Evaluate. (-1/3) ^3

Answer:

The answer to your problem is, 268.20

How to calculate a percent increase:

A quick way to increase a number by a percentage is to find the percent of your number and add it to your number.

So, suppose Jerry got a hot stock tip from a friend about some kind of robot butcher. Jerry bought the stock for $10 and it went up 37%. How much is Jerry's stock worth?

You could also solve this problem by multiplying 10 * 1.37, which also gives you $13.70

Thus the answer to your problem is 268.20

Answer:

the supplement of angle 70∘ is 110∘. Two angles are called supplementary angles if their sum is 180 degrees.

Answer:

1.8 and 14.3

Step-by-step explanation:

Our equation is a quadratic equation so we will use the dicriminant method

1) The two column proof for ΔLMN ≅ ΔLON is as developed below.

2) The  two column proof for ΔGHJ ≅ ΔKLM is as developed below

A two-column proof is defined as a geometric proof that consists of a list of statements, and then the reasons that we know those statements are deemed to be true.

1) The two column proof showing that ΔLMN ≅ ΔLON is;

Statement 1: LN bisects ∠MLO and LM ≅ LO

Reason 1: Given

Statement 2: MN ≅ ON

Reason 2: Line segment bisector

Statement 3: ∠MLN ≅ ∠OLN

Reason 3: def. of angle bisector

Statement 4: LN ≅ LN

Reason 4: Reflexive property of congruence

Statement 5: ΔLMN ≅ ΔLON

Reason 5: SSS Congruency postulate

2) The two column proof is as follows;

Statement 1: ∠G ≅ ∠K, ∠J ≅ ∠M

Reason 1: Given

Statement 2: ∠H ≅ ∠L

Reason 2: 3rd angle theorem

Statement 4: ΔGHJ ≅ ΔKLM

Reason 4: ASA Congruency Postulate

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Answer: 3.8%

Step-by-step explanation:

First find the interest cost:

= Amount repaid - Amount borrowed

= 11,052 - 9,000

= $2,052

This cost is the simple interest and because it is the same figure per year, the annual simple interest can be determined by dividing the above by the number of years:

= 2,052 / 6

= $342

Now that we have the simple interest amount, divide it by the amount borrowed to find the rate:

= 342 / 9,000

= 3.8%

The area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

Area of regular polygon = 1/2 × apothem × perimeter

perimeter = (s)side length of octagon × (n)number of side.

apothem = s/[2tan(180/n)].

11 = s/[2tan(180/12)]

s = 11 × 2tan15

s = 5.8949

perimeter = 5.8949 × 12 = 70.7388

Area of dodecagon = 1/2 × 11 × 70.7388

Area of dodecagon = 389.0634 in²

Area of pentagon = 1/2 × 5.23 × 7.6

Area of pentagon = 19.874 in²

Therefore, the area of the regular polygons with 12 sides(dodecagon) and 5 sides (pentagon) are 389.06 in² and 19.87 in² respectively.

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Divide the interval [2, 4] into equal subintervals and use the Trapezoidal Rule, Midpoint Rule, and Simpson's Rule to calculate the approximate integral of n(2 to 4) 1/ln(x) dx when n = 10.

a) Trapezoidal Rule: The integral is approximated by summing the areas of trapezoids produced by the function and line segments linking points on the curve.

The Trapezoidal Rule formula is: f(x) dx / (h/2) × [f(a) + 2f(x1) + 2f(x2) +... + 2f(xn−1) + f(b]

h = (b - a) / n, where n is the number of subintervals.

In our situation, a=2, b=4, and n=10. Trapezoidal Rule approximation:

h = (4 - 2) / 10 = 0.2

x0 = 2 x1 = 2.2 x2 = 2.4... x9 = 3.8 x10 = 4

We get:

Approximation: (0.2/2) × [1/ln(2) + 2×(1/ln(2.2)) +... + 2×(1/ln(3.8)) + 1/ln(4)]

Calculate 1/ln(x) for each x and aggregate them to get the final approximation.

b) Midpoint Rule: The Midpoint Rule approximates the integral by evaluating the function at the midpoint of each subinterval and adding the areas of rectangles with the subinterval width.

f(x) dx h × [f(x1/2) + f(x3/2) +... + f(xn−1/2)] is the Midpoint Rule formula.

h = (b - a) / n, where n is the number of subintervals.

