What is 3 5/9 - (-1 1/6)?
Again, I'm terrible at farctions.

The rate of change of volume with respect to R is 4πR².

The rate of change function is defined as the rate at which one quantity is changing with respect to another quantity. In simple terms, in the rate of change, the amount of change in one item is divided by the corresponding amount of change in another. The rate of change formula gives the relationship describing how one quantity changes in relation to the change in another quantity. The rate of change from the coordinates of y to the coordinates of x can be found out as Δy/ Δx = (y2 - y1 )/ (x2 - x1 ). For a linear function, the rate of change m is represented in the slope-intercept form for a line: y=mx+b whereas the rate of change of functions is otherwise defined as, (f(b)-f(a))/ b-a.

The volume of the sphere is:

V = (4π/3)(R³)

Differentiating volume with respect to radius gives:

dV/dR  = (4π/3)× (3R²) = 4πR²

Thus, the rate of change of volume with respect to R is 4πR².

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Answer:

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Answer:

-8, -6, -4, -1, 3

Step-by-step explanation:

Hope it helps! =D

To prove the identity sinh(2x) = 2 sinh(x) cosh(x), we can use the definitions of sinh(x) and cosh(x) and apply trigonometric identities for exponential functions.

We start with the left-hand side of the identity, sinh(2x). Using the definition of the hyperbolic sine function, sinh(x) = (e^x - e^(-x))/2, we can substitute 2x for x in this expression, giving us sinh(2x) = (e^(2x) - e^(-2x))/2.

Next, we focus on the right-hand side of the identity, 2 sinh(x) cosh(x). Again using the definitions of sinh(x) and cosh(x), we have 2 sinh(x) cosh(x) = 2((e^x - e^(-x))/2)((e^x + e^(-x))/2).

Expanding this expression, we get 2 sinh(x) cosh(x) = (e^x - e^(-x))(e^x + e^(-x))/2.

By simplifying the right-hand side, we have (e^x * e^x - e^x * e^(-x) - e^(-x) * e^x + e^(-x) * e^(-x))/2.

This simplifies further to (e^(2x) - 1 + e^(-2x))/2, which is equal to the expression we derived for the left-hand side.

Hence, we have proved the identity sinh(2x) = 2 sinh(x) cosh(x) by showing that the left-hand side is equal to the right-hand side through the manipulation of the exponential functions.

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Answer:

The expression you use to find the amount of miles would be 5xT=X miles.

or 5t

In order to acquire a total of £1379. 2 from compound interest on a principal of £1,200 compounded once per year for two years, an interest rate of 7.207% per year is needed.

Formula for compound interest is –

A = P(1+r/n)^nt

Where, A = Amount at the end of investment

             P = Principal Amount or amount invested

       r = rate of interest

      n = number of times interest applications per period.

       t = number of time periods elapsed

Here in the question A is £1379. 2

          P = £1,200

          t = 2 years

          n = 1 (annually)

Solving for rate r as a decimal

r = n[(A/P)1/nt - 1]

r = 1 × [(1,379.20/1,200.00)1/(1)(2) - 1]

r = 0.0720696

Then convert r to R as a percentage

R = r * 100

R = 0.0720696 * 100

R = 7.207% per year

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Answer:

Step-by-step explanation:

1. -42

2. 6

3. -9

4. 545

5. 145

6. -183

7. -46

8. -15

9. -92

10. -111

Answer:

$30.60

Step-by-step explanation:

$25.50×1.2=30.60

Answer:

-6, -2, 0, 4, 8

Step-by-step explanation:

Answer: find the answer in the explanation.

Step-by-step explanation:

There are various real life applications of trigonometry ratio such in building construction, oceanography, cartography, e.t.c

Its application extends to aviation industry, astronomy and oil and gas industry. Just to mention a few.

We can solve real-world applications involving trigonometric ratios by applying calculus and periodic function table and chart, and calculation involving trigonometry ratio itself ( Soh Cah Toa) e.t.c.

simple interest = $1092

Total amount = $6292

Principal = $5200

rate = 3% = 0.03

time = 7 years

Applying simple interest formula:

I = 5200 × 0.03 ×7

I = $1092

simple interest = $1092

We are to find total amount after getting the interest:

Amount = principal + interest

Amount = $5200 + $1092

Amount = $6292

Step-by-step explanation:

1st buy greek yogurt granola and fruits of your choice

2nd i put mine in old fashioned ice cream sunday glass

3rd layer it how ever you feel

Answer:

1st Buy Greek yogurt, granola, and fruits of your choice.

2nd Put in old fashioned ice cream Sunday glass

3rd Layer it where ever you like.

Step-by-step explanation:

Hey you there, yeah you, this is a revision on what he put above me. I added commas, periods, and capitals. So please don't hate on me, and have a great day!

If the probability of failure is 0.001, then the probability that

(a) lot is accepted is 0.9277,

(b) lot is rejected on 20th test is 0.000981,

(c) lot is rejected in 10 or fewer trials is 0.01.

Let the random-variable "X" represent number of batteries to test to get the first-battery which fails; in other words, to get first success.

Since, the trials are independent, X has a geometric distribution

Part (a) :

Let X =  the number of trials,

So, the probability that the lot is accepted is :

⇒ P(X=75) = (0.999)⁷⁵×(0.001)⁰ = 0.9277,

Part (b) :

let Y = the numbers of trials before the first failure (geometric distribution and

So, the probability that lot is rejected on 20th-test is :

⇒ P(Y=20) = (0.001)⁰×(0.999)¹⁹ = 0.000981,

Part (c) :

The probability that it is rejected in 10 or fewer trials is :

⇒ 1- P(no Failures)

⇒ 1 – (0.001)⁰(0.999)¹⁰ = 0.01.

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Answer:

40 miles per hour, since the distance travelled is 80 miles in 2 hours, divide that in half and you have the proportion

To calculate the cost of holding stock for a year, we need to determine the carrying cost per unit and multiply it by the number of units being held in stock.

First, let's calculate the economic order quantity (EOQ) for the computing systems:

EOQ = sqrt((2DS)/H)

where

D = annual demand = 25 systems

S = setup cost per order = $6,000

H = holding cost per unit per year = ?

Assuming a holding cost of 20% of the unit cost, we have:

H = 20% of unit cost = 0.20*$6,000/46 = $24.78 per unit per year

So, the EOQ is:

EOQ = sqrt((225$6,000)/$24.78) = 46.17 (rounded to 46)

Since the EOQ is 46 systems, we need to order 46 systems at a time to minimize our total inventory costs.

The cost of holding stock for a year is then:

Cost of holding stock = number of units held in stock * holding cost per unit per year

= 46 * $24.78

= $1,139.88

Therefore, it will cost your company $1,139.88 to hold 46 computing systems in stock for a year.

Answer:

x = -24

Step-by-step explanation:

y = 1/4x+12 (Substitute 6 for y)

6 = 1/4x+12 (Subtract 12 from both sides)

6-12= -6 so its now -6 = 1/4x and since its a fraction you want to multiply both sides by the reciprocal

4*-6 = 1/4x*4 (1/4*4=1 which is 1x or x)

-24 = x

Answer:

y=1/4x+12

6=1/4x+12

1/4x=6-12

1/4x=-6

0.25x=-6

x=-6÷0.25

x=-24

Step-by-step explanation:

first put the given value into the equation

inverse rule:

+ve changes to -ve(vice versa)

÷changes to ÷(vice versa)

Answer:

k = 3

Step-by-step explanation:

Assuming the values in the table are in direct proportion, then

y = kx ← is the equation relating x and y with k the constant of proportion, thus

k = \(\frac{y}{x}\)

To find k substitute (28, 84 ) into the equation

k = \(\frac{84}{28}\) = 3

Answer:

Step-by-step explanation:

Perimeter is sum of the side lengths

Bases are 1 and 9 units

Sides are

Perimeter is:

A survey of car owners to determine the best bus route. Option C is correct.

These are errors that are derived from a population estimate using statistics from a given sample. Most sampling errors are caused by lack of precision and bias.

From the given option, we can see that Option C is the best example of sampling error because there are possibilities that car owners are not familiar with bus routes.

Answer: 84 2/3

Step-by-step explanation:

x-66 2/3=18

x=18 + 66 2/3

x=18 + 66 + 2/3

x=84 + 2/3

x=84 2/3

Answer:

It would be 17%

Step-by-step explanation:

Answer:

B: 20%

Step-by-step explanation:

Answer:

decimal form; 0.22222...

exact form; 2/9

Step-by-step explanation:

Answer:

\(y=2x+5\)

Step-by-step explanation:

\((5,0)\)

Since the y-axis is cross on 5, that's the slope.

y=mx+5

To find x, let's use the formula;

\(m=\frac{rise}{run}\)

\(m=\frac{6}{3}=2\)

Answer:

\(\sqrt[15]{x^7}\)

Step-by-step explanation:

If we have the expression

\(\frac{x^{\frac{4}{5}}}{x^{\frac{1}{3}}}\), we have to think about exponent rules.

If we have \(a^b \div a^c\), then the value will be equal to \(a^{b-c}\).

So \(\frac{x^{\frac{4}{5}}}{x^{\frac{1}{3}}}\) simplified will be \(x^{\frac{4}{5} - \frac{1}{3}}\)

Converting \(\frac{4}{5}\) and \(\frac{1}{3}\) into fifteenths (lcm) gets us \(\frac{12}{15} - \frac{5}{15} = \frac{7}{15}\).

We can convert \(x^{\frac{7}{15}}\) into a radical by taking the denominator root of x to the numerator.

\(\sqrt[15]{x^7}\).

Hope this helped!

The inner product of two vectors A = (2, -3,0) and B = (-1,0,5) is -2 / √(13×26).

Solving the given system of equations using Gaussian elimination:

2x + 3y + z = 2 y + 5z = 20 -x+2y+3z = 13

Matrix form of the system is

[A] = [B] 2 3 1 | 2 0 5 | 20 -1 2 3 | 13

Divide row 1 by 2 and replace row 1 by the new row 1: 1 3/2 1/2 | 1

Divide row 2 by 5 and replace row 2 by the new row 2: 0 1 1 | 4

Divide row 3 by -1 and replace row 3 by the new row 3: 0 0 1 | 5

Back substitution, replace z = 5 into second equation to solve for y, y + 5(5) = 20 y = -5

Back substitution, replace z = 5 and y = -5 into the first equation to solve for x, 2x + 3(-5) + 5 = 2 2x - 15 + 5 = 2 2x = 12 x = 6

The solution is (x,y,z) = (6,-5,5)

Therefore, the solution to the given system of equations using Gaussian elimination is (x,y,z) = (6,-5,5).

The given two vectors are A = (2, -3,0) and B = = (-1,0,5). The inner product of two vectors A and B is given by

A·B = |A||B|cosθ

Given,A = (2, -3,0) and B = (-1,0,5)

Magnitude of A is |A| = √(2²+(-3)²+0²) = √13

Magnitude of B is |B| = √((-1)²+0²+5²) = √26

Dot product of A and B is A·B = 2(-1) + (-3)(0) + 0(5) = -2

Cosine of the angle between A and B is

cosθ = A·B / (|A||B|)

cosθ = -2 / (√13×√26)

cosθ = -2 / √(13×26)

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Answer:

1) 0.12

2) 52.5

3) 185.32

4) 77.85

5) 313.75

6) 1.536

7) 0.0167

8) 64

9) 21

10) 282.4

11) 136.64

12) 88.56

Step-by-step explanation: