figure is that of a line parallel to [tex]\overrightarrow{HJ}[/tex] through the point N.
Learn more about construction of parallel lines here:
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Is this a parallelogram
Answer:
Yes!
Step-by-step explanation:
Since it has four sides and has parallel sets of lines on each side.
Find perimeter of square with its each side a cm.
Answer:
4cm
Step-by-step explanation:
Each side of the square = 1cm
Perimeter of a square = 4xside
= 4x1 = 4
Answer From Gauth Math
In a class of 70 pupils, 36 like tasty time , 34 like ice-
cream, 6 like both tasty time }
draw a Venn diagram to show the data.
find how
many
like neither tasty time nor ice-cream
Step-by-step explanation:
I think this might be the correct answer
The number of pupils that like neither tasty-time nor ice cream is 6 if in a class of 70 pupils, 36 like tasty time, 34 like ice cream, 6 like both tasty times.
What is the Venn diagram?It is defined as the diagram that shows a logical relation between sets.
The Venn diagram consists of circles to show the logical relation.
We have:
In a class of 70 pupils, 36 like tasty time, 34 like ice cream, 6 like both tasty time.
Total = 70 pupils
Number of like tasty time = 36
Number of like ice cream = 34
Number of like both = 6
Let x be the total number of pupils that like neither tasty-time nor ice cream
The number of pupils that like ice cream only = 34 - 6 = 28
The number of pupils that like tasty-time only = 36 - 6 = 30
From the Venn diagram:
28 + 30 + 6 + x = 70
x = 70 - 64
x = 6
Thus, the number of pupils that like neither tasty-time nor ice cream is 6 if in a class of 70 pupils, 36 like tasty time, 34 like ice cream, 6 like both tasty times.
Learn more about the Venn diagram here:
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#SPJ2
I need help really bad
Answer:
1 ???????
Step-by-step explanation:
find the value of the trigonometric ratio. make sure to simplify the fraction if needed.
Answer:
36/39
Step-by-step explanation:
Cos(theta) = Base/Hypotenuse
Cos(X) = 36/39
83. For what value of K will the points (1, 4), (-3, 16) and (k, -2) lie on one straight line.
Answer:
I don't know
Step-by-step explanation:
I don't know
Answer:
k = 3
Step-by-step explanation:
If the points lie on the same line then the slope between the points will be equal.
Calculate the slope m using the slope formula
m = [tex]\frac{y_{2}-y_{1} }{x_{2}-x_{1} }[/tex]
with (x₁, y₁ ) = (1, 4) and (x₂, y₂ ) = (- 3, 16)
m = [tex]\frac{16-4}{-3-1}[/tex] = [tex]\frac{12}{-4}[/tex] = - 3
Repeat the process and equate to - 3
with (x₁, y₁ ) = (1,4) and (x₂, y₂ ) = (k, - 2)
m = [tex]\frac{-2-4}{k-1}[/tex] = [tex]\frac{-6}{k-1}[/tex] , then
[tex]\frac{-6}{k-1}[/tex] = - 3 ( multiply both sides by k - 1 )
- 6 = - 3(k - 1) ← divide both sides by - 3
2 = k - 1 ( add 1 to both sides )
3 = k
What are the x-intercepts of y = (x - 2)(x + 5)?
x-intercepts —> (2,0) , (–5,0)
y=(x-2)(x+5)
x-2=0—> x=2 —> (2,0)
x+5=0—> x=–5 —> (–5,0)
I hope I helped you ^_^
x-intercepts —> (2,0) , (–5,0)
y=(x-2)(x+5)
x-2=0—> x=2 —> (2,0)
x+5=0—> x=–5 —> (–5,0)
I hope I helped you ^_^
Which point on the number line shows the graph of 0.5?
Point A
Point B
Point C
Point D
Answer: D
Step-by-step explanation:
D
Answer:
D
Step-by-step explanation:
it is between 0 and 1
graph the inaquality 16>_w
Answer:
A graph is below.
