On solving the given question, by the Help of LaPlace Inverse form we got - [tex]y(t) = \frac{-7}{2} + \frac{1}{2}e^{-8t}[/tex]
What is The Laplace transform?In terms of its usefulness in resolving physical issues, the Laplace transform is an important transform that is probably second only to the Fourier transform. The Laplace transform is especially helpful in solving linear ordinary differential equations, such as those that arise in the analysis of electronic circuits.
Take Laplace for DE we get -
[tex]L(y)" + 8L(y)' =0\\s^2Y (s) - sy(0) - y'(0) 8(sY(s) - y(0))=0\\Y(s)(s^2 + 8s) + 3s 4 + 24 =0\\Y(s)(s^2 + 8s) = -3s - 28\\Y(s) = \frac{-3s - 28}{(s^2 + 8s) } \\Right Side = \\\frac{-7}{2s} + \frac{1}{2(s+8)} \\ Now taking inverse LaPlace - \\y(t) = \frac{-7}{2} + \frac{1}{2}e^{-8t}[/tex]
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If a cyclist rides at an average speed of 18 miles per hour, how many miles does she ride in seven hours?.
If a cyclist rides at an average speed of 18 miles per hour then she ride 126 miles in seven hours.
What is Equation?Two or more expressions with an Equal sign is called as Equation.
A cyclist rides at an average speed of 18 miles per hour.
We have to find the number of miles she ride in seven hours
Assume x be the number of miles she ride
Let us form a proportional equation
18/1 = x/7
Apply cross multiplication
18×7=x
126=x
Hence, if a cyclist rides at an average speed of 18 miles per hour then she ride 126 miles in seven hours.
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You have a bag with five different colored marbles in it; red, green, blue, orange, and purple. Each marble has an equal chance of
being drawn from the bag and a marble is replaced after each draw.
After four draws from the bag what is the probability that you have seen both the red and green marbles at least once?
This question is based on the probability. Therefore, 1/20 is the probability that the red marble is drawn first and the green marble is drawn second.
Given:
There are 5 marbles in a bag. Each marble is a different color. The colors are: red, orange, green, blue, purple. Two marbles are randomly drawn from the bag without replacement.
We need to determined the probability that the red marble is drawn first and the white marble is drawn second.
According to the question,
It is given that, there are 5 different marbles. In the first draw, you have a one out of 5 chance of getting the red is 1/5 .
In the second draw, there are 4 marbles remaining, so a one out of 4 chance of drawing a white marble i.e. 1/4.
Now, calculating the total probability of drawing the red and then white marble, we multiply the probabilities if each draw.
⇒ 1/5 × 1/4 = 1/20
Therefore, 1/20 is the probability that the red marble is drawn first and the green marble is drawn second.
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y is five times X +15
exhibit 9-4 a random sample of 16 students selected from the student body of a large university had an average age of 25 years. we want to determine if the average age of all the students at the university is significantly different from 24. assume the distribution of the population of ages is normal with a standard deviation of 2 years. the test statistic is . a. 1.645 b. 2.00 c. 1.96 d. .05
It can be deduced that the mean age is substantially different from 24 at the.05 level of significance.
If the average student age is not substantially different from 24 years, then the null hypothesis is tested, which is:
[tex]H_{0}[/tex] : μ = 24
If it differs from 24 years, the alternative premise is tested, so:
[tex]H_{1}[/tex] : μ ≠ 24
The z-distribution is utilized because we have the population's standard deviation. The test statistic comes from:
z = x - μ÷ σ/[tex]\sqrt{n}[/tex]
The parameters in this issue have the following values:
x(mean) = 25
μ = 24
σ = 2
n=16
As a result, the test statistic's value is:
z = 25-24÷ 2/[tex]\sqrt{16}[/tex]
z = 2
The probability of a sample mean older than 25 years determines the test's p-value, which is 1 less than the p-value of z = 2.
The p-value for z = 2 in the z-table is 0.9772; 1 - 0.9772 = 0.0228.
Given that the test's p-value is 0.0228 0.05, we may say that:
It can be deduced that the mean age is substantially different from 24 at the.05 level of significance.
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an efficiency expert claims that a new ergonomic desk chair makes typing at a computer terminal easier and faster. to test it, volunteers are selected. half of the volunteers will use the new chair and half will use their old chairs. each volunteer types a randomly selected passage for 2 minutes and the number of correct words typed is recorded. choose the correct answer below. a. the data are independent and not paired. b. the data are paired where the pairing involves the volunteers who use the new chair and the volunteers who use their old chair. c. the data are paired where the pairing involves the random passages the volunteers type
with the help of Advanced Placement statistics correct answer is option B.
what is Advanced Placement statistics?
In the United States, the College Board's Advanced Placement programme offers a college-level high school statistics course known as Advanced Placement Statistics.
explanation:
The data are paired where the pairing involves the volunteers who use the new chair and the volunteers who use their old chair.
hence the correct option is B by Advanced Placement statistics
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rosie is driving from knoxvile, tennesse orlando, florida. she drives 317.88 miles before she stops for lunch and then another 203 4/5 miles before taking a break. rosie has driven 4/5 of the entire trip. how many total miles is her trip?
The total miles of the trip are 521.68 miles.
What is addition?Addition in maths, a process of combining two or more numbers.
Given that, Rosie drives 317.88 miles before lunch and then [tex]203\frac{4}{5}[/tex] miles before break,
Total miles = 317.88 + [tex]203\frac{4}{5}[/tex] miles = 521.68 miles
Hence, The total miles of the trip are 521.68 miles.
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a summer squash, spinach, and leek frittata recipe requires 6 ounces of spinach. if the ep unit cost of the ingredient is $2.25 per pound, what is the total cost of the ingredient?
The total cost of the ingredient is $0.84 for 6 ounces.
Define fixed cost.
The cost or expense known as fixed cost is unaffected by a short-term horizon's growth or reduction in the number of units produced or sold. To put it another way, it refers to a cost that is linked to a time period rather than a specific economic activity.
It can be viewed as costs that a business must pay regardless of the volume of business activity, such as the number of units produced or sales made. One of the two main parts of the overall manufacturing cost is the fixed cost.
Solution Explained:
Given,
1 pound = $2.25
Since 1 pound = 16 ounces
So, 16 ounces = 2.25
1 ounce = 2.25/16 = 0.14
Therefore, 6 ounces = 0.14 X 6 = 0.84
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2. how long does it take to cook a potato? consider a cylindrical potato, sliced into thin slices with thicknesses l
The boundary value and initial value statement are,
T surrounding = 100°c
IVP = [tex]T_i = 20^oc, T_f = 75^oc\\[/tex].
What is Initial Value Problem?
In multivariable calculus, an initial value problem is an ordinary differential equation that also includes an initial condition that identifies the value of the unknown function at a specific location in the domain. An initial value problem is frequently solved when modelling a system in physics or another scientific field.
Consider a cylindrical potato, sliced into thin slices with thickness L = 1 cm, much smaller than the diameter slices.
Initial temperature [tex]T_i = 20^o[/tex]
Final temperature = [tex]T_f = 75^o[/tex]
Now we have to solve the given cases.
Consider the heat equation,
q = k(∂T / ∂x) ..(1)
(a) Now we have to find the boundary value
Boundary Value:
[tex]T_i = 20^oc, T_f = 75^oc\\[/tex]
⇒ ΔT = [75 - 20]
⇒ΔT = 55°c
T surrounding = 100°c
IVP = [tex]T_i = 20^oc, T_f = 75^oc\\[/tex]
Hence, the boundary value and initial value statement are,
T surrounding = 100°c
IVP = [tex]T_i = 20^oc, T_f = 75^oc\\[/tex].
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Complete question:
Complete question is attached below,
pls help :( The table shows the sizes of Farmer Reuben's fields. Use the table and a separate sheet of paper to help you answer each question.
The areas of each of Reuben's fields are given as follows:
Corn Field: 24,000 square feet.Wheat Field: 140,000 square feet.Barley Field: 40,000 square feet.Hence the total area of all of Reuben's fields is given as follows:
204,000 square feet.
How to obtain the areas of the fields?The areas of the fields is given by the multiplication of each of the dimensions of the field, as the fields have a rectangular format.
Then the total area is obtained as the sum of the areas of each field.
The dimensions of each field are given as follows, from the table given by the image at the end of the answer:
Corn Field: 400 feet by 60 feet.Wheat Field: 700 feet by 200 feet.Barley Field: 200 feet by 200 feet.Hence the areas of each of the fields are given as follows:
Corn Field: 400 x 60 = 24,000 square feet.Wheat Field: 700 x 200 = 140,000 square feet.Barley Field: 200 x 200 = 40,000 square feet.Then the total area is given as follows:
24,000 + 140,000 + 40,000 = 204,000 square feet.
Missing InformationThe problem asks for the areas of each field and the total area.
The dimensions are given by the image shown at the end of the answer.
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The weight (in pounds) and height (in inches) for a child were measured every few months over a two-year period. The results are given in the table.
A 2-column table with 9 rows. Column 1 is labeled Weight (x) with entries 8, 12, 18, 24, 30, 32, 35, 37, 40. Column 2 is labeled Height (y) with entries 22, 23, 26, 30, 32, 33, 35, 36, 38.
Using technology, what is the correlation coefficient?
–0.997
–0.503
0.503
0.997
Using technology, the correlation coefficient is 0.997
How to calculate correlation coefficient?We should know that correlation coefficient is a statistical model which is used to determine or measure the relationship between two variables.
The table is
x y x² y² xy
8 22 64 484 176
12 23 144 529 276
18 26 324 676 468
24 30 567 900 720
30 32 900 1024 960
32 33 1024 1089 1056
35 35 1225 1225 1225
37 36 1369 1369 1332
40 38 1600 1444 1520
Total 236 275 7226 8740 7733
[tex]r= \frac{nExy)-(Ex)(Ey)}{\sqrt{[n(EX^{2}][nEy^{2}(Ey)^{2} } }[/tex]
applying the figures from the table we have
r=[tex]\frac{9*7733-(236)(275)}{\sqrt{[9*7226-55696][9*8740-75625]} }[/tex]
Simplifying the expression we have
r=[tex]\frac{4697}{\sqrt{28340830} }[/tex]
r=0.88
r=0.9 approximately
Therefore the correct answer is 0.997 which is the correlation coefficient.
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A bucket can hold a total of 5 gallons of water. If the bucket is 9/20 full, how much water is in the bucket?
Answer:2.25 gallons
Step-by-step explanation:
Raise seven to the second power then find the sum of the result of Z
Answer: We write J raised to the 9th power as J9 (which means J multiplied by J a total of nine times). "Sum" means "add them" so J9 + K
Step-by-step explanation:
What is the slope of the line that passes through the points (-5, 8) and (-5, 4)? Write your answer in simplest form.
(I NEED HELP URGENTLY, THIS IS DUE TOMORROW!)
The table represents a proportional relationship.
A. Find the constant of proportionality:
B: Write a equation to represent the relationship. Equation: y=
The constant of proportionality is 1/3 and the equation is y = 1/3x
A. The constant of proportionalityThe table of values represents the given parameter
From the table of values, we have the following ordered pair
(x, y) = (3, 1)
The constant of proportionality (k) is then calculated as
k = y/x
So, we have
k = 1/3
B: The equation to represent the relationship.Recall that, we have
k = y/x
Substitute k = 1/3
y/x = 1/3
So, we have
y = 1/3x
Hence, the equation is
y = 1/3x
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what fraction of seven number combinations formed used the numbers of the patter 3795523 will have the 2 3's always together
By using the concept of permutation, it can be calculated that
Fraction of seven number combinations formed used the numbers of the pattern 3795523 will have the two 3's always together = [tex]\frac{360}{1260}[/tex]
= [tex]\frac{2}{7}[/tex]
What is permutation?
Permutation is the arrangement technique that determines how many possible arrangement that can be made in a set where the order of arrangement matters.
Here, concept of permutation is used
Number of 7 number combinations that can be formed using the number 3795523 = [tex]\frac{7!}{2! \times 2!}[/tex] = 1260
The two 3's are always together
Number of 7 digit numbers formed = [tex]\frac{6!}{2!}[/tex] = 360
Fraction of seven number combinations formed used the numbers of the pattern 3795523 will have the two 3's always together = [tex]\frac{360}{1260}[/tex]
= [tex]\frac{2}{7}[/tex]
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would it be unusual for a random sample of 500 adult americans to result in 210 or more who believe marriage is obsolete?
Yes, it would be unusual for a 500 adult Americans to result in 210 or more who believe marriage is obsolete. The probability value is 0.39 for adult Americans.
We know very well that probability is defined as the ratio of number of favorable outcomes to the total number of outcomes.
We have given that 39% american adults women believes that marriage is now obsolete.
So,39% of 500 adult American women is =[(39/100)×500]
=39×5=195
So,probability of adult women who believes marriage is obsolete is =(195/500)=0.39
Now, we need to check that whether 210 women believes marriage is obsolete or not.
So, number of favorable outcome is 210 and total number of outcomes=500.
Therefore, probability of adult women who believes marriage is obsolete is=(210/500)=0.42
Now,we can see that 195 women probability is lower than 210 women probability. It means that more number of women considered marriage is obsolete.
Hence, yes it is unusual and the probability value of adult Americans is 0.39
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(Complete question) is:
would it be unusual for a random sample of 500 adult americans to result in 210 or more who believe marriage is obsolete?If so determine the probability, otherwise type 0 for this result NOT to be unusual
Which ordered pair is a solution to the equation?
-4x + 7 = 2y - 3
Choose 1 answer:
A Only (2, 1)
B Only (5, -5)
C Both (2, 1) and (5,-5)
D Neither
Answer: Neither (5/2, 0)
Step-by-step explanation:
-4x + 7 = 2y - 3
+3 +3
2y = -4x + 10
(Divide both sides by 2)
y = -2x +5
—————————————————
-4x + 7 = 2(-4x + 10) - 3
-4x + 7 = -8x + 20 - 3
-4x + 7 = -8x + 17
+8x -7 +8x -7
8x - 4x = 17 - 7
4x = 10
(Divide both sides by 4)
x = 5/2
—————————————
y = -2(5/2) + 5
y = -5 + 5
y = 0
——————————
Check Work:
-4x + 7 = 2y - 3
-4(5/2) + 7 = 2(0) -3
-10 + 7 = 0 - 3
-3 = -3 ✔️
Answer please! I couldn’t figure it out.
By solving a system of equations we will see that she sold 80 phones and 240 accessories.
How many phones and accessories were sold?
Let's define the variables:
x = number of phones.
y = number of accessories.
We know that she makes $160 on commissions, and that she sold 3 times as many accessories as phones, so we can write the system of equations:
y = 3x
x*$8 + y*$4 = $160
To solve the system, we can replace the first equation into the second one.
x*$8 + (3x)*$4 = $160
x*$8 + x*$12 = $160
x*$20 = $160
x = $160/$20 = 80
She sold 80 phones, and the number of accessories is:
y = 3x
y = 3*80 = 240
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The Myer family purchased a bedroom set for $2,480. The sales tax rate is 7%. Find the total cost of the set and the tax.
The total cost of the set and the tax is 2653.6 dollars.
How to find the total cost of the set and the tax?The Myer family purchased a bedroom set for $2,480. The sales tax rate is 7 percent.
Therefore, the total cost of the set and the tax can be calculated as follows:
tax = 7% of 2480
tax = 7 / 100 × 2480
tax = 17360 / 100
tax = $173.6
Therefore, let's find the total cost of the set and tax.
total cost = 173.6 + 2480
total cost = 2653.6 dollars
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vv7 of 107 of 10 items 10:32 skip to resources question the height of an ostrich is 20 inches more than 4 times the height of a kiwi. if an ostrich is 108 inches tall, how tall is a kiwi?
The kiwi as per the given relation of ostrich and kiwi's height is equal to 22inches tall.
As given in the question,
Ostrich height is equal to 108 inches
Let us consider 'x' inches be the height of the kiwi.
Ostrich is 20inches more than four times of x.
Ostrich height = 20 + 4x
⇒ 108 = 20 + 4x
Subtract 20 from both the sides we get,
108 - 20 = 20 + 4x -20
⇒ 88 = 4x
Divide by 4 on both the sides we get,
88/ 4 = 4x / 4
⇒ x = 22 inches
Therefore, as per the given relation of ostrich and kiwi's height , kiwi is 22inches tall.
The complete question is :
The height of an ostrich is 20 inches more than 4 times the height of a kiwi. if an ostrich is 108 inches tall, how tall is a kiwi?
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6 3/ 4 divide by 4 1/2
The value of the equation A = ( 6 3/4 ) / ( 4 1/2 ) is 3/2 or 1 1/2
What is an Equation?
Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.
It demonstrates the equality of the relationship between the expressions printed on the left and right sides.
Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.
Given data ,
Let the first number be A = 6 3/4
A = 27/4
Let the second number be B = 4 1/2
B = 9/2
Now , the equation is C = A/B
The value of C = A / B
Substituting the values of A and B in the equation , we get
Value of C = ( 6 3/4 ) / ( 4 1/2 )
Value of C = ( 27/4 ) / ( 9/2 )
Value of C = ( 27 / 9 ) / 2
Value of C = 3 / 2
Therefore , the value of C is 3/2 or 1 1/2
Hence , The value of the equation A = ( 6 3/4 ) / ( 4 1/2 ) is 3/2 or 1 1/2
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a rectangle has a length of 1 inches and a width of 6 inches whose sides are changing. the length is increasing by 4 in/sec and the width is shrinking at 2 in/sec. what is the rate of change of the perimeter?
The rate of change of the perimeter is 4 in/sec .
In the question ,
it is given that ,
the length of the rectangle is [tex]=[/tex] 1 inch
the width of the rectangle is = 6 inch
the rate of increasing length is (dL/dt) = 4 in/sec
rate of shrinking width is (dW/dt) = -22 in/sec ,
We know that the perimeter of the rectangle is = 2(L + W) ,
that is , P = 2L + 2W ,
Differentiating perimeter with respect to time "t" ,
we get ,
dP/dt = 2 × ( dL/dt) + 2 × (dW/dt )
Substituting the values from above ,
we get ,
= 2 × (4) + 2 × (-2)
= 8 - 4
= 4
Therefore , the required rate of change is = 4 in/sec .
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Assume that the probability a child is a boy is 0.51 and that the sexes of children born into family are independent. What is the probability that a family of five children hasa. exactly three boys?b. all girls?c. at least one girl?
a) Probability of exactly three boys is 0.3185
b) Probability of at least one boy is 0.9717
c) Probability of at least one girl is 0.9655
d) Probability of all of same sex is 0.06275
What is probability?
Probability refers to potential. A random event's occurrence or the outcome is the subject of this area of mathematics. The range of the value is 0 to 1. Mathematics has incorporated probability to forecast the likelihood of various events. The degree to which something is likely to happen is basically what probability means.The potential outcomes for a random experiment using this fundamental theory of probability, which is also applied to the probability distribution.a) Probability of exactly three boys
Choose 3 out of 5 in C(5,3)=10 ways
So probability is:10*0.51^3*0.49^2
~0.3185
(b) Probability of at least one boy
p(at least one boy)=1-p( all girls)
=1-0.49^5
=0.9717
c) Probability of at least one girl
p(at least one girl)=1-p( all boys)
=1-0.51^5
=0.9655
d) Probability of all of same sex
p(all of same sex)=p(all boys)+p(all girls)=
0.51^5+0.49^5
=0.06275
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If the bond angle between two adjacent hybrid orbitals is 120°, which is the hybridization?.
If the bond angle between two adjacent hybrid orbitals is 120° the hybridization is Sp2 hybridization .
Hybridization is a theory that is used to explain certain molecular geometries that would have not been possible otherwise.
sp2 hybridization
There are other ways to combine the orbitals than sp3 hybridization when an excited state carbon atom is produced. As opposed to the three p orbitals in the sp3 hybridization, the s orbital only interacts with two p orbitals in the sp2 hybridization. As a result, three orbitals are combined to create three hybrid orbitals, also known as sp2 hybrid orbitals.
The sp2 hybridization occurs when the s orbital is mixed with only two p orbitals as opposed to the three p orbitals in the sp3 hybridization
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Suppose that a monopolistically competitive firm must build a production facility in order to produce a product. The fixed cost of this facility is FC = $24. Also, the firm has constant marginal cost, MC = $3. Demand for the product that the firm produces is given by P = 27- 3Q.
Fill in the entire table below. All of the numbers you fill in will be integers (no decimals), some have been added.
Quantity of Output Price Total Cost Average Total Cost Total Revenue Profits
1 2 3 4 5 7.8 6 7 6.4 8 9 5.7 B. How many units of output will the firm produce if it maximizes its profit?
C. What price should this firm charge if it wants to maximize its profit?
The output firm will get maximum profits when the quantity is 4 units and the company will charge a price of $15 for maximum profit.
The fixed cost of this facility is FC = $24. Also, the firm has constant marginal cost, MC = $3
Demand for the product that the firm produces is given by P = 27- 3Q.
The total cost is calculated by adding fixed cost and variable cost.
TC = FC + VC
Average total cost = total cost / quantity
Quantity price (37 - 3Q) fixed cost variable cost total cost average cost
1 27 - 3(1) = 24 24 3 (1) 27 27
2 27 - 3(2) = 21 24 3(2) = 6 30 15
3 27 - 3(3) = 18 24 3(3) = 9 33 11
4 27 - 3(4) = 15 24 3(4) = 12 36 9
5 27 - 3(5) = 12 24 3(5) = 15 39 7.8
Upon analysing the table we can say that
B) the number of output units is 4
C) Maximum profit is when price is $15
Therefore, the maximum profit is when the output units is 4 and the company will charge a price of $15 for maximum profit.
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write a quadratic function in standard form whose graph passes through the given points (10,0), (1,0), and (4,3).
The quadratic function in standard form whose graph passes through the given points (10,0), (1,0), and (4,3) is; y = 0.2x² - 2.2x + 2
How to write the standard form of the quadratic equation?
The standard form of a quadratic equation is;
y = ax² + bx + c
where a, b and c are constants
Thus, for the coordinate (10,0), we have;
0 = a(10)² + b(10) + c
100a + 10b + c = 0 -----(1)
For the coordinate (1,0), we have;
0 = a(1)² + b(1) + c
a + b + c = 0 -----(2)
For the coordinate (4,3), we have;
3 = a(4)² + b(1) + c
16a + b + c = 3 ------(3)
Using online simultaneous equation, we have;
a = 0.2 and b = -2.2 and c = 2
The quadratic function is;
y = 0.2x² - 2.2x + 2
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Given the algebraic expression (125x^7/3) ^-1/3 create an equivalent expression
The resulting value of the given indices expression is: [tex]\frac{1}{5x^{7/3}}[/tex]
What is indices and exponents?A term's multiplicative history can be determined by an index, which is a discrete number. Indexes is the plural of index.
The exponentiation operator is the caret (). It is important to distinguish the exponent operator from the base-10 exponent sign. In a numeric literal, a base-10 exponent sign (scientific notation) can be represented by either an uppercase "E" or a lowercase "e."
[tex](125x^{7/3})^{-1/3}[/tex]
Using the indices law that states;
[tex](a^n)^m = a^{mn}[/tex]
Given,
[tex](125x^{7/3})^{-1/3}[/tex]
Since, [tex](125x^{7/3})^{-1/3}[/tex]= [tex][((5x)^3)^{7/3}]^{-1/3}[/tex]
= [tex][(5x)^7]^{-1/3}[/tex]
= [tex]5x^{-7/3}[/tex]
= [tex]\frac{1}{5x^{7/3}}[/tex]
Hence the resulting value of the given indices expression is: [tex]\frac{1}{5x^{7/3}}[/tex]
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the ph of a solution is measured eight times by one operator using the same instrument. she obtains the following data: 7.15, 7.20, 7.18, 7.19, 7.21, 7.20, 7.16 and 7.18. calculate the a. sample mean b. sample variance and standard deviation c. coefficient of variation
a. sample mean = 7.1838
b. sample variance = 0.0004 and standard deviation = 0.0207
c. coefficient of variation = 0.29%
What is sample variance?
The expectation of a random variable's squared deviation from its population mean or sample mean is known as variance in probability theory and statistics. Dispersion is a measure of how far apart a group of numbers is from their mean value, and variance is a measure of dispersion.
A probability distribution's variance is defined as the mean of the squared deviation from the distribution's mean. The expected value, commonly known as the mean, is the value you will obtain on average if you take several samples of a probability distribution.
Solution Explained:
a) Mean x=∑x/n
=7.15+7.2+7.18+7.19+7.21+7.2+7.16+7.18/8
=57.47/8
=7.1838
b) Sample Variance S2=∑x2-((∑x)^2/n)/n-1
=(412.8531-(57.47)^2/8)/7
=412.8531-412.8501/7
=0.003/7
=0.0004
Sample Standard deviation S=√∑x^2-((∑x)^2)/n)/n-1
=√(412.8531-((57.47)^2/8))/7
=√412.8531-412.8501/ 7
=√0.003/7
=√0.0004 =0.0207
c) Coefficient of Variation (Sample) =
S/x X100%
=(0.0207/7.1838) X 100%
=0.29%
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Find the 70th term of the arithmetic sequence
Answer:
753
Step-by-step explanation:
Arithmetic sequences are sequences that change by a constant factor.
Explicit Rule
The formula that describes an arithmetic sequence is called the "explicit rule". This formula is f(x) = f(1) + d(x-1). Sometimes the rule will be written with [tex]a_{n}[/tex] instead of f(x) but the equations are still the same.
In this equation, f(1) is the first term of the sequence, d is the common difference, and x is the term. The common difference is the factor that the sequence changes by.
Setting Up the Equation
To set up the equation, we need to find f(1) and d.
The first term, f(1), is directly given to us in the equation. The first term written is -6, so f(1)=-6.
It is slightly more difficult to find d. But, one easy way to find d is by subtracting terms. Take the second term, 5, and subtract the first term, -6.
5 - (-6) = 11So, d = 11. Each term in the sequence increases by 11.
The final equation is f(x) = -6 + 11(x-1).
Finding the 70th Term
Now, all we have to do is plug 70 in for x. To find any term in the sequence, all you have to do is plug the term number in for x.
f(70) = -6 + 11(70-1)f(70) = 753The 70th term in the sequence is 753.
Let f(x) = 6x. The graph of f(x) is transformed into the graph of g(x) by a vertical compresion of 1/2 and a translation of 4 units up.
The equation for of graph of g(x) = 3x-4
Functionsy = afb(x +c) + d
where a represent the vertical stretch
b represent the horizontal stretch
c represent the horizontal translation
d represent the vertical translation
from the equation we are given g(x) has a vertical stretch and a vertical translation ( y-axis represent up and down therefore its a vertical translation)
The equation of g(x) is:
g (x) = 1/2(6x) - 4
g(x) = 3x-4
Therefore, the equation for of g(x) = 3x-4
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