As a set of inputs with one output for each, a function is defined as a relationship between them.
What is meant by functions?An equation, rule, or law in mathematics that establishes the link between the independent variable and the dependent variable (the dependent variable). Mathematics is rife with functions, and the sciences depend on them for constructing physical relationships.
We have given, f(0) = 3 for all parts.
a) f(n+1) = -2 f(n)
For f(1) put f(n) = f(0), f(0+1) = -2 f(0)
f(1) = -2(3) = -6
For f(2) put f(n = 1), f(1+1) = -2 f(1)
f(2) = -2(-6) = 12
For f(3) put f(n) = f(2), f(2+1) = -2 f(2)
f(3) = -2(12) = -24
For f(4) put n = 3, f(3+1) = -2 f(3)
f(4) = -2(-24) = 48
For f(5) put n = 4, f(4+1) = -2 f(4)
f(5) = -2(48) = -96
b) f(n+1) = 3, f(n) + 7
For f(1) put n = 0, f(0+1) = 3 f(0)+7
f(1) = 3(3)+7 = 16
For f(2) put n = 1, f(1+1) = 3 f(1)+7
f(2) = 3(16)+7 = 55
For f(3) put f{n}=f{2}, f(2+1)=3 f(2)+7
f(3) = 3(55) + 7 = 172
For f(4) put n = 3, f(3+1) = 3 f(3)+7
f(4) = 3(172)+7 = 523
For f(5) put n = 4, f(4+1) = 3 f(4)+7
f(5) = 3(523)+7 = 1576
c) f(n+1) = f(n)²-2 f(n)-2
For f(1) put n = 0, f(0+1) = f(0)²-2 f(0)-2
f(1) = 3²-2(3)-2 = 1
For f(2) put n = 1, f(1+1) = f(1)²-2 f(1)-2
f(2) = 1²-2(1)-2 = -3
For f(3) put n = 2, f(2+1) = f(2)² - 2 f(2) - 2
f(3) = -3² - 2(-3) - 2 = 13
For f(4) put n = 3, f(3+1) = f(3)² - 2 f(3) - 2
f(4) = 13² - 2(13) - 2 = 141
For f(5) put n=4, f(4+1) = f(4)² - 2 f(4) - 2
f(5) = 141² - 2(141) - 2 = 19597
d) f(n+1)[tex]=3^{\frac{f(n)}{3}}$[/tex]
For f(1) put n = 0, f(0+1) [tex]$=3^{\frac{f(0)}{3}}$[/tex]
f(1) = [tex]3^{\frac{3}{3}}[/tex] = 3
For f(2) put n = 1, f(1+1) [tex]=3^{\frac{f(1)}{3}}$[/tex]
f(2) [tex]=3^{\frac{3}{3}}[/tex] = 3
For f(3) put n = 2, f(2+1) [tex]=3^{\frac{f(2)}{3}}$[/tex]
f(3) [tex]=3^{\frac{3}{3}}[/tex] = 3
For f(4) put n = 3, f(3+1) [tex]$=3^{\frac{f(3)}{3}}$[/tex]
[tex]$f(3)=3^{\frac{3}{3}}=3$[/tex]
For f(4) put n = 3, f(3+1) = [tex]$3^{\frac{f(3)}{3}}$[/tex]
f(4) [tex]$=3^{\frac{3}{3}}[/tex] = 3
For f(5) put n = 4, f(4+1) = [tex]3^{\frac{f(4)}{3}}$[/tex]
f(5) [tex]=3^{\frac{3}{3}}[/tex] = 3
The complete question is:
Find f( 1 ) , f( 2 ) , f( 3 ) , f( 4 ) , and f( 5 ) if f(n) is defined recursively by f( 0 ) = 3 and for n = 0 , 1 , 2 ,... a) f(n + 1 ) = − 2 f(n) . b) f(n + 1 ) = 3 f(n) + 7. c) f(n + 1 ) = f(n) 2 − 2 f(n) − 2. d) f(n + 1 ) = 3 f( slader
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f(2)=4, f(3)=7, f(4)=19, f(5)=40
What is a function?
In mathematics, a function is an expression, rule, or law that establishes the relationship between an independent variable and a dependent variable (the dependent variable). In mathematics, functions exist everywhere, and they are crucial for constructing physical links in the sciences. German mathematician Peter Dirichlet initially provided the contemporary concept of function in 1837.
Given, the function is f(n+1) = f(n) + 3f(n-1)
Calculating f(2) by substituting n=1 in the above equation.
f(2) = f(1) + 3f(0)
⇒f(2) = 1 + 3
⇒f(2) = 4
f(3) is calculated by substituting n=2
f(3) = f(2) + 3f(1)
⇒f(3) = 4 + 3
⇒f(3) = 7
f(4) is calculated by substituting n=3
f(4) = f(3) + 3f(2)
⇒f(4) = 7 + 12
⇒f(4) = 19
f(5) is calculated by substituting n=4
f(5) = f(4) + 3f(3)
⇒f(5) = 19 + 21
⇒f(5) = 40
f(2)=4, f(3)=7, f(4)=19, f(5)=40
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16. The volume of a cone is one-third the area of the base times the
height. A cone has a volume of 207 cubic inches. Write an equation
that can be used to solve for the height of the cone.
Answer:
1/3 * [tex]4\pi[/tex] * h = 207, h = 155.25[tex]\pi[/tex]
Step-by-step explanation:
Since we know the area of the base is [tex]4\pi[/tex], that means the volume of the cone is:
1/3 * [tex]4\pi[/tex] * h
If we substitue, we get:
1/3 * [tex]4\pi[/tex] * h = 207
(This is the answer! If you want to solve, go below)
Now, we just solve
[tex]4\pi\\[/tex] * h = 621
h = 621/[tex]4\pi\\[/tex]
h = 155.25[tex]\pi[/tex]
write an equation of the line passing through the point (7,3) that is parallel to the line 4x - 7y = 9
Answer:
first you need to write the given equation in a standard form
4x - 7y = 9
-7y = -4x + 9
y = 4/7x - 9/7
*parallel lines have equal gradient
m = 4/7
y - y1 = m(x - x1)
y - 3 = 4/7(x -7)
y - 3 = 4/7x - 4
y = 4/7x - 1
your equation is y = 4/7x - 1
Answer:
[tex]y = \frac{4}{7} + 5[/tex]
Step-by-step explanation:
Isolate the variable, y. Note the equal sign, what you do to one side, you do to the other. Do the opposite of PEMDAS.
PEMDAS is the order of operations, and stands for:
Parenthesis
Exponent (& Root)
Multiplication
Division
Addition
Subtraction
~
First, subtract 4x from both sides of the equation:
4x (-4x) - 7y = 9 (-4x)
-7y = -4x + 9
Next, divide -7 from both sides of the equation:
(-7y)/-7 = (-4x + 9)/-7
[tex]y = \frac{-4x}{-7} + \frac{9}{-7}[/tex]
[tex]y = \frac{4}{7}x - \frac{9}{7}[/tex]
Next, as long as your slope (4/7) is the same, you can adjust the b (-9/7 for original) to get a parallel line.
In this case, I will utilize 5
[tex]y = \frac{4}{7}x + 5[/tex]
See attached image for the result. The blue line is the adjusted parallel line, while the red line is the original line given by the question.
~
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what is the product of (5.1x10^3)x(3.2x10^3)
Answer:
Step-by-step explanation:
0 is the answer
If P is true, Q is false, R is true, and S is false, determine the truth value of the following.
~[P v (Q v R)] >~ (SVP)
O a. True
O b. False
The truth value of the ~[P v (Q v R)] >~ (S v P) is true.
Truth-value, in logic, is the degree to which a particular proposition or assertion is true (T or 1) or false (F or 0). Because the truth-value of a compound proposition is a function of, or a quantity depending upon, the truth-values of its component components, logical connectives like disjunction and negation can be conceived of as truth-functions.
Given, ~[P v (Q v R)] >~ (S v P) since P v (Q v R) is true, thus ~ [ P v ( Q v R ) ] is false, therefore the implication is true.
⇒~[T v (F v T)] >~ (F v T)
⇒[F v (F v T)]>(T v T)
⇒[F v (F v T)]>(T v T)
⇒F v T
⇒T
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1000 centimeters is equal to 1 what
Answer: 1 decameter
Step-by-step explanation:
Answer:
1 decameter
Step-by-step explanation:
1 decameter is 10 meters or 1000 centimeters
How many kilometers are in 100 meters?
Answer:
100 metere is 1 km
Thanks for the question
Which of the following is not the test of congruence of two triangles ? ASA test ,
AAS test, SSA test , SAS test.
Answer:
Answer Option C: SSA test
Math 2 MYP | 2.2a Checking for understanding
5 For the points P(10, 13), Q(17, 37), R(24, 13), and S(17, -11):
a Find the distances PQ, QR, RS and SP.
b Robin says: 'the lengths PQ, QR, RS and SP are all equal, so the shape
PQRS must be a square.' Determine whether Robin is correct.
c Robin's logical process was:
Premises:
Reasoning process:
Conclusion:
The four lengths are equal.
If a quadrilateral has four equal sides, then it is a square.
Since PQRS has four equal sides, it is a square.
PQRS is a square.
Explain the fault in Robin's logic.
Trevor is making payments on a car that costs 26,555 dollars. He makes 36 equal payments. If he rounds the equal payments up to the nearest whole dollar, about how much will he overpay after 36 months? Explain.
Answer:
$13 overpayment
Step-by-step explanation:
We can find the amount Trevor should pay each month by dividing the $26,555 by 36 months:
($26,555/(36 months)) = $737.64 per month
Since Trevor decide to round up to the nearest dollar, he will pay $738 each month. That's an overpayment of $0.361 each month.
After 36 months of overpaying by $0.361 each month, Trevor will have overpaid:
($0.36/month)*(36 months) = $13 overpayment
I need help.... I can't figure it out!!
The area of the given irregular figure is 143 square inches.
What is area of irregular figure?
We divide an irregular shape into its component common shapes before calculating its area. After that, we add the areas of each shape. For instance, if a square and a triangle make up an irregular polygon, the area of the polygon is equal to the sum of their areas.
We have to divide the given irregular figure into known shapes.
That is rectangle and square.
Rectangles with sides '7 in and 10 in' and '12 in and 4 in' and the square of side 5 in.
So, the area of irregular figure is,
Area = Area of rectangle + Area of rectangle + Area of square
= (7 x 10) + (12 x 4) + 5^2
= 70 + 48 + 25
Area = 143
Hence, the area of the given irregular figure is 143 square inches.
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p and q are two numbers such that p > q
When you subtract 5 from p and subtract 5 from q the answers
are in the ratio 9 : 1
When you add 20 to p and add 20 to q the answers
are in the ratio 7 : 3
Find the ratio p: q
Give your answer in its simplest form.
The ratio of p : q in its simplest form is 5 : 1
How to write ratio in its simplest formThe unknown numbers are p and q
(p - 5) / (q - 5) = 9/1
(p + 20) / (q + 20) = 7/3
From equation (1)
cross product
1(p - 5) = 9(q - 5)
p - 5 = 9q - 45
p = 9q - 45 + 5
p = 9q - 40
From equation (2)
3(p + 20) = 7(q + 20)
3p + 60 = 7q + 140
Substitute p = 9q - 40 into 3p + 60 = 7q + 140
3p + 60 = 7q + 140
3(9q - 40) + 60 = 7q + 140
27q - 120 + 60 = 7q + 140
27q - 60 = 7q + 140
27q - 7q = 140 + 60
20q = 200
divide both sides by 20
q = 200/20
q = 10
Substitute q = 10 into p = 9q - 40
p = 9q - 40
p = 9(10) - 40
p = 90 - 40
p = 50
In conclusion, the ratio of p to q = 50 : 10
= 50/10
= 5/1
= 5:1
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need help on this please!!!
