The function f(x) = x(x+4√x) is concave down on (0, 9/4) and concave up or (9/4, ∞)
According to the question,
Given equation is f(x) = x(x+4√x)
f(x) = [tex]x^2 + 4x^{\frac{3}{2}}[/tex]
Derivative the function with respect to x
f'(x) = 2x - 6√x
Derivative the function again ,
f''(x) = 2 - 3/√x
Domain of f(x): x ≥ 0.
Let f''(x) = 0
Putting f"(x) = 0,
2x1/2 = 3
=> x = 9/4
f'(x) Doesn't exist for x = 0 and at x = 0
we have not inflection point, because x < 0 not in domain.
For 0 <x< 9/4,
f''(x) < 0 and graph concave down or (0, 9/4)
For x > 9/4 f''(x) > 0 and graph concave up or (9/4, ∞)
f(9/4) = -135/16. So, point (9/4, -135/16) is point of inflection
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What are the 3 types of proofs?.
The 3 types of proofs are the proof by induction, direct proof and the proof by contradiction.
Proof is a logical or mathematical argument that shows that the given statement is true.
Though proofs might later on be proven wrong and/or have exceptions.
The three types of proof are:
(i) Proof by Induction
(ii) Direct Proof
(iii) Proof by Contradiction
Proof by Induction:
Proof by induction is the proof in which we generalize a particular for the entire equation.
In the inductive step we generalize the conclusion from the basis, where we prove the equation for a particular value for the entire theorem or equation.
On solving this, if the answer observed follows the theorem used then it is proven
Proof by Contradiction:
In this type of proof we take a contradicting equation to the one that has to be proven. If this equation when further solved turns out to be false or untrue, the equation is considered proven.
Direct Proof:
In the direct proof we assume that the given equation or theorem, to be proven is correct. We then go on to slow the question with the given assumption. If the on solving the answer comes out to be correct, we say that the theorem has been proven.
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Let n be the largest integer for which 14n has exactly 100 digits. Counting from right to left, find the 68th digit of n
Counting from right to left, find the 68th digit of n is 10.
An integer, is a whole number that can be positive, negative, or zero and is not a fraction. Integer examples include: -5, 1, 5, 8, 97, and 3,043. 1.43, 1 3/4, 3.14, and other numbers that are not integers are some examples.
The largest integer with exactly 100 digits is the integer that consists of 100 copies of the digit 9.
This integer is equal to 10100 = 10
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Which formula should be used to correctly calculate the monthly mortgage payment? m = p startfraction left-bracket r (1 minus r) superscript n baseline right-bracket over (1 r) superscript n baseline endfraction m = p startfraction left-bracket r (1 r) superscript n baseline right-bracket over left-bracket (1 r) superscript n baseline minus 1 right-bracket endfraction m = p startfraction r over left-bracket (1 r) superscript n baseline minus 1 right-bracket endfraction m = p startfraction left-bracket r (1 r) superscript n baseline right-bracket over (n r) endfraction
The correct formula to calculate monthly mortgage payment on a loan is [tex]M= P\frac{ [R(1+R)^n]}{[(1+R)^n-1]}[/tex]
Where, M is the total monthly payment
P is the total amount of loan
R is the interest rate
N is the total time
The primary advantage of a mortgage loan is that, unlike most other loans, you can get one without giving up ownership of your house to anybody else and at extremely low interest rates. The monthly mortgage repayment is symbolized by the mortgage payment. The standard four components of a mortgage payment are principal, interest, taxes, and insurance. The principal, term, and interest rate of the mortgage loan, as well as other factors, influence the monthly mortgage payment. The monthly mortgage payment can be calculated using the aforementioned formula or a financial calculator online.
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What is the lateral area of the prism? 73.5 feet 73.5 square feet 84 feet 84 square feet
Answer:The lateral surface area of the triangular prism will be 84 square feet.correct option is D.
What is the surface area of the triangular prism?Let the sides of the triangle be a, b, c, and a height of H. Then the surface area of the prism is given as SA = H(a + b + c)A triangular prism has bases with three congruent sides, each measuring 4 feet. The height of each triangle is approximately 3.5 feet.The distance between the triangular bases is 7 feet.Then the lateral surface area will beSA = 7 (4 + 4 + 4)SA = 7 x 12SA = 84 square feet. the correct option is D
Step-by-step explanation:
pope john paul ii's 1979 visit to this eastern bloc nation, his homeland, drew millions of followers and helped spark a decade-long underground movement against the communist government.
In June 1979, the Pope travelled to Poland for the second time.
The foundation of the Solidarity trade union, which was a crucial force in the overthrow of Communism in eastern Europe, was reportedly set in motion as a result of this journey, which some historians claim was the most important of all his travels.
John Paul paid visits to Warsaw, Gniezno, Kraków, Nowy Targ, Auschwitz, and Jasna Gora while in Poland. Millions of fans attended the nine-day tour.
His visit to his homeland drew millions of followers and helped spark a decade-long underground movement against the communist government.
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cost $210. tax rate 12%. What is the total cost
Answer: $235.2
Step-by-step explanation:
We just multiply 210 by 12%
which gives us 25.2
Then we just add 25.2 + 210 = 235.2
A sales position needs to be filled. There are two candidates available. The first candidate has 10 years of experience and can sell 10 units a week making a $3,000 profit per week for the company. He is asking for $80,000 salary. The second candidate has one year of experience and can sell eight units a week making a $2,400 profit for the company. He is asking for $45,000 salary. What candidate would make the company the most money their first year of employment?.
The candidate that would make the company the most money in their first year of employment is Candidate B
Which candidate would make more money?The amount of profit that a candidate can make for the company is:
= ( Number of weeks in year x Profit per week ) - Salary for the year
We shall assume 48 working weeks in a year.
The amount of money made by Candidate A would be:
= ( 48 x 3, 000 ) - 80, 000
= $64, 000
The amount of money made by Candidate B is:
= ( 48 x 2, 400 ) - 45, 000
= $70, 200
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list the two types of sampling procedures group of answer choices causation and exact sampling precise and imprecise sampling probability and nonprobability sampling statistical and linear sampling large and small size sampling
The correct answer is Probability and non probability sampling procedure.
There are two distinct exits from sampling procedures.
There are two types of sampling: probability sampling and non-probability sampling.
In probability sampling each population has equal and independent chance to comes in the study . There are various types of probability samplings technique exists . These are simple random sampling , stratified random sampling, cluster sampling , systematic random sampling etc.
In non probability sampling the samples are selected on the basis of personal biasness, judgments and preferences. Judgemental sampling , quota sampling, dimensional sampling etc comes under this type of sampling procedure.
So here the correct answer is
Option -E- Probability and non probability sampling procedure.
Except it all other options are wrong.
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Review the process chart given below. Assume that an ankle injury patient is willing to pay for both operation and inspection steps. Which of these statements is true? a. Value-added time is less than 50% of cycle time. b. Value-added time is more than 50% of cycle time. c. Value-added time is exactly 50% of the time.
If an ankle injury patient is willing to pay for both operation and inspection steps, Value-added time is less than 50% of cycle time
The ankle injury is under 1.5 times as much pressure with each stride .
In an avergae we travel 1000 miles on foot annully.
Over 14.2 million visits to doctors is due to ankle injuries every year.
However only 15% of the total injuries results in fractures.
Therefore, if an ankle injury patient is willing to pay for both operation and inspection steps, the statements which is true is Value-added time is less than 50% of cycle time
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Identify the parent function for the function g(x) = (x − 2)^3 from its function rule. Then graph g and identify what transformation of the parent function it represents.
NEED ASAP
The transformation from the parent function f(x) = x³ is a translation to the right by 2 units
How to describe the transformation from the parent function?From the question, we have the following function that can be used in our computation:
g(x) = (x − 2)³
To determine the parent function, we leave only the variable in the expression
So, we have
f(x) = x³
Next, we determine the transformation
We have the transformation to be from f(x) = x³ to g(x) = (x − 2)³
This means the function is translated right by 2 units
Hence, the transformation is 2 unit right
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A urvey of 100 tudent wa taken concerning their knowledge of foreign
language. The reult were a follow: How many tudent do NOT know any of
the three language?
30 know French
19 know German
16 know Spanih
2 know both French and Spanih
12 know both French and German
7 know both German and Spanih
8 Know all three language
There are 48 such students who did not know any of the three languages.