Step-by-step explanation:
11.) Michael earns $2 for every pizza he delivers, plus $30 each day. How many pizzas does he need to deliver today to earn $80? First, write the eqation that fits this model. Let p be the amount of pizza he delivers
Answer:
2p + 30 = 80
p=25
Step-by-step explanation:
he earns $2 for each pizza, so we get 2p.
Because he earns an extra 30 for the day, we add that to 2p and set it equal to 80
2p+30=80
subtract 30 on both sides
2p=50
Divide by 2 on both sides to find the number of pizzas
2p/2=50/2
So
p=25
After how many years, to the nearest whole year, will an investment of $100,000 compounded quarterly at 4% be worth
$213,022?
Provide your answer below:
9514 1404 393
Answer:
19 years
Step-by-step explanation:
The compound interest formula tells you the future value of principal P invested at annual rate r compounded n times per year for t years is ...
A = P(1 +r/n)^(nt)
Solving for t, we get ...
t = log(A/P)/(n·log(1 +r/n))
Using the given values, we find t to be ...
t = log(2.13022)/(4·log(1 +0.04/4)) ≈ 19.000
The investment will be worth $213,022 after 19 years.
Use distributive property to remove parantheses
9(2/3-3x)
Solve. x+y+z=6 3x−2y+2z=2−2x−y+3z=−4
Answer:
-4?
hope dis helps ^-^
Q12 A baker wants to order enough flour for 10 loaves of bread weighing 750g each. She has a recipe for a 500g loaf of bread which needs 480g of flour. How many kilograms of flour does the baker need? Show your working
Answer:
7.2kg of flour
Step-by-step explanation:
Total weight of bread = 10 x 750g
= 7500g = 7.5kg
500g of bread = 480g of flour
0.5kg of bread = 0.48kg of flour
7.5kg of bread = 7.2kg of flour
Fourteen boys and 21 girls will be equally divided into groups. Find the greatest number of groups that can be created if no one is left out.
Answer:
7 groups can be made each with five people :)
The cost of producing pens with the company logo printed on them consists of a onetime setup fee of $265.00 plus $0.95 for each pen produced. This cost can be calculated using the formula C=265.00+0.95p, where p represents the number of pens produced and C is the cost. Use the formula to calculate the cost of producing 2900 pens.
Three measurements are made on each of three individuals in a random sample from a population. X 1 = 2, X2 = 8
and
1
1
187
X3 = 4. The distances d(X1, X2)between X1, X, and d(X2, X3) between X2, X3 respectively are (Use Euclidean inner
L5.
product)
Step-by-step explanation:
here is the answer hope it helps
Reflect the given triangle over
the y-axis.
[3 6 3 ]
[-3 3 3]
Answer:
Step-by-step explanation:
[tex]\left[\begin{array}{ccc}x_{1} &x_{2} &x_{3} \\y_{1} &y_{2} &y_{3} \end{array}\right][/tex] ---------> [tex]\left[\begin{array}{ccc}-x_{1} &-x_{2} &-x_{3} \\y_{1} &y_{2} &y_{3} \end{array}\right][/tex]
[tex]\left[\begin{array}{ccc}-3&-6&-3\\-3&3&3\end{array}\right][/tex]
Nine million, twenty-seven thousand, four hundred and forty-eight
9,027,448
9027448
9027448
9027448
What is the recursive formula for this
geometric sequence?
-3, -21, -147, -1029, ...
Answer:
an = an-1 *7
a1 = -3
Step-by-step explanation:
We are multiplying by 7 each time
-3*7 = -21
-21 *7 = -147
The formula for a geometric sequence is
an = a1 * (r)^(n-1) where r is the common ratio and n is the term number
an = -3 ( 7) ^(n-1)
The recursive formula is
an = an-1 * r
an = an-1 *7
a1 = -3
Answer:
Step-by-step explanation:
common ratio = 7
nth term = ((n-1)th term)×7 = a₁×7ⁿ⁻¹
What do these have in common
Answer:
All Equal to 0
Step-by-step explanation:
0 = 0
3 - 3 = 0
0/4 = 0
12 - 3*4 = 0
