Solve for a
6a-15=72

Answer:

You're asked to find the cube root of 125.

That is,to cancel the power of y, you'd have to cube root both sides.

answer is 5

Answer:

There isn't any data, maybe you could put the rest of the question in the comment area.

Answer:

180

Step-by-step explanation:

length of arc GJ ≈ 31.42 units.

A circle's arc is a bent portion of the circle's circumference. Its perimeter is determined by its two ends and the area of the circle that lies in between them. An arc's length or the angle it makes with the circle's center can be used to measure it.

The formula L = θr states that the length of an arc is inversely proportional to the radius of the circle and the angle it subtends. L is the length of the arc, r is the radius of the circle and θ is the angle the arc subtends in radians.

To find the length of arc GJ, we first need to find the circumference of the circle.

The circumference of a circle is given by the formula:

C = 2πr

where C is the circumference, π is a constant approximately equal to 3.14, and r is the radius of the circle.

Since GH = 20 units and HJ is the radius of the circle, we have:

HJ = GH = 20 units

So the radius of the circle is 20 units.

The formula for the length of the arc is 2πr(θ/360)

Since the angle is given 90, the length of the arc:

2*π*20(90/360)

=10 π

Therefore, the length of arc GJ is 10π or 31.42 units.

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Answer:

718.38

Step-by-step explanation:

Answer:

1,900 square feet; f(3) represents the total number of square feet the construction crew has paved after 3 hours.

The function of the construction crew is an illustration of a linear function

The value of f(3) is 1900, and f(3) represents the total number of square feet paved after working for 3 hours

The function is given as:

To calculate f(3), we substitute 3 for x

Multiply 300 and 3

Add 900 and 1000

This means that the value of f(3) is 1900.

And it represents the total number of square feet paved after working for 3 hours

1,900 square feet; f(3) represents the total number of square feet the construction crew has paved after 3 hours.

The values of the expressions, obtained by the combination of the functions, f(x), g(x), and h(x), and found by plugging in the values of the specified function at the indicated value of x are;

17. g(9) + h(-14) = 15

19. (1/2)·g(-6) + f(-2) = -22

21. x = -12

A function defines the relationship between an input variable and an output variable, such that each input produces only one value of the output.

The functions, f(x), g(x), and h(x), are defined as follows;

f(x) = -x² + 8·x - 11

\(g(x) =14-\dfrac{2}{3} \cdot x\)

h(x) = -x - 7

17. The value of g(9) can be found by plugging x = 9, in the function for g(x) as follows;

\(g(9) =14-\dfrac{2}{3} \times 9= 8\)

g(9) = 8

Similarly, the value of h(-14), can be found by plugging in x = -14, in the function for h(x) as follows;

h(-14) = -(-14) - 7 = 7

h(-14) = 7

Therefore, g(9) + h(-14) = 8 + 7 = 15

19. The value of g(-6), can be found as follows;

\(g(-6) =14-\dfrac{2}{3} \times (-6)= 18\)

g(-6) = 18

Similarly, for f(-2), we get;

f(-2) = -(-2)² + 8 × (-2) - 11 = -31

Therefore;

\(\dfrac{1}{2}\cdot g(-6) +f(-2) = \dfrac{1}{2} \times 18 + (-31) = 9 - 31 = -22\)

21.  h(x) = -x - 14

If the value of h(x) = -2, we get;

h(x) = -2 = -x - 14

14 - 2 = -x

-x = 12 (symmetric property)

Dividing both sides by (-1), we get;

-x/(-1) = x = 12/(-1) = -12

x = -12

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Answer:

\(14 \times 0.5 = 70 \\ 70\)

The two step equation for the scenario that your cousin is in where they pay for their textbooks is:

7x + 20 = 230

x = (230 - 20) / 7

The cost of the textbooks would be $30.

The total amount paid by your cousin in order to be able to cover a book for their 7 classes and the fee for art class is $ 230.

Assuming that the cost of each book from his 7 classes is denoted as x, then the expression would be:

= 7 x number of classes

= 7x

This amount is then added to the cost of the art class which is $ 20 so it becomes:

= 7x + 20

The two step equation is therefore:

7x + 20 = 230

x = (230 - 20) / 7

The cost of the textbooks is:

x = (230 - 20) / 7

x = $ 30

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Answer:

15/4

Step-by-step explanation:

m=(y2-y1)/(x2-x1)

m=(35-5)/(14-6)

m=30/8

simplify

m=15/4

Answer:

Step-by-step explanation:

Slope is defined as

m=(y2-y1)/(x2-x1), we have points (6,5) and (14,35) so

m=(35-5)/(14-6)

m=30/8

m=3.75

Spherical harmonics are an integral part of quantum mechanics. They describe the shape of the orbitals, which electrons occupy in atoms. Moreover, the spherical harmonics provide the angular distribution of a wave in spherical coordinates. In 3D, the spherical harmonics can be written as:

Ylm(θ, φ) = √(2l + 1)/(4π) * √[(l - m)!/(l + m)!] * Plm(cosθ) * e^(imφ)

Here, l and m are known as the angular quantum numbers. They define the shape and orientation of the orbital. Plm(cosθ) represents the associated Legendre polynomial, and e^(imφ) is the exponential function. The spherical harmonics have various forms, including:

Y1,1 = -Y1,-1 = 1/2 √(3/2π) sinθe^(iφ)

Y1,0 = 1/2 √(3/π)cosθ

Y2,2 = 1/4 √(15/2π)sin²θe^(2iφ)

Y2,1 = -Y2,-1 = 1/2 √(15/2π)sinθcosφ

Y2,0 = 1/4 √(5/π)(3cos²θ-1)

Y0,0 = 1/√(4π)

The spherical harmonics have various applications in physics, including quantum mechanics, electrodynamics, and acoustics. They play a crucial role in understanding the symmetry of various systems. Hence, the spherical harmonics are an essential mathematical tool in modern physics. Thus, this is how one can show another form for spherical harmonics.

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Answer: 9 × 6 = 54

Step-by-step explanation:

In the Product Game, we need to multiply the both number of factor markers.

Chris and Katie were playing The Product Game. Their factor markers were on 9  and 2.

Number = 9 × 2 = 18

Chris decided to move the marker from 2 to 6.

Now, one maker is on 9 and other is on 6. So,

Number = 9 × (2 + 4)

Number = 9 × 6 = 54

Therefore, 9 × 6 = 54 is a numerical expression  to represent his move.​

Answer:

$2.95

Step-by-step explanation:

8x+8y=83.60

8 is the amount of friends/amount of tickets/amount of small popcorn

x is the cost 1 ticket

y is the cost 1 small popcorn

We know that the price of a ticket is 7.50 so we replace "x" with 7.50

8(7.5)+8y=83.60

Simplify

60+8y=83.60

Now subtract 60 from both sides

8y=23.60

Now divided both sides by 8

y=2.95

the cost of 1 small popcorn is $2.95

As per the given confidence interval, the lower and upper bounds is 68.6 to 71.4 and the Confidence Interval is written as 70 ± 1.39

Here let us consider that in cells j18 and j19, use the information you calculated about the confidence interval for weight to determine the lower and upper bounds for the 95% confidence interval for your prediction of Jim's weight in cell j15.

Let us consider that the value of Short Styles is written as,

=> 70 (95% CI 68.6 to 71.4)

=> 70, 95% CI [68.6, 71.4]

And the Margin of Error is calculated from the confidence interval as,

=> 1.39

Here we have identified that  Sample Size is  50 through this we have know that the value of Sample Mean is 70 and then the Standard Deviation is  5 and finally, the value of Confidence Level is 95%.

Based on this we have know that With 95% confidence the population mean is between 68.6 and 71.4, based on 50 samples.

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Let's solve each of the given parts one by one.1. Use the definition of "big Oh" to prove that n2​ is O(n). (3 marks). The definition of Big Oh states that for a given function f(n) to be O(g(n)), if and only if there exist positive constants c and n0 such that:f(n) ≤ c*g(n), for all n >= n0Given f(n) = n2​ and g(n) = n, we need to show n2​ is O(n). So, we need to find a positive constant c and n0 such that:n2​ ≤ c*n, for all n >= n0.

Let's solve the inequality:n2​ ≤ c*n⇒ n ≤ c(when n is positive)Hence, for any value of c>=1 and n0 = 1, the above inequality will always hold. Therefore, n2​ is O(n).2. Let f(n) and g(n) be positive functions such that f(n) is O(g(n)). Use the definition of "big Oh" to prove that f(n)×g(n) is O(g2(n)), where g2(n)=g(n)×g(n). (3 marks)Solution:Given f(n) is O(g(n)). So, there exist positive constants c and n0 such that:f(n) ≤ c*g(n), for all n >= n0Now, we need to show that f(n)×g(n) is O(g2(n)), where g2(n)=g(n)×g(n)We can write, f(n)×g(n) ≤ c*g(n)×g(n) ≤ c*g2(n), for all n >= n0Thus, by the definition of Big Oh, we can say that f(n)×g(n) is O(g2(n)).3.

Use the definition of "big Oh" to prove that n3+4n4​ is not O(n3).Solution:We need to prove that there does not exist any constant c such that n3+4n4​ <= c*n3 for all n >= n0.By taking the limit of the ratio of the two functions as n approaches infinity, we can show that n3+4n4​ grows faster than n3. So, the ratio of n3+4n4​ to n3 is greater than or equal to 4 for all values of n greater than 1.We can write:n3+4n4​/n3 >= 4 for all n > 1Therefore, n3+4n4​ is not O(n3).Hence, we have proved that n3+4n4​ is not O(n3).

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Answer:

11.

Step-by-step explanation:

100-32    = money after hat purchase

(100-32) dollars  / 6 dollars / scarf   = 11.33   or 11 scarves (because you cannot buy a fraction of a scarf)

a) The probability of randomly selecting 4 males out of 7 spectators, given that 70% of the spectators are males, can be calculated using the binomial probability formula.

b) To find the probability that at most 5 of the randomly selected spectators are females, we need to calculate the cumulative probability of selecting 0, 1, 2, 3, 4, and 5 females from the total number of selected spectators.

a) To calculate the probability of selecting 4 males out of 7 spectators, we can use the binomial probability formula:

P(X = k) = C(n, k) * p^k * (1 - p)^(n - k)

Where:

- n is the total number of trials (number of people selected)

- k is the number of successful trials (number of males selected)

- p is the probability of success in a single trial (probability of selecting a male)

- C(n, k) is the binomial coefficient, calculated as C(n, k) = n! / (k! * (n - k)!)

In this case, n = 7, k = 4, and p = 0.70 (probability of selecting a male). Therefore, the probability of selecting 4 males out of 7 spectators is:

P(X = 4) = C(7, 4) * (0.70)^4 * (1 - 0.70)^(7 - 4)

b) To find the probability that at most 5 of the selected spectators are females, we need to calculate the cumulative probability of selecting 0, 1, 2, 3, 4, and 5 females. This can be done by summing the individual probabilities for each case.

P(X ≤ 5 females) = P(X = 0) + P(X = 1) + P(X = 2) + P(X = 3) + P(X = 4) + P(X = 5)

To calculate each individual probability, we use the same binomial probability formula as in part a), with p = 0.30 (probability of selecting a female).

Finally, we sum up the probabilities for each case to find the probability that at most 5 of the selected spectators are females.

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option (A) cy + b/a is the main answer.

The given expression ax - b = cy is an equation with one variable 'x.'

We need to find the value of x. The steps to solve the equation are given below:

Solve for x:Adding 'b' to both sides,ax = cy + b.

Divide both sides by 'a,'x = (cy + b) / a.\

Therefore, option (A) cy + b/a is the main answer.

Therefore, we can conclude that the result of solving the equation ax - b = cy for x is x = (cy + b) / a, and the main answer is option (A) cy + b/a.

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Using the formula of the combination and for the values of 'p' and 'q'. The statement is false.

Combinations are mathematical operations that count the number of potential configurations for a set of elements when the order of the selection is irrelevant. You can choose the components of combos in any order.

The formula is:

\(C(p,q) = \frac{p!}{q!(p-q)!}\)

p=4 and put q=0 to 4

C(4,2) > C(4,0),C(4,1),C(4,3),C(4,4)

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So to find any last digit of 3^2011 divide 2011 by 4 which comes to have 3 as remainder. Hence the number in units place is same as digit in units place of number 3^3. Hence answer is 7.

Answer:

This group review serves an important role in the protection of the rights and welfare of human research subjects. The purpose of IRB review is to assure, both in advance and by periodic review, that appropriate steps are taken to protect the rights and welfare of humans participating as subjects in the research

Answer: 143°

Step-by-step explanation:

140+146=286

360-286=74

74/2=37

vertical angles are equal so using supplementary angles or vertical angle rule I can prove the angle labeled x is 143°

Student will kill the app and refuse to turn back to ongoing session

But session is in session history already

Even though it's not finished yet

Updates to answer are realtime

Answer:

5 years

Step-by-step explanation:

Given that

The current population is 45,000

The rate of interest in declining would be 4.5% per year

The expected population is 35,746

We need to find out the no of years

Since the rate of interest decrease by 4.5% per year so after decreasing it the percentage would be 0.955

Now

Year 1 = 45,000 × 0.955 = 42,975

Year 2 = 42,975 × 0.955 =  41,041.125

Year 3 = 41,041.125 × 0.955 = 39,194.27

Year 4 = 39,194.27 × 0.955 = 37,430.53

Year 5 = 37,430.53 × 0.955 = 35,746.16

Hence, the no of years would be 5

One faces a tradeoff between the number of courses and hours of work due to limited available time. Taking X courses while working X hours per week is impossible as it exceeds the time constraint.

The tradeoff between the number of courses and hours of work arises due to the finite number of hours available in a week. Assuming an individual has X hours per week, this time must be divided between courses and work.

To achieve a B or better in a course, it is necessary to dedicate at least X hours per course per week. Therefore, taking X courses while working X hours per week would require dedicating X hours per course, resulting in a total time commitment exceeding the available X hours.

Conversely, if only one class is taken while working X hours per week, the time commitment for a single course is less than X hours. This scenario leaves a significant amount of free time remaining, as the total time dedicated to the course and work does not exhaust the available X hours.

In summary, the tradeoff occurs because the time available is limited, and the minimum time requirement per course restricts the number of courses that can be taken while maintaining a specific work schedule.

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The laplace transform of f(t) is \(F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}\) and it's values exists for \(s=w\pm\sqrt{3}wi\).

Given,

\(f(t)=sin^2(wt)\\\\\therefore sin^2x=\frac{1-cos2x}{2}\\\\f(t)=\frac{1-cos2wt}{2}\)

applying laplace transform on both sides,

\(L[f(t)]=L[\frac{1-cos2wt}{2}]\\\\F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}\)

The range for values of s for which F(s) exists is when F(s)≥0

\(\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)} \geq0\\\\\frac{1}{2s} \geq\frac{2w}{2(s^2+4w^2)}\\\\2(s^2+4w^2) \geq 2sw\\\\s^2-2sw+4w^2 \geq0\)

using formula to find roots,

\(s=\frac{-(-2w)\pm\sqrt{(-2w^2)-4(4w^2)}}{2}\\\\s=\frac{-(-2w)\pm\sqrt{(12w^2}}{2}\\\\s=w\pm\sqrt{3}wi\)

Thus,  the laplace transform of f(t) is \(F(s)=\frac{1}{2s}-\frac{2w}{2(s^2+4w^2)}\) and it's values exists for \(s=w\pm\sqrt{3}wi\).

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Answer:

im thinking its 40.. tho im not sure im pretty sure it is so im sorry if its wrong

Step-by-step explanation:

Answer:

310

Step-by-step explanation:

1.Find your constant difference of the sequence by subtracting from left to right which is 9

2. find your fomula by using Tn=bn+C (b is your constant difference you can find C by C=T1 -b ) which will then give us 9n-5

3. T(35)=9n-5=9(35)-5=310

Answer:

Option 1

Step-by-step explanation:

5(3x+2) + 2(x-7)

15x + 10 + 2x -14

15x + 2x + 10 - 14

17x - 4

The rate of change of the balance after 1 year is approximately $72.98 per year, and after 2 years is approximately $78.20 per year.

a) The given equation is dP/dt = 0.068P. This is a first-order linear differential equation. To find the function P(t) that satisfies this equation, we can solve the equation by integrating both sides:

dP/P = 0.068 dt

Integrating both sides, we get:

ln(P) = 0.068t + C, where C is the integration constant.

Taking exponent of both sides, we get:

P(t) = e^(0.068t + C) = e^(0.068t) * e^C.

Now, let's find the value of e^C using the initial condition P(0) = P0:

P0 = e^(0.068 * 0) * e^C => P0 = e^C.

Thus, the function that satisfies the equation is:

P(t) = P0 * e^(0.068t).

b) If $1000 is invested, then P0 = 1000. To find the balance after 1 year and 2 years, plug in t=1 and t=2 into the equation:

P(1) = 1000 * e^(0.068 * 1) ≈ $1073.20
P(2) = 1000 * e^(0.068 * 2) ≈ $1150.06

The balance after 1 year is approximately $1073.20, and after 2 years is approximately $1150.06.

c) The rate of change of the balance is given by dP/dt. Use the equation dP/dt = 0.068P and the function P(t) to find the rate of change after 1 year and 2 years:

dP/dt(1) = 0.068 * P(1) = 0.068 * 1073.20 ≈ $72.98
dP/dt(2) = 0.068 * P(2) = 0.068 * 1150.06 ≈ $78.20

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