Given,
Since we have given that
Number of students were taken for survey n(U)= 100
Number of students who know French n(F) = 30
Number of students who know German n(G) = 19
Number of students who know Russian n(R) = 16
Number of students who know both French and Russian n(F∩ R) = 11
Number of students who know both German and French n(G ∩ F) = 12
Number of students who know both Russian and German n(R ∩ G) = 6
Number of students who know all three languages = 4
So, n(F∪G∪R)=n(F)+n(G)+n(R)-n(F∩G)-n(F∩R)-n(G∩R)+n(F∩G∩R)
n(F∪G∪R)=30+19+16-12-11-6+4
n(F∪G∪R)=52
So, the number of students who do not know any of the three languages is
[tex]n ( F ∩ G ∩ R )' = n (U) - n ( F ∩ G ∩ R )\\n ( F ∩ G ∩ R )' = 100- 52\\\\n ( F ∩ G ∩ R )' = 48[/tex]
Hence, there are 48 such students who did not know any of the three languages.
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the probability pete will catch fish when he goes fishing is 0.9. pete is going fishing 4 days next week. the expected number of days pete will catch fish is . a. 0.4 b. 0.9 c. 3.6 d. 4
The expected number of days pete will catch fish is 0.36. So the option 3 is correct.
In the given question, the probability pete will catch fish when he goes fishing is 0.9.
Pete is going fishing 4 days next week.
We have to find the expected number of days pete will catch fish.
From the question,
Pete is going fishing 4 days next week. So n=4
The probability pete will catch fish when he goes fishing is 0.9. So P(F)=0.9
The formula for variance is:
Variance = n*p*(1-p)
Variance = 4*0.9*(1-0.9)
Variance = 4*0.9*0.1
Variance = 0.36
So the expected number of days pete will catch fish is 0.36. So the option 3 is correct.
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A car that travel at 20 mile in 1/2 hour at contant peed i traveling at the ame peed a a car that travel 30 mile in 3/4 at a contant peed. Explain why
It is true that the speed of both cars is the same.
What is an example of continuous speed?
When something is going at a fixed, steady pace or at an average speed, it is said to be moving at constant speed or uniform rate. As an illustration, a car travels 3 hours. In the first hour, it travels 30 miles, in the second hour, 45 miles, and in the third hour, 75 miles.
Detailed explanation:
Car A is moving at a pace of 40 miles per hour since it covers 20 miles in less than 30 minutes.
In order to determine whether or not Car B is moving at the same speed as Car A, let's build up a proportion for the 30 miles it travels in 3/4 of an hour.
30 miles in one hour equals x miles in one hour. multiply by cross
Divide both sides by (3/4) to get 30.
40 = x
As a result, the speeds of Car A and Car B are equal.
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What is the measure of the angle of an isosceles?.
The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.
What is the measure of the angle of an isosceles?
Properties of an Isosceles Triangle
The isosceles triangle has three acute angles, meaning that the angles are less than 90°. The sum of three angles of an isosceles triangle is always 180°.
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find an equation of the line tangent to the curve at the point corresponding to the given value of t. x=t^2-23, y=t^3 + t; t=5
The equation of the line tangent to the curve at the point corresponding to the given value of t.
x = t²-23 and y = t³ + t, at t = 5 is
38x - 5y + 574 = 0
Given, a curve with the points represented by
x = t²-23 and y = t³ + t, at t = 5
we have to find an equation of the line tangent to the curve at the given point on the curve.
so, the given point is (x , y) = (5² - 23 , 5³ + 5)
(x , y) = (2 , 130)
Now, the slope of the curve at that point be,
dy/dx = (3t² + 1)/(2t)
dy/dx = 76/10
Now, on using the slope-intercept form, we get
(y - 130)/(x - 2) = 38/5
5(y - 130) = 38(x - 2)
5y - 650 = 38x - 76
38x - 5y + 574 = 0
Hence, the equation of the line tangent to the curve at the point corresponding to the given value of t.
x = t²-23 and y = t³ + t, at t = 5 is
38x - 5y + 574 = 0
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frog took three jumps. The first jump was 2/3 m long, the second was 5/6 m long and
the third was 1/3 m long. How far did the frog jump in all?
The frog jumped the total length of 11/6m.
How to add two fractions?If the fractions have the same denominators then their numerators are added keeping the denominators as the same.
For fractions with different denominators the LCM of the denominators are taken then that is divided by the numerators of each fraction and the number obtained is multiplied to each of them to get the equivalent fraction.
Given that,
The length of first jump of the frog is 2/3m.
The length of second jump of the frog is 5/6m.
And, length of third jump of the frog is 1/3m.
Thus, the sum of all the jumps is given as,
2/3 + 5/6 + 1/3
The LCM of denominators is 6. So, the sum becomes,
(2 × 2 + 5 × 1 + 1 × 2)/6
= 11/6.
Hence, total length of the frog's jump is 11/6m.
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a firm has two plants(x and y) producing the same product which sells for $12 each. fixed costs are $5,000/year at plant x and $7,000/year at plant y and variable costs are $3.00/unit and $2.00/unit for x and y, respectively. the total profit at x and y are equal when the volume of each plant(units) is: group of answer choices 1,500 2,000 500 none of the above 1,000
A firm has two plants (X and Y) producing the same product which sells for $12 each. The total profit at plant X and plant Y are equal if the volume of each plant is 2,000 units.
To solve the problem, first translate the given problem into equations.
The formula for profit is:
profit = revenue from sales - total cost
total cost = fixed cost + variable cost
revenue = selling price x number of units sold
Let:
x = the number of units sold in plant X
y = the number of units sold in plant Y
From the problem, we can conclude:
Profit X = profit Y
x = y
Profit X = 12x - (5000 + 3x) (equation 1)
Profit Y = 12 y - (7000 + 2y) (equation 2)
Substitute y = x into equation 2
Profit Y = 12 x - (7000 + 2x)
Hence,
12x - (5000 + 3x) = 12 x - (7000 + 2x)
3x - 2x = 7000 - 5000
x = 2,000
Therefore, total profit at plant X and plant Y are equal if the volume of each plant is 2,000 units.
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A fancy bed and breakfast inn has 5 rooms, each with a distinctive color-coded decor. One day 5 friends arrive to spend the night. There are no other guests that night. The friends can room in any combination they wish, but with no more than 2 friends per room. In how many ways can the innkeeper assign the guests to the rooms?
A. 2100
B. 2220
C. 3000
D. 3120
E. 3125
In 2220 ways the innkeeper can assign the guests to the rooms i.e. Option B is correct.
As per the question,
Number of rooms = 5Number of friends = 5The rooms are distinctive colour-coded decor i.e. the rooms have to be distinct.There are Five friends and Five rooms,
⇒ 0 rooms of 2, 5 rooms of 1
⇒ 1 room of 2, 3 rooms of 1
⇒ 2 rooms of 2, 1 room of 1
Guests can be allotted rooms by the innkeeper as
1, 1, 1, 1, 1, 1, 2, 2, or 1, 1, 1, 2
To assign ( 1, 2, 2 ) = ways to assign guests to the rooms × ways to assign frequencies to rooms= 5 × ( 4 2 ) × ( 5 2 ) ( 3 2 )
To assign ( 1, 2, 2 ) = ways to assign guests to the rooms × ways toassign frequencies to rooms
= 5 × 4 × 3! ( 5 2 )
To assign ( 1, 1, 1, 1, 1 ) = 5!Total number of ways ( N ) = To assign ( 1, 2, 2 ) + To assign ( 1, 2, 2 ) +
To assign ( 1, 1, 1, 1, 1 )
= 5 × ( 4 2 ) × ( 5 2 ) ( 3 2 ) + 5 × 4 × 3! ( 5 2 ) +
5!
= 5 × ( 4 2 ) × ( 5 2 ) ( 3 2 ) + 120 ( 5 2 ) + 120
N = 2220 ways
Therefore, The innkeeper can assign guests to the rooms in 2220 ways with no more than two friends per room i.e. option B is valid.
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What are the parts of graph of a rational function?.
The parts of graph of a rational function is the asymptotes and the intercepts of the graph.
The graph of a rational function is a hyperbola
The asymptote is a line or curve that acts as the limit of another line or curve. For example, a descending curve that approaches but does not reach the horizontal axis is said to be asymptotic to that axis, which is the asymptote of the curve whereas the intercept of the graph is a point on the y-axis, through which the slope of the line passes. It is the y-coordinate of a point where a straight line or a curve intersects the y-axis
Therefore, The asymptotes and the intercepts of the graph are the parts of graph in case of a rational function.
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Problem 1 (A Few Random Steps) Consider four molecules, all starting at the origin, which undergo a 1d random walk, each with a 50% chance of going left or right along the x-axis at each time step. A. After 1 time step, what is the probability that 2 particles have gone left and 2 have gone right? Give your answer as a decimal number between 0 and 1 to 3 decimal places. B. After 2 time steps, what is the probability that all of the particles are at the origin? Give your answer as a decimal number between 0 and 1 to 3 decimal places. C. After 2 time steps, what is the probability that none of the particles are at the origin? Give your answer as a decimal number between 0 and 1 to 3 decimal places. D. After two time steps, what is the probability that one or more particles are not at the origin? Give your answer as a decimal number between 0 and 1 to 3 decimal places.
The probability that 2 particles have gone left and 2 have gone right is 0.375, considering four molecules, all starting at the origin, which undergo a 1d random walk, each with a 50% chance of going left or right along the x-axis at each time step.
Define probability.Probability measures how likely something is to happen. It is calculated mathematically as a fraction, ratio, or percentage. The formula of the favourable outcome over the total outcomes is used to describe probability. The likelihood of flipping a coin heads is one example. Given that there is only one head and two total sides, 50% of the time, a head will land up-side-down.
Given,
4 particles given,
P(left) = 0.5 = P(right)
Possible combinations in total,
2 × 2 × 2 ×2
16
Combinations that are accepted,
RRLL, LLRR, LRLR, RLRL, RLLR, LRRL
Probability of 2 left and 2 right:
= 6/16
= 3/8
= 0.375
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At a real estate agency, an agent sold a house for $307,000. The commission rate is 5.5% for the real estate agency and the commission rate for the agent is 25% of the amount the real estate agency gets. How much did the agency make on the house? How much did the agent earn in commission?
The commission which real estate agency gets is $16885.
The commission which the agent get is $76750
How to calculate the commission?The selling price for a house = $ 307,000
The commission rate for real estate agency = 5.5 %
The commission rate for the agent = 25 %
So, the commission which real estate agency gets:
= 5.5 % of $307,000
= 0.055 × $ 307,000
= $16885
The commission which agent get:
= 25% of $ 382,000
= 0.25 × $ 307,000
= $76750
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Andres is a high school basketball player. In a particular game, he made some two point shots and some free throws (worth one point each). Andres made a total of 12 shots altogether and scored a total of 16 points. Determine the number of two point shots andres made and the number of free throws he made.
The total number of free throws shots Andres made was 8 and the total number of two point shots Andres made was 4.
First, let us understand the variables:
Any number, vector, matrix, function, its argument, set, or one of its elements can be specifically represented by a variable.
Let x and y be the quantity of shorts.
x is the number of attempts at the free throw line.
y is the quantity of two-point attempts.
According to the question, we have;
x + 2y = 16 ............equation 1
x + y = 12 ............equation 2
From equation 2 we can take out the value of x;
x = 12 - y ............equation 3
substituting the value of x in equation 1, we will get;
(12 - y) + 2y = 16
12 - y + 2y = 16
12 + y = 16
y = 16 - 12
y = 4
putting the value of y in equation 3, we will get
x = 12 - 4
x = 8
Thus, the total number of free throws shots Andres made was 8 and the total number of two point shots Andres made was 4.
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i walk around the perimeter of a regular hexagonal ornamental pond. Through how many degrees do I turn at each corner? and altogether?
The number of degrees of each turn made in the regular hexagonal pond is: 120°.
Altogether is 720°.
What is a Hexagonal Shape?A hexagonal shape is a six (6) sided polygon that has 6 interior angles.
The sum of all interior angles of an x-sided polygon can be calculated as:
(n - 2)180.
To find the sum of all the interior angles of the hexagonal pond, substitute the n = 6 into (n - 2)180:
(6 - 2) × 180
= 4 × 180
= 720°
The measure of each interior angle of the hexagonal pond = 720/6 = 120°.
Therefore, it implies that, you made 120 degrees turn at each corner, and altogether, you made 720°.
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Reflect the given triangle over the line y=-x. 3 6 3 -3 3 3 [?] [ -3 [ ] [ 3
The points of the vertices of the triangle after reflection on the line y = -x is given by A'(3,-3) , B'(-3,-6) and B'(-3,-6) .
We know that when a point is reflected around a line on the coordinate axes then the coordinates reflect following some rules.
Now when the point (a,b) is reflected around the line y = -x then ,the coordinates of the image becomes (-b,-a)
Therefore :
A(3,-3)→A'(3,-3 , does not change as the point lies on the line y=-x)
B(6,3)→B'(-3,-6)
C(3,3)→B'(-3,-6)
In a transition known as reflection over a line k, each point of the original figure (pre-image) must have an image that is the same distance from the line of reflection as the first comment but is on the other side of the line. Remember that a flip is a reflection. The size of the figure does not alter when it is reflected.
A figure created by a line reflection that is consistent with the original figure is called an isometry (a transformation that preserves length). Because naming the figure in a reflection implies changing the order of the letters, a reflection is more accurately referred to as a non-direct or opposing isometry .
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Answer: 3 -3 -3
-3 -6 -3
Step-by-step explanation:
Here is a circle with a center Z and some line segments and curves joining points on the circle. Complete the table by identifying each segment or curve as a radius, diameter, or neither and explaining your reasoning.
in this scenario, what is the test statistic? a sociologist would like to test the claim that the average age of a u.s. adult getting married is different than 27 years old. sample size
There is not sufficient evidence to claim that the average age of a US adult getting married is different than 27 years old.
μ₀ = 27
h = 30
X = 26
σ = 7
Hypothesis test at α = 0.025
Null & Alternative hypothesis
H₀: μ = 27
Ha: μ = 27
Test statistics = Z
Z= x-μ/(σ/√h)
= 26-27/(7/√30)
Z = -0.78
p-value
p-value from Z-table at |Z|= 0-78,
two-tailed is p-value = 0.4354
decision-
here p-value = 0-4354 > α=0·025 Since we fail to reject H₀ at 2.5%
Hence, there is not sufficient evidence to claim that the average age of a US adult getting married is different than 27 years old.
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What is a parent in a graph?.
The parent graph is the graph of a relatively simple function.
Graph:
Graph refers the diagram that represents the variation of a variable in comparison with that of one or more other variables.
Given,
Here we need to define the parent in a graph.
Parent function refers the simplest form of a given family of functions.
Here by transforming the function in various ways, the graph can be translated, reflected, or otherwise changed.
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water flows into an empty reservoir at a rate of gal/hour . what is the quantity of water in the reservoir after 9 hours?
The quantity of water in the reservoir after 9 hours be, 2835 gallons.
Given, water flows into an empty reservoir at a rate of 2800 + 15t gal/hour.
we have to find the quantity of water in the reservoir after 9 hours.
at the rate of 2800 + 15t
put t = 9
So, the quantity of water in the reservoir after 9 hours be,
2800 + 15(9)
2800 + 135
= 2835
So, the quantity of water in the reservoir after 9 hours be, 2835 gallons.
Hence, the quantity of water in the reservoir after 9 hours be, 2835 gallons.
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find the area of the shaded region under the standard normal distribution to the right of the given z-score. round your answer to three decimal places.
The area of shaded region is 0.171.
Given z-score is z = 0.95.
We have to calculate P(z > 0.95).
We can write this as
P(z > 0.95) = 1 - P(z < 0.95)
From the z-table we know that
P(z < 0.95) = 0.828
We will put this value in above equation, we get
P(z > 0.95) = 1 - 0.828
Therefore
P(z > 0.95) = 0.171.
Z-score tables are very useful in determining the probabilities of normally distributed random variables. The z-score standardizes the normally distributed variable to make any normal distribution fit into the standard normal distribution.
The z-score is calculated using the random variable, the mean, and standard deviation of a particular normal distribution of variables.
To know more about Z-score here
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Annika's flight to Ottawa took 45 min. The bus ride to the airport took 3 h. Write a ratio to compare the time on the bus to the time on the plane.