Using the Midpoint Rule, let's calculate the approximation:

h = (4 - 2) / 10 = 0.2

x₁/₂ = 2.1 x₃/₂ = 2.3 ... x₉/₂ = 3.9

Approximation 0.2 ×[1/ln(2.1), 2.3,..., 3.9)].

Calculate 1/ln(x) for each x and aggregate them to get the final approximation.

c) Simpson's Rule: Quadratic interpolation over pairs of neighboring subintervals approximates the integral.

Simpson's Rule is: f(x) dx / (h/3) × [f(a) + 4f(x1) + 2f(x2) + 4f(x3) +... + 2f(xn−2) + 4f(xn−1) + f(b)].

h = (b - a) / n, where n is the number of subintervals.

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Jose can plow 7.5 acres of land in an hour. it will take Jose 12 minutes to plow 1.5 acres of land.

To calculate how long will it take Jose to plow 1.5 acres of land, we can use the following steps:

1: Determine the number of acres Jose can plow per minute. Dividing 7.5 acres by 60 minutes will give us the number of acres Jose can plow in 1 minute:7.5 ÷ 60 = 0.125 acres/minute

2. Determine the number of minutes it will take Jose to plow 1.5 acres of land. To calculate the number of minutes, we can divide the number of acres by the acres Jose can plow in 1 minute: 1.5 ÷ 0.125 = 12 minutes

Therefore, it will take Jose 12 minutes to plow 1.5 acres of land.

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Answer:

p=-9

Step-by-step explanation:

11= p-7-3p

you can slove p-3p now which is -2p, then add -7 to both sides.

18=-2p

then divide by -2

p=-9

it’s 1/4 of a circle.

Answer:

Step-by-step explanation:

add up the exponents of each term and select the highest sum.

An equation highlighting the discount: y = (65 - 7)x

A simpler equation: y = 58x

Answer:

Step-by-step explanation:

1. Proportion.

\(\frac{3}{7.5}\)  =  \(\frac{1}{x}\)

2.Lets cross multiply.

\(3x=7.5\)

3.Solve

\(3x=7.5\\divide 3x -on- both-sides\\\\\)

________________

\(x=2.5\)

\(1=2.5\\1:2.5\)

Hope this helps :)

The product of the two expressions is equal to 36n²-6n-12

According to this property, multiplying the sum of two or more addends by a number will give the same result as multiplying each addend individually by the number and then adding the products together.

Given here: The expression (6n+ 3)(6n- 4)

Using the distributive property of multiplication we get

(6n+ 3)(6n- 4)

6n(6n-4)+3(6n-4)

Now arranging the like terms and again applying the distributive property we get

36n²-24n+18n-12

36n²-6n-12

Hence, The product of the two expressions is equal to 36n²-6n-12

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Answer:

50.4 or 50.4%

Step-by-step explanation:

decimal calculator to find what's an equivalent decimal for the fractional number 252/5. 50.4 is a decimal and 5040/100 or 5040% is the percentage for 252/5.

Answer:

Step-by-step explanation:

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The mean of the first population is not significantly larger than that of the second population. The p-value is 0.093.

Population 1: N = 35,X = 5.3, S = 2.8

Population 2: N = 21, X = 4.9, S = 3.2

We can use the t-test to test if the mean of the first population is larger than that of the second population. The formula for this is:

t = (x1 - x2) / (S√((1/N1) + (1/N2)))

Where x1 is the mean of population 1, x2 is the mean of population 2, S is the pooled standard deviation, and N1 and N2 are the sample sizes of the two populations.

Plugging in our values, we get:

t = (5.3 - 4.9) / (3.2√((1/35) + (1/21))) = 1.68

Using an online calculator, we find that the corresponding p-value is 0.093. Therefore, we fail to reject the null hypothesis that the two populations have the same mean and conclude that the mean of the first population is not significantly larger than that of the second population. The p-value is 0.093.

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The number of times the sum would occur as 9 when the cube is tossed 180 times is 20.

The number of positive outcomes to all possible outcomes of an event is the ratio, which is known as probability. The number of good outcomes can be represented by the symbol x for an experiment with 'n' number of outcomes. The following equation can be used to determine an event's probability.

Favorable Results/Total Results = x/n, where Probability(Event)

Let us suppose you toss two cubes 180 times.

The sum of nine occurs when the combinations are:

(6, 3), (5, 4), (4, 5) and (3, 6).

The probability of getting a sum of 9 is:

P (9) = 4 / 36 = 1/9

The number of times we would the sum would occur as 9 when the cube is tossed 180 times.

180 (1/9) = 20

Hence, the number of times the sum would occur as 9 when the cube is tossed 180 times is 20.

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Answer:

-2x-10=-2(x+5)

Step-by-step explanation:

Just multiply and find the pair that matches which happens to be the 3rd pair. you're welcome

The George needs to add approximately 6.67 ml of pure acid to achieve the desired concentration.

To determine how much pure acid George needs to add, we can set up an equation based on the concentration of the acid in the solutions.

Let x represent the amount of pure acid George needs to add in milliliters.

The equation can be set up as follows:

0.15(50) + 1(x) = 0.25(50 + x).

In this equation, 0.15(50) represents the amount of acid in the 15% solution (50 ml at 15% concentration), 1(x) represents the amount of acid in the pure acid being added (x ml at 100% concentration), and 0.25(50 + x) represents the amount of acid in the resulting mixture (50 ml of 25% solution plus x ml of pure acid at 25% concentration).

Now, let's solve the equation:

7.5 + x = 12.5 + 0.25x.

Subtracting 0.25x from both sides, we have:

x - 0.25x = 12.5 - 7.5,

0.75x = 5,

x = 5 / 0.75,

x = 6.67 ml.

Therefore, George needs to add approximately 6.67 ml of pure acid to achieve the desired concentration.

In the given problem, we are given two solutions with different concentrations of acid: a 15% acid solution and a 25% acid solution. George wants to add a certain amount of the 15% acid solution to the 25% acid solution to obtain a final mixture with a desired concentration. However, he also needs to add some pure acid to achieve the desired concentration.

By setting up the equation based on the amount of acid in the solutions, we can solve for the amount of pure acid George needs to add. The equation equates the amount of acid in the 15% solution plus the amount of acid in the pure acid to the amount of acid in the resulting mixture.

By solving the equation, we find that George needs to add approximately 6.67 ml of pure acid to achieve the desired concentration.

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Step-by-step explanation:

(gof)(x)=(x+1)²

hope it helps

The function (gof)(x) is x²+x+1.

The function of function, as the name suggests, is functions applied over functions themselves. This is also called function composition.

We have input. We apply one function on that input. Then we apply another function on the output obtained by the first function. This whole function application on the first input is called the function of functions.

The resultant function which maps the input x to the final output is called the function of a function.

If the first function is g and the other function is f, then we can write the resultant function of the function as

(fog)x = f(g(x))

It is Given f(x) = x + 1 and g(x) = x^2, we need to find (g o f) (x)

(g o f)(x) = g(x) + f(x)

=  x² + x + 1

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The payback period is longer than Project B. Hence, even if the total cash inflows are the same for both projects, the timing of the cash flows is different. This difference in cash flow timing leads to different project evaluations.

For Project A: Initial Investment: $875,000, Sale of old equipment: $30,000, Incremental Revenues: $380,000, Incremental Cash Costs: $175,000, Major overhaul at the end of 3 years: $80,000, Initial working capital: $60,000

Equipment life: 6 years, Salvage value at the end of 6 years: $0

For Project B: Initial Investment: $875,000

Equipment life: 6 years: Salvage value at the end of 6 years: $90,000, Revenues: Year 1: $150,000

Year 2: $250,000

Year 3 to 6: $450,000, Cash costs: Year 1: $125,000, Year 2: $175,000, Year 3 to 6: $210,000, Hurdle rate: 8%

The requested analysis has to be done using Net Present Value (NPV), Profitability Index (PI), Payback Period (PBP), and Internal Rate of Return (IRR) calculations.

Formula view for each of the measures is given below: Net Present Value (NPV) calculation: Negative cash flows have to be entered with a negative sign and positive cash flows with a positive sign.

We have to use the NPV formula as given below: NPV = PV of cash inflows - PV of cash outflows

where, PV = Present Value of Cash Flow, i = The time period, n = The total number of time periods, r = Discount rate (hurdle rate)

Profitability Index (PI) calculation: Profitability Index is the ratio of present value of cash inflows to the present value of cash outflows.

The formula for PI is as follows: Profitability Index = PV of Cash Inflows / PV of Cash Outflows

Payback Period (PBP) calculation: Payback Period is the time period required to recover the initial investment. The formula for Payback Period is as follows: Payback Period = Initial Investment / Annual Cash Inflows

Internal Rate of Return (IRR) calculation: IRR is the discount rate at which the present value of cash inflows equals the present value of cash outflows. The IRR formula is as follows: NPV = 0 = PV of cash inflows - PV of cash outflows

Summing up the above-mentioned formulas, the calculations for Project A and Project B are shown below:

Calculations for Project A: Calculations for Project B:

Evaluation and brief explanation of relative benefits:

For Project A: Net Present Value (NPV)

= $34,328.70 > 0

Profitability Index (PI) = 1.039 > 1,

Payback Period (PBP) = 3.87 years < 6 years

Internal Rate of Return (IRR) = 13.03% > 8%

For Project B: Net Present Value (NPV)

= $191,738.43 > 0

Profitability Index (PI) = 1.22 > 1

Payback Period (PBP) = 2.84 years

< 6 years

Internal Rate of Return (IRR) = 18.28%

> 8%

The NPV and PI are positive for both projects, which means that they are expected to be profitable.

However, the payback period is less than the life of the project only for Project B. Also, the IRR is higher than the hurdle rate for both projects, but it is higher for Project B.

Hence, Project B is more preferable than Project A.

Project A and Project B are not identical because of their different cash flow patterns.

Project A has higher cash outflows in the initial years, which reduces the NPV and PI.

Also, the payback period is longer than Project B. Hence, even if the total cash inflows are the same for both projects, the timing of the cash flows is different. This difference in cash flow timing leads to different project evaluations.

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Answer: she can run \(6\dfrac54\) mile sin 1 hour.

Step-by-step explanation:

Given : Distance run by Jasmine in \(\dfrac23\) of an hour = \(4\dfrac56\text{ miles}=\dfrac{24+5}{6}\text{ miles}\)

\(=\dfrac{29}{6}\) miles

Distance run by Jasmine in 1 hour = \(\dfrac{29}{6}\times\dfrac{3}{2}=\dfrac{29}{4}\) miles.

\(=6\dfrac{5}{4}\)   miles.

Hence, she can run \(6\dfrac54\) mile sin 1 hour.

Solution

Blue = 21%

Brown = 14 %

green = 18%

orange =21 %

red = 11%

yellow = 15%

Total = 100 %

(1)

The probability that it would be red or blue?

(2) The probability that it wouldn’t be yellow?

(3) The probability that they would both be orange

Answer:

k = 11

Step-by-step explanation:

Given the points are collinear then the slopes between consecutive points are equal.

Using the slope formula

m = \(\frac{y_{2}-y_{1} }{x_{2}-x_{1} }\)

with (x₁, y₁ ) = (5, 1) and (x₂, y₂ ) = (1, - 1)

m = \(\frac{-1-1}{1-5}\) = \(\frac{-2}{-4}\) = \(\frac{1}{2}\)

Repeat with another 2 points and equate to \(\frac{1}{2}\)

with (x₁, y₁ ) = (1, - 1) and (x₂, y₂ ) = (k, 4)

m = \(\frac{4+1}{k-1}\) , then

\(\frac{5}{k-1}\) = \(\frac{1}{2}\) ( cross- multiply )

k - 1 = 10 ( add 1 to both sides )

k = 11

The value of the variable 'y' will be square root 21 that is √21.

The polygonal shape of a triangle has a number of sides and three independent variables. Angles in the triangle add up to 180 °.

The ratio of the matching sides will remain constant if two triangles are comparable to one another.

The ratio of the corresponding sides of a similar triangle remains constant. Then the equation is given as,

y / 3 = 7 / y

Simplify the equation, then we have

y / 3 = 7 / y

y² = 21

y  = √21

The value of the variable 'y' will be square root 21 that is √21.

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Answer:

L = \(\sqrt{52^2 + 30^2}\)

L = 60.033

Step-by-step explanation:

Answer:

Step-by-step explanation:

A reflection over the x-axis changes all the y-values. The reflection is modeled as -f(x)

For example:

\(\sqrt{x}\) would look like --\(\sqrt{x}\) .

If the negative sign is outside of the bracket ( what it's called sorry), then it is a reflection over the x-axis

However if the negative sign was inside the bracket: \(\sqrt{-x}\) then this would be a reflection over the y axis.

Hope this helps!

Answer:

Step-by-step explanation:

Let the speed of Masha = s, speed of Dasha = d

As per above info we get following equations:

Substitute s and solve for d:

Get rid of fraction by multiplying all terms by 3d(d + 2):

Find s:

The answer is

B.) (-1, 3) , (3, 2)

Step-by-step explanation:

Not sure how to explan...

Answer: B: 3,2 A: -1,3

Step-by-step explanation: