Timmy has a collection of 95 coins consisting of dimes and nickels in his bank, The total value of his bank is $6.50. We can infer that he has 60 nickels and 35 dimes.
Define equation.In algebra, an equation is a declaration of equivalence that includes one or more variables or unknowable quantities.
Given,
Timmy has a collection of 95 coins consisting of dimes and nickels in his bank, The total value of his bank is $6.50.
Set d and n to the appropriate numbers.
Timmy has 95 coins in total, all of which are dimes and nickels, as far as we know.
Equation,
So d + n = 95
His bank is worth a total of $6.50.
A nickel is worth $0.05, while a dime is worth $0.10.
So
0.10d + 0.05n = $6.50
Take note that we have just produced an equation system that we can solve.
The two equations exist.
D + n = 95
and
0.10d + 0.05n = 6.50.
The replacement approach is probably going to be the simplest way to solve this problem out of all the options available to us.
First, we'll want to change the second equation's terms so that one of the variables is defined.
d+ n = 95
Take d off on both sides.
n = 95 - d
Now, let's define "n."
After defining one of the variables, we can now enter (or replace) its value in the other equation. After replacing it, we can find a solution for the other variable.
0.10d + 0.05n = 6.50
n = 95 - d
0.10d + 0.05(95 - d) = 6.50
We now determine d.
0.10d + 0.05(95 - d) = 6.50
distribution of the 0.05 in step 1
0.05 × 95 = 4.75
and
0.05 × -d = -0.05d
0.10d + 4.75 - 0.05d = 6.50
Step 2: Add like terms together (0.10 - 0.05) to get 0.05
0.05d + 4.75 = 6.50
step 3: Take 4.75 off of each side.
0.05d = 1.75
step 4: Subtract 0.05 from both sides.
0.05d / 0.05 = d and 1.75 / 0.05 = 35
d = 35
Now that we know the value of one variable, we can use it to solve for the second variable by plugging it into one of the equations ( note that the equation that we use does not matter, we will acquire the same answer )
d + n = 95
d = 35
35 + n = 95
Take 35 off both sides.
n = 60
We can infer that he has 60 nickels and 35 dimes.
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Can a probability sum to 1.07 or does it have to be exactly 1?
Answer:
Step-by-step explanation:
probability ≤|1|
or -1≤ probability ≤1
Answer:
No
Step-by-step explanation:
The sum of the probabilities in a probability distribution is always 1.
prove if f is a function from [0,1] to r and f is continuous then there exists an x in [0,1] such that f(x)
If f is a function from [0,1] to R and f is continuous, then there exists an x in [0,1] such that f(x) = 0.
What is a function?
In mathematics, a function is a rule that assigns a unique output to each input in a set. A function is continuous if the output value changes smoothly as the input value changes, without any sudden jumps or breaks.
To prove that if f is a function from [0,1] to R and f is continuous, then there exists an x in [0,1] such that f(x) = 0, we can use the intermediate value theorem.
The intermediate value theorem states that if a function f is continuous on a closed interval [a,b], and if y is any value between f(a) and f(b), then there exists at least one x in the interval [a,b] such that f(x) = y.
In our case, f is a function from [0,1] to R, which is a closed interval, and f is continuous on this interval. Therefore, the intermediate value theorem applies to f.
To prove that there exists an x in [0,1] such that f(x) = 0, we can use the intermediate value theorem with y = 0. Since 0 is between f(0) and f(1), the intermediate value theorem guarantees that there exists at least one x in [0,1] such that f(x) = 0.
Hence, if f is a function from [0,1] to R and f is continuous, then there exists an x in [0,1] such that f(x) = 0.
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A distribution of values is normal with a mean of 120 and astandard deviation of 21. From this distribution, you are drawingsamples of size 13. Find the interval containing the middle-most76% of sample means:Enter your answer using interval notation. In this context,either inclusive or exclusive intervals would be acceptable. Roundyour numbers to one decimal place. Answers obtained using exactz-scores or z-scores rounded to 3 decimal places are accepted.
The interval containing the middle-most76% of sample means [tex]102.836 < \mathrm{x} < 137.164[/tex].
As per the data given in the above question,
A distribution of values is normal with a mean of [tex]\mu=120[/tex].
A standard deviation of [tex]\sigma=21[/tex].
Drawing samples of size n=13.
The middle-most76% of sample means.
Find the interval containing the middle-most76% of sample means?
[tex]\mathrm{P}(-\mathrm{z} < \mathrm{x} < \mathrm{z})=0.76\\\mathrm{P}(\mathrm{x} < \mathrm{z})-\mathrm{P}(\mathrm{x} < -\mathrm{z})=0.76\\[/tex]
Further
[tex]\mathrm{P}(\mathrm{x} < -\mathrm{z})=\mathrm{P}(\mathrm{x} > \mathrm{z})[/tex]
[tex]\mathrm{P}(\mathrm{X} < \mathrm{Z})-\mathrm{P}(\mathrm{X} > \mathrm{Z})=0.76\\\mathrm{P}(\mathrm{X} < \mathrm{Z})-1+\mathrm{P}(\mathrm{X} < \mathrm{Z})=0.46\\2 \mathrm{P}(\mathrm{X} < \mathrm{Z})=1.76\\\mathrm{P}(\mathrm{X} < \mathrm{Z})=0.88[/tex]
[tex]= NORMSINV (0.73)\\\mathrm{Z}=0.613[/tex]
[tex]& \mathrm{X}=\mathrm{z} \sigma+\mu \\& \mathrm{X}=0.613 \times 28+120 \\& \mathrm{X}=137.164-\mathrm{x} & =\mu-\mathrm{z} \sigma \\-\mathrm{x} & =120-0.613 \times 28 \\-\mathrm{x} & =102.836[/tex]
Now the interval sample is as follow,
[tex]102.836 < \mathrm{x} < 137.164[/tex]
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2) If you wish to save up $220,000 using an annuity, what monthly payment is required into the
annuity if the annuity has an APR of 8.0% compounded annually and you wish to reach your
savings goal in 30 years?
The monthly payment required into the annuity with an APR of 8.0% compounded annually and you wish to reach your savings goal in 30 years is $156.19.
How the monthly payment is determined?The monthly payment is required for 360 months (30 years x 12).
We can compute this periodic payment using an online finance calculator by inputting the parameters below:
N (# of periods) = 360 months (30 years x 12)
I/Y (Interest per year) = 8%
PV (Present Value) = $0
FV (Future Value) = $220,000
P/Y (# of periods per year) = 12
C/Y (# of times interest compound per year) = 1
Results:
Monthly Payments (PMT) = $156.19
Sum of all periodic payments = $56,228.40
Total Interest = $163,771.60
Thus, to reach a future value of $220,000, the monthly annuity deposit should be $156.19 for 30 years at 8%.
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You are given the rate of investment dI/dt. Find the capital accumulation over a five-year period by evaluating the definite integral Capital accumulation = 5 dI dt dt 0 where t is the time in years. (Round your answer to two decimal places.) dI dt = 16,000t (t2 + 2)2
Evaluate the definite integral.
Evaluate the definite integral.
Use any basic integration formula or formulas to find the indefinite integral. (Use C for the constant of integration.)
capital accumulation is 3,973,910.14.
To evaluate the definite integral, we will have to find the indefinite integral. We use integral by substitution to find the indefinite integral.
Capital Accumulation = ∫ dI/dt dt
= ∫ 16,000t (t^2 + 2)^2dt
If u = t^2 + 2 then du = 2t dt so the integral is
Capital accumulation = ∫ 16,000t (t^2 + 2)^2 dt
= ∫ 16,000 × (u - 2) × u^2 du/2
= ∫ 16,000u^3 - 64,000u^2 + 64,000udu/2
= 8,000u^4/4 - 32,000u^3/3 + 32,000u^2/2 + C
= 2,000u^4 - 10,667.7u^3 + 16,000u^2 + C
Substituting u again gives us:
Capital Accumulation = 2,000(t^2 + 2)^4 - 10,667.7(t^2 + 2)^3 + 16,000(t^2 + 2)^2 + C
To evaluate the definite integral, we need to find the values of this expression at t=0 and t=5 and subtract the two.
Capital Accumulation = [2,000(5^2 + 2)^4 - 10,667.7(5^2 + 2)^3 + 16,000(5^2 + 2)^2] - [2,000(0^2 + 2)^4 - 10,667.7(0^2 + 2)^3 + 16,000(0^2 + 2)^2]
= [2000(27)^4 - 10667.7(27)^3 + 16000(27)^2] - [2000(2)^4 - 10667.7(2)^3 + 16000(2)^2]
= 4,607,143.47 - 1,333,333.33 + 691,200
= 3,973,910.14
Therefore, the five-year capital accumulation is 3,973,910.14.
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Universal Electric manufactures sell two models of lamps X and Whose profit being $ 15 and $ 10 respectively. The Process involves two workers A and B who are available for this kind of work with 100 and 80 hours per month respectively. A assembles X in 20 minutes and Y in 30 minutes. B paints X in 20 minutes and Y in 10 minutes. Assuming that all lamps made can be sold without difficulty, determine production figures that maximize profit.
y
The production figure to maximize the profit is is Z = 15x + 10y subject to
2x + 3y ≤ 600 ; 2x + y ≤ 480 ; x,y≥ 0 .
In the question ,
it is given that ,
a company named Universal Electric manufactures sell two models of lamps that is Lamp X and Lamp Y and
Whose profit is $ 15 and $ 10 respectively.
let the number units the company manufactures of lamp X be = x units
let the number units the company manufactures of lamp Y be = y units
let the total profit be = Z ,
So , the profit to maximize be Z = 15x + 10y
worker A assembles Lamp X in 20/60 hours and Lamp Y in 20/60 hours ; and that he is available for 100 hours per month;
So , the inequality is
(20/60)x + (30/60)y ≤ 100.
20x + 30y ≤ 6000
2x + 3y ≤ 600
Similarly , worker B assembles Lamp X in 20/60 hours and Lamp Y in 10/60 hours ; and that he is available for 80 hours per month;
the inequality will be ,
(20/60)x + (10/60)y ≤ 80.
20x + 10y ≤ 4800
2x + y ≤ 480 .
Therefore , the LPP to maximize the profit is Z = 15x + 10y subject to
2x + 3y ≤ 600 ; 2x + y ≤ 480 ; x,y≥ 0 .
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assuming the roc to be lzl < 113, use long division to determine the values of x[o], x[ -1], and x[ -2].
Long division can be used to determine the absolute value of x[0], x[-1], and x[-2] when the roc is known. To do this, divide the roc (113) by the coefficient of the highest power in the polynomial (x2). Then, divide the remainder (3) by the coefficient of the next highest power (x), which gives x[-1] = 3. Finally, divide the remainder (8) by the coefficient of the lowest power (1), which gives x[-2] = 8.
To use long division to determine the values of x[0], x[-1], and x[-2], begin by dividing the roc (113) by the coefficient of the highest power in the polynomial (x2). This gives a result of 113/x2 = 10. This means that x[0] = 10. This number is then used as the divisor for the next step, which is to divide the remainder (3) by the coefficient of the next highest power (x). This gives a result of 3/x = 3, so x[-1] = 3. Finally, divide the remainder (8) by the coefficient of the lowest power (1), which gives 8/1 = 8, so x[-2] = 8. This process can be repeated to determine the values of x[n] for any polynomial.
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The angle θ lies in Quadrant III.
cosθ=−16
What is tanθ?
Responses
35−−√
square root of 35
−35√6
negative fraction numerator square root of 36 end root over denominator 6 end fraction
−35−−√
negative square root of 35
35√6
The tanθ for the angle θ that lies in Quadrant III is √35
How to determine tanθ?Trigonometry simply means the branch of mathematics that is concerned with functions of angles as well as their applications to calculation. It also deals with the relationship between ratios and their angles.
Given: The angle θ lies in Quadrant III
cosθ= −1/6 (adjacent/hypotenuse)
adjacent = -1 and hypotenuse = 6
We can draw the position of the angle as shown in the image attached.
Using Pythagoras' theorem:
opposite = √6²-(-1)² = √35
tanθ = (-√35) / (-1) = √35 (tanθ = opposite/adjacent)
Note: opposite in Quadrant III is negative
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assuming no employees are subject to ceilings for their earnings, calculate salaries payable and employer payroll tax expense.
Assuming no employees are subject to ceilings for their earnings IS $7,450
The computation of Salaries Payable is shown below:-
Gross Payroll $10,000
Less:
Federal income tax withheld $1,800
Social security rate at 6% -$600
Medicare rate at 1.5% -$150
Total deduction -$2,550
Salary Payable $7,450
We simply deduct three above taxes from the gross payroll so that we get to know for the salary payable amount
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Investment The future value S of an investment earning 6% compounded continuously is a function of the principal P and the length of time t that the principal has been invested. It is given by
S = f(P, t) = Pe0.06t
Find f(2000, 20), and interpret your answer.
The value of f(2000 , 20) is $6640.24 and the interpretation is "if 2000 was invested initially then $6640.24 will be the amount after 20 years" .
In the question ,
it is given that,
the future value (S) on investment earning is compounded continuously at 6% .
the function of the principal P and the length of time t that the principal has been invested is given by
S = f(P, t) = P×[tex]e^{0.06 \times t}[/tex]
to find f(2000 , 20) ,
we substitute P = 2000 and t = 20 ,
we get ,
f(2000 , 20) = 2000×[tex]e^{0.06 \times 20}[/tex]
Simplifying further ,
we get ,
= 6640.2338
≈ 6640.24
Its interpretation is "if 2000 was invested initially then $6640.24 will be the amount after 20 years .
Therefore , the value of f(2000 , 20) is $6640.24 .
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Help pls plssssssssssssssssssssssssssssssssssss asap no cap
How to find the length of a line segment in a circle?
Additional Topics in Math
Calculator: Not Permitted
Circle Geometry
The semicircle above has a radius of r inches, and chord CD is parallel to the diameter AB. If the length of CD is 2/3 of the length of AB, what is the distance between the chord and the diameter in terms of r?
The semicircle above has a radius of r inches, The distance between the chord and the diameter in terms of r is √5 r/3 inches.
What is chord of Circle ?A chord of a circle can be defined as a line segment connecting any two points on the circumference. It should be noted that the diameter is the longest chord of a circle which passes through the center of the circle.
To find the distance required one can use either the Pythagorean theorem or the trigonometric ratios. Let the semicircle have center O. The diameter AB has length 2r. Because chord CD is 2/3 of the length of the diameter,
CD=2/3(2r) = 4r/3
let the distance between diameter AB and chord CD be x inches. To find x draw a right triangle connecting center O, the midpoint, E of chord CD, and point C . Using Pythagorean theorem here,
r² = x² + (CD/2)²
=> r² = x² + (2r/3)²
=> r² = x² + 4r²/9
=> x² = r² - 4r²/9 = 5r²/9
=> x = √5 r/3
Hence, the distance between the chord and the diameter in terms of r is √5r/3..
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Can someone help please? Picture is already attached. If its wrong please correct it. This isn’t mine by the way, I’m posting it for someone else to double check if it’s right
The possible values of B in the number line are option A, C, D and E
Number LineA number line is a visual representation of numbers on a straight line. This line is used to compare numbers that are placed at equal intervals on an infinite line that extends on both sides, horizontally or vertically. As we move towards the right side of a horizontal number line, the numbers increase; as we move towards the left, the numbers decrease.
In this problem, the value of B is between 3 and 2 since B is located between them.
Checking the given options;
A = 2.5
This is possible because B can be at the middle between 2 and 3
B = 2/5
This fraction isn't possible because the value of B is greater than this.
C = 5 / 2
This fraction is possible because the decimal value is 2.5 which is the same as option A
D = 25 / 10
This fraction is also possible because the decimal value is 2.5 which is same as option A and C
E = 2.49
This is also a likely possibility as this can be approximated to 2.5
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let x and y be i.i.d. unif(0, 1). (a) compute the covariance of x y and x y . (b) are x y and x y independent studysoup
If x and y be i.i.d. unif(0, 1), then the covariance of x + y and x - y is zero
Here x and y be i.i.d. unif(0, 1)
The i.i.d stands for independent and identically distributed
unif means that the uniformly distributed
Here x and y are i.i.d unif (0,1)
The covariance is defined as the relationship between the two random variables . Therefore, variance of one variable is equal to the change in another variable
Here we have to find the covariance of x + y and x - y
According to the properties of covariance
Cov(x+ y, x - y) = Cov (x, x) + Cov(y, x) - Cov(x, y) - Cov(y, y) = 0
Because Cov(x, x) = Cov (y, y)
Cov(y, x) = Cov(x, y)
Therefore, the covariance of x+y and x - y is 0
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#9.
The table represents some points on the graph of linear function f.
Which function represents f ?
f(x)=32(3 x-1)
f(x)=-32(x-3)
f(x)=-2(32 x-3)
f(x)=16(2 x-1)
The function represents f ( x ) is f ( x ) = 32 ( 3x - 1 )
Given :
The table represents some points on the graph of linear function f.
Table :
x -2 1 5 10
f ( x ) -224 64 448 928
take two points ( 5 , 448 ) and ( 1 , 64 )
slope m = 64 - ( 448 ) / 1 - ( 5 )
= 64 - 448 / 1 - 5
= -384 / -4
= 384 / 4
= 192 / 2
= 96
( 1 , 64 ) on
y - 64 = 96 ( x - 1 )
y - 64 = 96x - 96
y = 96x - 96 + 64
y = 96x - 32
take 32 as common
= 32 ( 3x - 1 )
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Al is single, age 60, and has gross income of $140,000, of which $120,000 is salary and $20,000 is rental income. His deductible expenses are as follows:
Charitable contributions 4,000
Contribution to a traditional IRA 6,000
Expenses paid on rental property 7,500
Interest on home mortgage and property taxes on personal residence 7,200
State income tax 2,200
What is Al's AGI?
a.$140,000.
b.$126,500.
c.$114,000.
d.$134,000.
Al's AGI is $126,500.
What is gross income?
Before any deductions or taxes, gross income is the total of all wages, salaries, profits, interest payments, rentals, and other sources of income. It differs from net income, which is calculated as gross income less any applicable taxes and other deductions.
Here, we have
Given
Gross income of $140,000
Fewer Deductible expenses :
Alimony ($20,000)
Contribution to a traditional IRA ($6,000)
Expenses paid on rental property ($7,500)
AGI = Gross income - Contribution to a traditional IRA- Expenses paid on rental property
AGI = $140,000 - $6,000 - $7,500
AGI = $126,500.
Hence, Al's AGI is $126,500.
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A police department collected the statistics for the number of tickets police officers wrote each day over the last 6 weeks.
Mean =5.23
Median =3
Mode =2
What does the median represent in this situation?
It is the average number of tickets police officers wrote per day,
More than half the police officers wrote this number of tickets.
More police officers wrote this number of tickets per day than any other number.
It is the total number of tickets police officers wrote in 6 days.
The median represents here as, Option B; More than half the police officers wrote this number of tickets.
Given,
A police department collected the statistics for the number of tickets police officers wrote each day over the last 6 weeks.
Mean =5.23
Median =3
Mode =2
We have to find the representation of median in this situation;
Median;-
The value that, when a dataset is arranged, falls exactly in the middle is the median. It is a measure of central tendency that distinguishes between the values' lowest and maximum 50%. Depending on whether you have an odd or an even number of data points, the processes for calculating the median change.
Here,
The median 3 represents that, More than half the police officers wrote this number of tickets.
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LetVbe the vector space of continuous functions defined on the interval[0,1]. Define an inner product onVby the following rule:⟨f,g⟩=∫01f(x)g(x)dx.Use the Gram-Schmidt orthonormalization procedure to produce an orthonormal basis for the subspace spanned by1,x,x2. Use the results to find the closest-point projection ofx3into this subspace.
The closest projection will have a value of -29/360.
we will follow these steps to use the Gram-Schmidt orthonormalization procedure for producing an orthonormal basis for the subspace spanned by 1, x, and x²,
Set u₁ = 1, a unit vector.
Set v₂ = x and u₂ = v₂ / ||v₂||.
Set v₃ = x² - (x², u₁)u₁ - (x², u₂)u₂, and u₃ = v₃ / ||v₃||.
Thus we get the orthonormal basis for the subspace spanned by 1, x, and x² to be {u₁, u₂, u₃}.
Now we will use the formula for the projection of a vector onto a subspace to find the closest-point projection of x³ into this subspace,
proj_subspace(x³) = (x³, u₁)u₁ + (x³, u₂)u₂ + (x³, u₃)u₃
The inner products will be calculated as follows:
(x³, u₁) = ∫x³ X 1 dx = 1/4
(x³, u₂) = ∫ x³ X x dx = 1/5
(x³, u₃) = ∫ x³ * (x² - (x², u₁)u₁ - (x², u₂)u₂) dx
Here all the integrals will have limits of 0 and 1.
Hence we get
= 1/9 - 1/4 X 1/2 - 1/5 X 1/3
= 1/9 - 1/8 - 1/15
= (40 - 45 - 24)/360
= -29/360
Thus, the projection of x³ onto the subspace spanned by 1, x, and x² is:
proj_subspace(x³) = 1/4 X u₁ + 1/5 X u₂ + (1/9 - 1/4 X 1/2 - 1/5 X 1/3) X u₃
This projection is the closest point in the subspace to x³, in the sense that the distance between x³ and proj_subspace(x³) is minimized.
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Maya spent 40% of her savings to pay for a bicycle
How much
money does she have left in her savings after buying the bicycle?
Answer:
60% because the total should be 100% and if you take 40% away you should be left with 60%
match the following descriptions with the method. group of answer choices a model is an automatic, flexible, non-linear regression model, not interpretable, and retains all predictor variables although it may limit the effects of some. [ choose ] a model handles outliers well, handles many potential predictor variables easily, and sorts through predictor variables repeatedly to divide the data into groups to best determine the response variable.
decision tree and neutral network
What is decision tree?
The most effective and well-liked technique for categorization and prediction is the decision tree. A decision tree is a type of tree structure that resembles a flowchart, where each internal node represents a test on an attribute, each branch a test result, and each leaf node (terminal node) a class label.
A model is an automatic flexible non linear regression model not interpretable and retains all predictor variables although it may limit the effect of some decision tree
A model is handles outliers well handle many potential predictor variable easy and short through predictor variables repeatedly to divide the data into group to best determine the response variable is neutral network
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Community center sells a total of 297 tickets
Adult tickets are $3
Student tickets are $1
They collect $479 in ticket sales
How many of each type of ticket were sold ?
They sold $479 in ticket sales and they had a total of 297 tickets sold, so they must have sold $479/297 = $<<479/297=1.61>>1.61 per ticket.
There are two types of tickets, adult tickets and student tickets, and adult tickets are $3, so the student tickets are $1.61 - $3 = $<<1.61-3=-1.39>>-1.39.
However, a ticket cannot be negative so we know that all of the tickets must have been adult tickets and they sold 297 tickets for $479, so they sold 297 tickets * $3/ticket = $<<297*3=891>>891 worth of adult tickets. Answer: \boxed{891}.
First use appropriate properties of logarithms to rewrite f(x) and then find f’(x)
Answer:
f(x) = 6ln(8) -6ln(x)f'(x) = -6/xStep-by-step explanation:
You want to rewrite f(x) and differentiate it for f(x) = 6·ln(8/x).
Rules of logarithmsThe log of a ratio is the difference of logs:
ln(a/b) = ln(a) -ln(b)
ApplicationUsing this to rewrite f(x), we have ...
f(x) = 6ln(8/x) = 6(ln(8) -ln(x))
f(x) = 6·ln(8) -6·ln(x)
DerivativeThe derivative of the constant is zero, so ...
f'(x) = -6/x
onvert the integral below to polar coordinates and evaluate the integral. instructions: please enter the integrand in the first answer box, typing theta for . depending on the order of integration you choose, enter dr and dtheta in either order into the second and third answer boxes with only one dr or dtheta in each box. then, enter the limits of integration and evaluate the integral to find the volume. a
Evaluation of the integral is [tex]\frac{81}{16}[/tex]
In mathematics, an integral is either a definite value representing the region under a function's graph for a certain interval or a new function whose derivative represents the original function (indefinite integral). The fact that a definite integral of any function that can be integrated may be found using the indefinite integral and a corollary to the calculus fundamental theorem connects these two interpretations.
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Find the critical values, to, to test the claim that H, H2. Two samples are randomly selected and come from populations that are normal. The sample statistics are given below. Assume that of to. Use a = 0,05 ny = 25, n = 30, X = 23, X2 = 21,5 = 1.5,82 = 1.9 OA 2064 OB 2.797 Oct2492 OD 1.711
The critical values for the following sample are ±2.0064.
Here it is given that α = 0.05,
To calculate the critical values we will use the t-statistic.
Here n₁ = 25 and n₂ = 30
Hence, the degrees of freedom
d.f = n₁ + n₂ - 2 [Since it's a 2-sample test]
= 25 + 30 - 2
= 53
Now our significance level is α = 0.05,
To know the critical value we will make use of a t-distribution table and look up the value corresponding to a 0.05 significance level and 53 degrees of freedom.
Here we will get the critical values ±2.0064
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Evaluate the integral by making the given substitution. (Use C for the constant of integration.) x3(3 + x4)6 dx, u = 3 + x4 Evaluate the integral by making the given substitution. (Use C for the constant of integration.)
dt(1 â 3t)6, where u = 1 â 3t
The answer to this integration is - [tex]\frac{u^{7} }{28} + c[/tex] .
u = 3 + x⁴
differentiate both sides,
⇒ du = 0 + 4x³ dx
⇒ du = 4x³ dx
⇒[tex]dx = \frac{du}{4x^{3} }[/tex] ..........(1)
The integration is :
[tex]\int x^{3} ( 3 +x^{4} )^{6} dx[/tex]
Substitute the values from equation (1)
= [tex]\int x^{3} u^{6} \frac{du}{4x^{3} }[/tex]
= [tex]\frac{1}{4} \int u^{6} du[/tex]
=[tex]\frac{1}{4} . \frac{u^{7} }{7} + c[/tex] ( c = integration constant )
= [tex]\frac{u^{7} }{28} + c[/tex]
Hence, the answer to this integration is - [tex]\frac{u^{7} }{28} + c[/tex] .
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Hi please order the side lengths from least to greatest thank you
Answer:
Step-by-step explanation:
ok
alr
Answer:
below
Step-by-step explanation:
Largest angle = largest opposite side , smallest angle = smallest opposite side
EF < ED <DF
The two cotton processing companies are producing different products and those are sold out the products one year before. The sold sum of both the two companies salaries are $44,000,000. The sold price of company x is 1000 more than the other. Therefore, find the value of each company's product sold price by framing a linear equation?
The value of each company's product sold price is given as follows:
Company x: $22,000,500.Company y: $21,999,500.How to obtain the values?The values of each company's product sold price is obtained using a system of equations, for which the variables are defined as follows:
Variable x: Company's x sold price.Variable y: Company's y sold price.The sold sum of both the two companies salaries are $44,000,000, hence:
x + y = 44000000.
The sold price of company x is 1000 more than the other, hence:
x = 1000 + y.
Then the sold price of company y can be found replacing the second equation into the first, as follows:
1000 + y + y = 44000000
2y = 44000000 - 1000
y = (44000000 - 1000)/2
y = $21,999,500.
The sold price for company x is then calculated as follows:
x = 1000 + y = 1000 + 21999500 = $22,000,500.
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The following age structure diagrams were created for various counties in the United States from 2000 census data. Which of the following statements best describes the pattern seen in age structure diagram C?
There is an imbalance between males and females, with a ratio of 1.5 men to every woman in the population.
Which age structure diagram represents a population's ages the best?
However, it is generally agreed that using a population pyramid is the most effective technique to graphically depict the age and sex distribution of a certain population. A population pyramid displays the numbers or percentages of men and women in each age group using a paired bar chart-style image.Age structure diagrams in nations with high population increase have a sharp pyramid shape.Age structure diagrams in nations with rapid growth have a pyramidal shape, indicating a majority of younger people, many of whom are of reproductive age.Hence, there is an imbalance between males and females, with a ratio of 1.5 men to every woman in the population.
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The length of a rectangle is twice its width.
If the perimeter of the rectangle is 48 cm, find its length and width.
If the perimeter of the rectangle is 48 cm, its length and width is equal to 16 cm and 8 cm respectively.
How to calculate the perimeter of a rectangle?Mathematically, the perimeter of a rectangle can be calculated by using this equation;
P = 2(L + W)
Where:
P represents the perimeter of a rectangle.L represents the length of a rectangle.W represents the width of a rectangle.Since the length is twice the width, we have;
L = 2W
Substituting the given parameters into the perimeter formula, we have;
48 = 2(2W + W)
48 = 6W
W = 48/6
Width, W = 8 cm.
For the length of this rectangle, we have;
L = 2W
L = 2(8)
L = 16 cm.
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The law allows marketers of herbs and other natural substances to make health claims that are not supported by evidence. Brands of ginkgo extract claim to "improve memory and concentration ." A randomized comparative experiment found no evidence for such effects. The subjects were 230 healthy people over 60 years old. They were randomly assigned to ginkgo or a placebo pill (a dummy pill that looks and tastes the same). All the subjects took a battery of tests for learning and memory before treatment started and again after six weeks.
(a) Following the model of previous figures, outline the design of this experiment.
(b) Use the Simple Random Sample applet, other software, or Table A to assign half the subjects to the ginkgo group. If you use software, report the first 20 members of the ginkgo group (in the applet's "Sample bin") and the first 20 members of the placebo group (those left in the "Population hopper"). If you use Table A, start at line 103 and choose only the first 5 members of the ginkgo group
a) Six-week learning and memory test: Both groups had a six-week learning and memory test.
b) According to Table A, the first five ginkgo trees are 103, 105, 107, 108, and 109.
(A) By randomly allocating people to treatment & control groups, randomized controlled trials are a form of experimental investigation that seeks to reduce bias. In this instance, the treatment group took tablets containing ginkgo extract, whereas the control group took pills containing a placebo. Prior to the initiation of therapy & again after six weeks, both groups underwent memory and learning tests.
The experiment's design may be summarized as follows:
Choosing the research population is folks over 60 who are in good health
Calculate the sample size: 230 people
Place individuals in control and treatment groups at random: The ginkgo group received half of the participants, while the placebo group received the other half.
Administering care: Pills containing ginkgo extract were given to the ginkgo group, whereas placebo pills were given to the placebo group.
Prior to starting therapy, both groups had their learning and memory skills tested.
Both groups underwent learning and memory ability tests six weeks later.
(b) According to the basic random sample applet, the first 20 members of the ginkgo Biloba subpopulation are:
11, 13, 15, 16, 18, 19, 20, 21, 22, 24, 25, 26, 27, 28, 29, 30, 32, 33, 34, 35
first 20 subjects using a placebo Those that participated are 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 12, 14, 17, 23, 31, 36, 37, 38, 39, and 40.
5 people: 103, 105, 107, 108, and 109
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