In step 1, y was made the subject of the second equation to get:
y=5x-4
To proceed, the next step is to substitute the expression into the other equation, not the equation we solved for y.
8x+2y=-12
8x+2(5x-4)=-12
8x+10x-8=-12
18x=-12+8
18x=-4
x=-[tex]\frac{4}{18}[/tex]
x=[tex]\frac-{2}{9}[/tex]
answer= the value of x is -2/9
how many revolutions will the circular helix make in a distance of 10 units measured along the z axis
At a = √25/π^2 - 0.04 revolutions will the circular helix r = acosti + asintj + 0.2tk make in a distance of 10 units measured along the z-axis.
In the given question, we have to find how many revolutions will the circular helix r = acosti + asintj + 0.2tk make in a distance of 10 units measured along the z-axis.
r = acosti + asintj + 0.2tk, length = 10 unit
So |r| = [tex]\int^{2\pi}_{0}\sqrt{(dx/dt)^2+(dy/dt)^2+(dz/dt)^2}dt[/tex]
From the given equation,
x = acost, y = asint, z = 0.2t
dx/dt = -asint, dy/dt = acost, dz/dt = 0.2
10 = [tex]\int^{2\pi}_{0}\sqrt{(-a\sin t)^2+(a\cos t)^2+(0.2)^2}dt[/tex]
10 = [tex]\int^{2\pi}_{0}\sqrt{a^2\sin^2 t+a^2\cos^2t+0.04}dt[/tex]
As we know that sin^2x+cos^2x = 1. So
10 = [tex]\int^{2\pi}_{0}\sqrt{a^2+0.04}dt[/tex]
10 = [tex]\sqrt{a^2+0.04}\int^{2\pi}_{0}dt[/tex]
10 = [tex]\sqrt{a^2+0.04}\cdot[t]^{2\pi}_{0}[/tex]
10 = √(a^2+0.04)∙[2π-0]
2π√(a^2+0.04) = 10
Divide by 2π on both side, we get
√(a^2+0.04) = 5/π
Taking square on both side, we get
a^2+0.04 = 25/π^2
Subtract 0.04 on both side, we get
a^2 = 25/π^2 - 0.04
taking square root on both side, we get
a = √25/π^2 - 0.04
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The right question is:
How many revolutions will the circular helix
r = acosti + asintj + 0.2tk
make in a distance of 10 units measured along the z-axis?
a doctor claims that people are more than 11 pounds overweight. to test the claim, 25 randomly selected people were weighed and the difference between their actual weight and their ideal weight was calculated. the sample mean and sample standard deviation of that difference were12 and 4 pounds, respectively. assuming a paired t-test is appropriate, can we conclude at the 1% level of significance that the claim is true? group of answer choices yes, conclude the claim is true by accepting h0.
There is enough evidence to conclude that the doctor's claim is true.
We have given that,
population mean μ = 11 pounds
sample size n = 25
sample mean x = 12 ponds
standard deviation σ = 4 pounds
so the null hypothesis is H₀ : μ = 11 pounds
and the alternative hypothesis is Hₐ : μ > 11 pounds
now we will calculate test statistics,
t = (x-μ)/(σ/√n)
= (12 - 11)/(4/√25)
= 1/(4/5)
t = 1.25
p-value from the z-table is 0.10565
the result is non significant at p < 0.01.
Hence the null hypothesis rejected .
Therefore there is enough evidence to conclude that the doctor's claim is true.
The level of significance is the measurement of the statistical significance. It defines whether the null hypothesis is assumed to be accepted or rejected. It is expected to identify if the result is statistically significant for the null hypothesis to be false or rejected.
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a simple random sample of 100 8th graders at a large suburban middle school indicated that 82% of them are involved with some type of after school activity. find the 95% confidence interval that estimates the proportion of them that are involved in an after school activity. a) [0.745, 0.895] b) [0.745, 0.695] c) [0.795, 0.800] d) [0.645, 0.845] e) [0.665, 0.895] f) none of the above
The 95% confidence interval that estimates proportion of 8th graders that are involved in an after school activity (0.745, 0.895) , the correct option is (a) .
In the question ,
it is given that ,
simple random sample of 100 8th graders is taken ,
that means ,
n = 100 ,
also given that , 82% of them are involved with some type of after school activity.
means ; p = 0.82 .
the level of significance (α) = 100 - 95 = 5% = 0.05 .
the critical value= [tex]Z_{\alpha /2}[/tex] = [tex]Z_{0.025}[/tex] = 1.959964 ......from the Z table .
the lower limit of the 99% confidence interval is = p - [tex]Z_{\alpha /2}[/tex]*SE
and the upper limit for the 99% confidence interval is= p + [tex]Z_{\alpha /2}[/tex]*SE .
the standard error is √(p(1-p)/n
= √(0.82(1 - 0.82)/100
= 0.0384
So , the lower limit is ⇒ 0.82 - 1.959964*0.0384
On simplification ,
we get ,
lower limit is = 0.7447006 ≈ 0.745 .
the upper limit is = p + [tex]Z_{\alpha /2}[/tex]*SE
= 0.82 + 1.959964*0.0384
On Simplification ,
we get ,
upper limit is = 0.8952994 ≈ 0.895 .
Therefore , the confidence interval is (0.745, 0.895) .
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Find the measure of the angle indicated.
, will give brain-lest if correct!
Answer:
50 degrees
Step-by-step explanation:
100 - 60 degrees
therorem
The present age of the father is three times the age of his son. If the age of the son after 10 years is equal to the age of the father before 20 years, find the present ages of father and the son.
Answer:
Hi
Step-by-step explanation:
I am just reply to see if i really understand that problem
Let's assume s the present age of the son, and f the present age of the father.
The age of the son After 10 years is equal to the age of the father before 20 years:
s+10=f+10-20
f=3s
=> s+10=f-10
=> s+10=3s-10
=> 2s=20
=> s=10 and f=30
A sports drinks recipe calls for 2 tablespoons of powder mix for every 12 ounces of water. how many can you make with 6 tablespoon and 36 ounces of water explain.
Answer: 3 sports drinks
Step-by-step explanation:
6 divde by 2= 3
36 divided by 12 =3
in other words
3x2=6
12x3=36
hope this helps
find the quotient and remainder when 6x^4+ 11x^3+13x^2 -3x+27 is divided by 3x+4. also check the remainder obtained by using the remainder theorem.
The division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 will have a quotient of 2x³ + x² +3x -5 and a remainder of 47 using the remainder theorem.
What is the remainder theoremThe remainder theorem states that if a polynomial say f(x) is divided by x - a, then the remainder is f(a).
We shall divide the 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 as follows;
x⁴ divided by 3x equals 2x³
3x + 4 multiplied by 2x³ equals 6x⁴ + 8x³
subtract 6x⁴ + 8x³ from 6x⁴ + 11x³ + 13x² - 3x + 27 will give us 3x³ + 13x² - 3x + 27
3x³ divided by 3x equals x²
3x + 4 multiplied by x² equals 3x³ + 4x²
subtract 3x³ + 4x² from 3x³ + 13x² - 3x + 27 will give us 9x² - 3x + 27
9x² divided by 3x equals 3x
3x + 4 multiplied by 3x equals 9x² + 12x
subtract 9x² + 12x from 9x² - 3x + 27 will give us -15x + 27
-15x divided by 3x equals -5
3x + 4 multiplied by -5 equals -15x - 20
subtract -15x - 20 from -15x + 27 will result to a remainder of 47
using the remainder theorem, x = -4/3 from the the divisor 3x + 4
thus:
f(-4/3) = 6(-4/3)⁴ + 11(-4/3)³ + 13(-4/3)² - 3(-4/3) + 27 {putting the value -4/3 for x}
f(-4/3) = (1536/81) - (704/27) + (208/9) + (12/3) + 27
f(-4/3) = (1536 - 2112 + 1872 + 324 + 2157)/81 {simplification by taking the LCM of the denominators}
f(-4/3) = (5919 - 2112)/81
f(-4/3) = 3807/81
f(-4/3) = 47
Therefore, the quotient of after the division of 6x⁴ + 11x³ + 13x² - 3x + 27 by 3x + 4 is 2x³ + x² +3x -5 and there is the remainder of 47 using the remainder theorem.
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SHOW WORK FOR BRAINLIST AND HEARTS
The true or false values of the statements are:
The book is $18 : TrueGiselle can earn up to $18 pulling weeds for her grandmaGiselle's grandma pays her $1 for every 5 weeds she pullsGiselle does not have to use any of her own money toward the purchase of the book when she pulls 90 weedsGiselle only needs to pull 18 weeds to not use any of her own money: FalseHow to determine the true statements from the scenario?From the question, we have the graph which represents the given parameters that can be used in our computation
Analysing the graph, we have:
The graph crosses the y-axis at y = 18
This means that the y-intercept of the graph is
y-intercept = 18
This in other words mean that:
The cost of the book is $18
So, (a) is true
Also, the graph crosses the x-axis at x = 90
This means that the x-intercept of the graph is
x-intercept = 90
This in other word mean that:
Giselle gets $18 if she pulls all the weed (i.e. 90 weeds) in the garden
So, (b) and (d) are true
The amount paid by her grandma is calculated as
Amount = 18/90
Amount = 1/5
So, (c) is true
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Emma and Jane were playing soccer in their backyard, and Emma kicked the ball to
Jane. The curve of the ball's path can be represented by
d=-16t² + 32t + 9, where d is the distance of the ball from Emma and t is
the time (in seconds). Find how long it takes the ball to reach Jane.
4
It takes 4 seconds for the ball to reach Jane.
It takes 2.25 seconds for the ball to reach Jane.
It could take 2.25 seconds or 0.25 seconds.
It could take 4 seconds or 3.25 seconds.
The number of seconds to reach Jane will be 2.25 seconds. Then the correct option is B.
What is a function?A function is an assertion, concept, or principle that establishes an association between two variables. Functions may be found throughout mathematics and are essential for the development of significant links.
The curve of the ball's path is given below.
d = -16t² + 32t + 9
The number of seconds to reach Jane is given as,
0 = -16t² + 32t + 9
16t² - 32t - 9 = 0
16t² - 36t + 4t - 9 = 0
4t(4t - 9) + 1(4t - 9) = 0
(4t - 9)(4t + 1) = 0
t = 9/4, -1/4
t = 2.25, -0.25
The number of seconds to reach Jane will be 2.25 seconds. Then the correct option is B.
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70 POINTS!!!WILL GIVE BRAINLIEST
A local animal rescue has 20 people that help foster pets while they are waiting on finding their homes. They expect to gain two additional people willing to foster animals each month. The amount of animals in need of homes in the community is currently 10 and growing at a rate of 15% per month. When will the amount of homeless pets surpass the amount of foster homes available?
A) Write the two functions that represent this situation. (10 pts) B) Create a table of values. (5 pts)
C) Approximate the solution(s). Why is this the approximate solution? (5 pts)
D) Using graph paper (and the table of values), sketch the situation to show the exact solution. (5 pts)
Answer: below
Step-by-step explanation:
A. x=20+2n n= number of months
y=10(1+0.15)^n
B.
x 20,22,24,26,28,30....40
y 12.5,13.225,15.2,....40.5
C. The solution is 11 months because at 10 months even though the number of animals surpass the number of homes, you cannot have half a animal.
D.
2. Find the number of ways eight people can be seated in an eight-passenger van.
Hii can someone help with this please and thank you
Answer:
There are 8! (8 factorial) ways for 8 people to be seated in an 8-passenger van. This is because there are 8 choices for the first person to sit, 7 choices for the second person, 6 choices for the third person, and so on, until there is only 1 choice for the last person. Therefore, the total number of ways for the 8 people to be seated is 8 x 7 x 6 x 5 x 4 x 3 x 2 x 1 = 8!, which is equal to 40,320.
the burning times of scented candles, in minutes, are normally distributed with a mean of 249 minutes and a standard deviation of 20 minutes. find the number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles. use excel, and round your answer to two decimal places.
The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles is 244 minutes.
When the distribution is normal, we use the z-score formula.
In a set with mean µ and standard deviation σ , the z-score of a measure X is given by:
Z = (X – µ) / σ
What is Z-score?The Z-score shows how many standard deviations the measure is from the mean. After finding the Z-score, need to look at the z-score table and discover the p-value associated with the z-score. This p-value is the probability that the value of the measure is smaller than X, means, the percentile of X. Subtracting 1 by the p-value, we get the probability that the value of the measure is greater than X.
So, in this case, given that:
µ = 249, σ = 20
The number of minutes a scented candle lasts if it burns out sooner than 80% of all scented candles:
100 – 80 = 20th percentile, which is X when Z has a p-value of 0.2. So, X when Z = –0.253.
Now, put all the values into the formula:
Z = (X – µ) / σ
–0.253 = (X – 249) / 20
X – 249 = –0.253 * 20
X = 244
Hence, the candle burns for 244 minutes.
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an equation of the line normal to the graph of y=sqrt(3x^2+2x) at (2 4)
The equation of the line normal to the curve y = square root(3x² + 2x) at point (2,4) is given as follows:
y - 4 = -4/7(x - 2).
How to obtain the equation of the line normal to the curve?The equation of the line normal to a curve follows the point-slope definition of a linear function, given as follows:
y - y' = m(x - x').
The function in this problem is defined as follows:
y = square root(3x² + 2x).
Then the derivative of the function, applying the chain rule, is given as follows:
y' = (6x + 2)/(2 x square root(3x² + 2x))
y' = (3x + 1)/square root(3x² + 2x)
At x = 2, the numeric value of the derivative is of:
y' = 7/square root(16) = 7/4.
The slope of the normal line is calculated as follows:
m x 7/4 = -1
m = -4/7.
(as the normal line is perpendicular to the tangent line, which has slope equals to the numeric value of the derivative at the point).
The coordinates of the point at (2,4), hence:
x' = 2, y' = 4.
Then the definition of the normal line is given as follows:
y - 4 = -4/7(x - 2).
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An employee receives a salary increase of 8% at the end of each full year working with a company. If the employee receives an initial salary of $35,400, which equation represents the employee’s salary, S, after t years since the employee began working with the company? Responses
The exponential function that represents the employee’s salary, S, after t years since the employee began working with the company is given as follows:
S(t) = 35400(1.08)^t.
What is an increasing exponential function?An increasing exponential function is modeled according to the rule presented as follows:
A(t) = A(0)(1 + r)^t.
The parameters are given as follows:
A(0) is the initial salary.r is the growth rate, as a decimal.An employee receives a salary increase of 8% at the end of each full year working with a company, hence the growth rate is given as follows:
r = 0.08.
The employee receives an initial salary of $35,400, hence the initial value is given as follows:
A(0) = 35400.
Thus the exponential function for this problem is defined as follows:
S(t) = 35400(1.08)^t.
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Use estimation to evaluate 8,627.5 ÷ 35
Answer:
246.5
Step-by-step explanation:
86275÷35
= 246.5
approximately 247
Shannon says that the lines y=-3x-4,y=-(1)/(3)x+6,y=-4x-5, and y=(1)/(4)x-5 could represent the sides of a rectangle. Explain Shannon's error.
The disadvantage is that the coefficients of x in the four equations can only take two values, so if one of every values is m, the alternative will be -1/m.
What is the equation?
A relationship between two terms on either side of an equal sign is depicted by a straightforward equation.
Simple equations also pursue one or a mixture of the four arithmetic computations of addition, simple arithmetic, multiplication, and division.
There are three basic forms of the system of equations: point-slope form, standard form, and slope-intercept form.
So, Shannon's error:
In a rectangle, the neighboring sides are perpendicular to one other, whereas parallel runs between the opposing sides.
The slope of line segments is equal, and the slope, of a perpendicular line to some other line with a slope, m, is -1/m , thus the slopes of the axis of symmetry should be equal, which gives:
The equation should consist of two sets of linear equations with equal slopes: B. Pair y = -x + 6 and y = -x - 5
Therefore, the slopes of the other two lines are -1/-1 = 1 and the equations of the other two lines are y = x - 4 and y = x - 5 respectively.
Therefore, the disadvantage is that the coefficients of x in the four equations can only take two values, so if one of every values is m, the alternative will be -1/m.
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for a two-factor experiment with 2 levels of factor a and 3 levels of factor b and 10 subjects in each treatment condition, how many participants are in each level of factor b?
We utilize a two factors, independent measurements ANOVA, where, factor has 2 level and a factor likewise has 2 levels.
What are factors?A factor in mathematics is an integer that evenly divides another number by itself, leaving no residue.
Factors and multiples are a part of our daily life. For example, they are employed in arranging objects in a box, handling money, recognizing patterns in numbers, solving ratios, and working with expanding
A number totally divides the provided number without leaving any residual is said to be the factor of that number.
The components of a number might be positive or negative. For example, let us find the factors of 8. Since 8 is divisible by 1, 2, 4, and 8, we may list the positive factors of 8 as, 1, 2, 4, and 8. Apart from this, 8 has negative elements as well, which might be stated as, -1, -2, -4,
According to our question-
Degrees of freedom for the F-test of the two way ANOVA
In this case, we utilize an ANOVA with two independent variables and two factors, each with two levels.
So, here,
= 2 for the number of layers of A
= B's level count is 2,
Moreover, n = sample size in each treatment condition is equal to 10.
So we have,
= df of the main effect A = ( - 1) = 2 - 1 = 1
= df of the main effect A = ( - 1) = 2 - 1 = 1
= df of interaction effect (A x B) = ( - 1)( - 1) ( - 1)
= (2-1)(2-1) (2-1)
= 1
And = df of within variation (i.e. error variation) =
= 2 x 2 x (10 - 1) (10 - 1)
= 36
Consequently, the df value for the F-ratio measuring factors-primary A's impact is
= () ()
= (1, 36) (1, 36)
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The total distance d, in meters, traveled by an object moving in a straight line can be modeled by a quadratic function that is defined in terms of t, where t is the time in seconds. At a time of 10.0 seconds, the total distance traveled by the object is 50.0 meters, and at a time of 20.0 seconds, the total distance traveled by the object is 200.0 meters. If the object was at a distance of 0 meters when t=0 then what is the total distance traveled, in meters, by the object after 30.0 seconds?
The total distance traveled by the object after 30.0 seconds is 450 meters.
Explain the term quadratic function?f(x) = ax2 + bx + c, for which a, b, and c represent constants and a = 0 represents a quadratic function. The function is known as the quadratic term (abbreviated as ax2), the linear term (abbreviated as bx), and the constant term (abbreviated as c).For the stated function;
Time = 10.0 seconds, distance = 50.0 meters.Time = 20.0 seconds, distance = 200.0 meters.Time = 0.0 seconds, distance = 0.0 meters.As, the total distance is modelled by the quadratic equation-
Let the quadratic equation be-
d = at² + bt + c
For (10, 50)
d = a(10)² + (10)b + c ....eq 1
For (20, 200)
d = a(20)² + (200)b + c ....eq 2
For (0, 0)
d = a(0)² + (0)b + c ....eq 3
Solving eq 1, 2 and 3
a = 1/2 ; b = 0 and c =0
Thus, equation for the distance travelled by the object is-
d = 1/2 t²
For t = 30. sec
d = 1/2 (30)²
d = 450 m
Thus, the total distance traveled by the object after 30.0 seconds is 450 meters.
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