What are the example of exponential equation?

Answer: The square

Step-by-step explanation:

The square has a 90 degree angle which is a right angle. Also all sides have the same length

The direction of greatest increase in heat from the point (1,4) is [15/17, -8/17].

The direction of greatest increase in heat at a point (x, y) on the metal plate is given by the gradient vector ∇T(x,y).

Let's first compute the partial derivatives of T(x,y) with respect to x and y:

∂T/∂x = \([(x^2+y^2) - 2x^2]/(x^2+y^2)^2 = (y^2-x^2)/(x^2+y^2)^2\)

∂T/∂y = \(-2xy/(x^2+y^2)^2\)

So the gradient vector ∇T(x,y) is:

∇T(x,y) = (∂T/∂x, ∂T/∂y) = \([(y^2-x^2)/(x^2+y^2)^2, -2xy/(x^2+y^2)^2]\)

At the point (1,4), we have:

∇T(1,4) = \([(4^2-1^2)/(1^2+4^2)^2, -2(1)(4)/(1^2+4^2)^2]\)= [15/625, -8/625]

So the direction of greatest increase in heat at (1,4) is the direction of the gradient vector ∇T(1,4), which is:

[15/625, -8/625] / \(\sqrt{[(15/625)^2 + (-8/625)^2] }\)= [15/17, -8/17]

Therefore, the direction of greatest increase in heat from the point (1,4) is [15/17, -8/17].

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The given statement "The diagonal of a parallelogram does not create alternate interior angles" is false because alternate interior angles are formed when two parallel lines are intersected by a transversal, and they are located on opposite sides of the transversal and between the two parallel lines.

In a parallelogram, the opposite angles are congruent, meaning they have equal measures. When a diagonal is drawn in a parallelogram, it creates two pairs of congruent opposite angles, but these angles are not considered alternate interior angles.

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Answ

3xmas8

-------------------------------

listo

Expression represents the radius of the cylinder, 2x units.

A cylinder is simply a 3-dimensional shape having two parallel circular bases joined by a curved surface.

Given that:

Volume of cylinder =\(4\pi x^{3}\)

we know that, Volume of cylinder = \(\pi r^{2} h\)

\(4\pi x^{3}\)= π * \(r^{2}\) *h

\(4x^{3} = r^{2}*h\)

\(4x^{3} = r^{2}*x\)      [since, height=x]

\(4x^{2} = r^{2}\)

r= 2x

Hence the radius of the cylinder is 2x units

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Carina have 300 cows and 400 goats originally.

for cows:

\(\frac{240}{(100-20)} =300\)

for goats:

\(\frac{240}{3} *5=400\)

Therefore, Carina have 300 cows and 400 goats originally.

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Answer:

c(x) =  16x + 22736

R(x) = -2x^2 + 524x  

[ -2x^2 + 508x  - 22736] = 0

Factored: f(x) = -2(x - 196)(x - 58)

58 to break even

Step-by-step explanation:

Your cost is the amount it cost you to "make" stuff.

You have fixed and variable costs (cost of oven is fixed cost of flower and sugar is variable to make cupcakes)

your cost is c(x) =  16x + 22736

"your oven and building cost $22736 per month and you use $16 worth of sugar butter flour to make one cupcake ( it  must be a huge one) ...

your revenue is the amount of money that "comes into your business"...

the amount of money in the cash register.... Note: this is only money IN you still have to pay for the building, sugar flour etc.

R(x) = -2x^2 + 524x  

Note: the minus and the square basically say that the more you charge the less cupcakes you will sell...

Profit is the money in minus the money out

P - R - E   [ -2x^2 + 524x  ] - [16x + 22736]

the break even point is where the two functions are the same

in other words where C=R or R-C=0

[ -2x^2 + 524x  ] = [16x + 22736]

[ -2x^2 + 508x  - 22736] = 0

Factored: f(x) = -2(x - 196)(x - 58)

Answer:

Step-by-step explanation:

C(x)=16x+22736

R(x)=-2x²+524x

P(x)=R(x)-C(x)

=-2x²+524x-16x-22736

=-2x²+508-22736

when profit is zero then no gain or loss.

so -2x²+508x-22736=0

or x²-254x+11368=0

196+58=254

196×58=11368

x²-54x-196x+11368=0

x(x-54)-196(x-54)=0

(x-54)(x-196)=0

x=54,196

so x=54 is the smallest number of bins to break even.

Your longitude in DMS is 135 degree. So the option D is correct.

This is because there are 12 hours left in the local time ( i.e. 12 hours noontime or mid-day).

As UT (or GMT) time is 9 p.m., there are 9 hours between GMT time and local time.

9 hours = 9 × 60 minutes = 540 minutes

Now, we know that:

Every four minutes, the Earth turns one degree.

Thus, 1-degree longitude difference = 4 minutes

Or, 4 minutes of time difference = 1 degree of longitude

Or, 1 minute of time difference = 1/4 degree of longitude

Or, 540 minutes of time difference = (1/4) × 540 degrees of longitude

540 minutes of time difference = 135 degrees of longitude

Also, we can infer that the current location is in the Western hemisphere because we know that it is 9 hours behind GMT (or UT) time.

Hence, the longitude of the current location = 135⁰

So the option 4 is correct.

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The complete question is:

Your chronometer is set for Greenwich Mean Time (GMT or Universal Tim, UT). High noon at your present location is 9 pm UT. What is your longitude in DMS (not decimal degrees)?

1. 30° 18'W

2. 30° 16'W

3. 30° 17'W

4. none of the above

Answer:

-26

Step-by-step explanation:

Sin 2 is the integral of -cos 2 plus c, where c is a constant integration equation sin2x dx = -cos2x + c.

1. Calculate sin 2 integral.

2. Apply the integration equation sin2x dx = -cos2x + c.

3. Increase the outcome by the constant C.

Sin 2 is the integral of -cos 2 plus c, where c is a constant. This integral must be calculated in several steps. Take the integral of sin 2 first. Use the integration formula sin2x dx = -cos2x + c to do this. According to this equation, the integral of sin 2 is equal to cos -2/c plus a certain constant. The next step is to add the constant c to the outcome after using this formula. This will result in the integral of sin 2 having a final value of -cos 2 + c. Any actual number may be used as the constant c, and the value will vary depending on the circumstances. It's crucial to keep in mind that the constant c must always be a part of the outcome.

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Answer:

The answer is 0.8-0.3=0.5.

Answer:

Step-by-step explanation:

Let the required number be 'n'.

Then, we need to find what the value of n is.

According to the question,

Multiply both sides by 1/7.

Answer:

  -20x -11

Step-by-step explanation:

You want to simplify -3(4x-3)-4(2x+5).

An expression is simplified by removing parentheses and combining like terms. The parentheses are removed by making use of the distributive property.

  -3(4x-3)-4(2x+5) . . . . . . . . . . . . given

  = -3(4x) -3(-3) -4(2x) -4(5) . . . . use the distributive property

  = -12x +9 -8x -20 . . . . . . . . . . . evaluate products

  = (-12-8)x +(9 -20) . . . . . . . . . . group like terms

  = -20x -11 . . . . . . . . . . . . . . . . evaluate sums

The derivative of the function g(x) = 3x^(-3) (x^4 - 3x^3 + 13x - 9) is g'(x) = -9x + 12 + (27/x - 27/x^2 - 26/x^3), obtained by using the product rule and the chain rule.

To differentiate the function g(x) = 3x^(-3) (x^4 - 3x^3 + 13x - 9), we can use the product rule and the chain rule:

g'(x) = 3(-3x^(-4))(x^4 - 3x^3 + 13x - 9) + 3x^(-3)(4x^3 - 9x^2 + 13)

     = -9x^(-4)(x^4 - 3x^3 + 13x - 9) + 3x^(-3)(4x^3 - 9x^2 + 13)

     = (-9/x^4)(x^4 - 3x^3 + 13x - 9) + (3/x^3)(4x^3 - 9x^2 + 13)

     = (-9x + 27/x - 39/x^3) + (12 - 27/x^2 + 13/x^3)

     = -9x + 12 + (27/x - 27/x^2 - 26/x^3)

Therefore, the derivative of g(x) is g'(x) = -9x + 12 + (27/x - 27/x^2 - 26/x^3).

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The solution is: :

A. The range of both data sets is 40, this statement correctly describes the two data sets .

Here, we have,

we know that,

Range = the maximum value - the minimum value

For the Seventh-Grade Students' data set,

Maximum value = 45

Minimum Value = 5

Range = 45 - 5 = 40

For the Eight-Grade Students' data set,

Maximum value = 45 (the value at the whisker to your far right)

Minimum Value = 5 (value indivl ated by the whisker on your far left)

Range = 45 - 5 = 40

Therefore, the two data sets can be described as having the same range of 40.

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complete question:

A school counselor asked a random sample of seventh- and eighth-

grade students how long it takes them to get ready for school each

morning. The dot plot and the box plot below summarize the results for

the two random samples. Which statement correctly describes the two

data sets below? *

It take 10.374 days for the sample to be 15% of the initial amount

Radioactivity decay half life formula:

                                                    N= \(N_{0} (\frac{1}{2} )^{t/t_{1/2} }\)

                     N = Quantity remaining

                     \(t_{1/2}\) = half life

                     t = time elapsed

                    \(N_{0}\) = initial amount

given,

        Half-life of radon-222 is 3.8 days

                        \(t_{1/2}\) = 3.8 days

        Initial amount of sample = 34 gm

                      15 % of 34 gm = 15 x 34 /100

                                 =  5.1 gm

               Quantity remaining = 5.1 gm

                           = 5.1 gm

                  Using the above formula

                                                          N= \(N_{0} (\frac{1}{2} )^{t/t_{1/2} }\)

                        5.1 = 34x \(0.5^{t/3.8}\)

                       \(0.5^{t/3.8}\) = 5.1/34

                         \(0.5^{t/3.8}\) = 0.15

                     taking ln both side

                       ln( \(0.5^{t/3.8}\)  ) = ln (0.15 )

                     t/3.8  ln (0.5) = ln (0.15)

                          t/3.8  = ln (0.15) /  ln (0.5)

                                    = 2.73

                          t = 3.8 x 2.73 days

                              = 10.374 days

It take 10.374 days for the sample to be 15% of the initial amount.

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The typical vertical section of a floor includes the following parts/sections: finished floor, subfloor, insulation layer, vapor barrier, and structural support. Insulation thickness varies but is commonly around 1-2 inches.

In a typical floor section, the finished floor material (e.g., hardwood, carpet) has a thickness of about 0.25-0.75 inches. The subfloor, usually made of plywood or oriented strand board (OSB), is around 0.75 inches thick. The insulation layer, like rigid foam board, has a thickness of 1-2 inches. The vapor barrier, often made of polyethylene, has a thickness of 0.01-0.02 inches. The structural support, composed of joists or beams, varies based on the floor's load requirements. The assumption for insulation thickness is based on general construction practices, where 1-2 inches of insulation provides adequate thermal resistance for most buildings. Older floors may have thinner or no insulation due to outdated standards and less focus on energy efficiency.

A typical floor section consists of finished floor, subfloor, 1-2 inches of insulation, vapor barrier, and structural support. Insulation thickness is based on standard construction practices and may be reduced in older floors.

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Answer:

7y=21

y=21/7

y=3 answer

Answer:

y = 3

Step-by-step explanation:

I hope this helps!

The Fourier series Using the complex form of f(x) is

f(x) = 1/2 + ∑[n=1, ∞] [2*(-1)^(n+k)/(nπ)]*sin(nπx), 2k-0.25 < x < 2k+0.25

where k is an integer.

To find the Fourier series of the function f(x) over the interval [-1, 1], we first note that f(x) is periodic with period T = 0.5. We can then write f(x) as a Fourier series of the form

f(x) = a0/2 + ∑[n=1, ∞] (ancos(nπx) + bnsin(nπx))

where

a0 = (1/T) ∫[0,T] f(x) dx

an = (2/T) ∫[0,T] f(x)*cos(nπx) dx

bn = (2/T) ∫[0,T] f(x)*sin(nπx) dx

Since f(x) = 0 for x < -0.25 and x > 0.25, we only need to consider the interval [-0.25, 0.25]. We can break this interval into subintervals of length 0.5 centered at integer values k

[-0.25, 0.25] = [-0.25, 0.25] ∩ [1.5, 2.5] ∪ [-0.25, 0.25] ∩ [0.5, 1.5] ∪ ... ∪ [-0.25, 0.25] ∩ [-1.5, -0.5]

For each subinterval, the Fourier coefficients can be calculated as follows

a0 = (1/0.5) ∫[-0.25, 0.25] f(x) dx = 1/2

an = (2/0.5) ∫[-0.25, 0.25] f(x)*cos(nπx) dx = 0

bn = (2/0.5) ∫[-0.25, 0.25] f(x)sin(nπx) dx = 2(-1)^k/(nπ)

Therefore, the Fourier series of f(x) is

f(x) = 1/2 + ∑[n=1, ∞] [2*(-1)^(n+k)/(nπ)]*sin(nπx), 2k-0.25 < x < 2k+0.25

where k is an integer.

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Answer

why cant a orfian play baseball..... they dont know where home is.

Step-by-step explanation:

Answer: 1.061

Step-by-step explanation:

1). Based on conditions, formulate: 1+6.1%

2). Then convert to a decimal: 1.061

Groups A, B, and C have means of 4, 6, and 8, respectively. There are 15 cases in total, with equal sample sizes in each group. Within is 120. 16-7. 16-4a, the value of omega-squared is 0.25.

What is omega-squared?

       In statistics, omega-squared is a measure of effect size that can be used for one-way ANOVA to determine how much variance is due to the treatment or independent variable. It is calculated by dividing the between-group variance by the total variance, which includes both the within-group and between-group variance.

       Omega-squared is used to determine the percentage of variance accounted for by a particular factor or treatment. It is represented as ω2 and ranges from 0 to 1, with higher values indicating a stronger relationship between the independent variable and the dependent variable.

       The formula for omega-squared is as follows:

                         ω2=SSBetween / SSTotalSSWithin

                              = SSTotal - SS Between

         Where SSTotal is the sum of squares for the total variance.SSBetween is the sum of squares between the groups, and within is the sum of squares within the groups.

     The given information is:

                       Mean of group A = 4Mean of group

                                                 B = 6Mean of group

                                                 C = 8Total cases

                                                    = 15SSWithin

                                                    = 120

             We can calculate the sum of squares between the groups as follows:

                        SSTotal = SSBetween + SSWithinSSTotal

                                      = (nA + nB + nC - 1) × (σA² + σB² + σC²)SSBetween

                                      = SSTotal - SS Within SS Between

                                      = (3 - 1) × (42 + 62 + 82) - 120SSBetween

                                      = 80 Next,

           we can calculate the total variance as:

                      SSTotal = SSWithin + SSBetweenSSTotal

                                    = 120 + 80SSTotal

                                     = 200

            Now, we can calculate omega-squared as follows:

                     ω2 = SSBetween / SSTotalω2

                           = 80/200ω2

                           =0.4

       Hence, the value of omega-squared is 0.25.

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The percentage of returns that were greater than 22% and the percentage of returns that were below -17% of historical returns on a portfolio that had an average return of 9 percent and a standard deviation of 13 percent.

What percentage of returns were greater than 22 percent? We know that returns on this portfolio follow a bell-shaped distribution and the percentage of returns greater than 22% is required.

The z-score for this value can be calculated as follows;

z=(X-μ)/σwhere X is the return percentage, μ is the average return percentage, and σ is the standard deviation.

z=(22-9)/13 = 1z = 1 gives a probability of 0.8413.

To calculate the percentage of returns greater than 22%, we need to subtract the z-score probability from 1;

P(z > 1) = 1 - 0.8413 = 0.158

The percentage of returns greater than 22% is therefore;

Percentage of returns greater than 22% = 0.1587 x 100 ≈ 16%2.

What percentage of returns were below -17 percent?

We need to find the percentage of returns that were below -17% using the same method as above;

z=(X-μ)/σz=(-17-9)/13 = -2z = -2 gives a probability of 0.0228.

To calculate the percentage of returns less than -17%, we need to add the z-score probability to 0.5 (since the bell-shaped curve is symmetric);

P(z < -2) = 0.5 + 0.0228 = 0.5228

The percentage of returns below -17% is therefore;Percentage of returns below -17% = 0.5228 x 100 ≈ 52.3%

Thus, the percentage of returns that were greater than 22 percent was 16%, and the percentage of returns that were below -17 percent was approximately 52.3%.

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Answer:

-18x + -144

Step-by-step explanation:

\(\textit{area of the rectangle}\\\\ A=Lw \begin{cases} L=length\\ w=width\\[-0.5em] \hrulefill\\ L=5\\ w=6 \end{cases}\implies A=(5)(6)\qquad \begin{cases} \textit{tripling the sides}\\[-0.5em] \hrulefill\\ L=3\cdot 5\\ w=3\cdot 6 \end{cases} \\\\\\ A=(3\cdot 5)(3\cdot 6)\implies (3\cdot 3)(5)(6)\implies 9(5)(6)\leftarrow \begin{array}{llll} \textit{new area is 9 times}\\ \textit{the old one}\\ \textit{a ratio of 9 : 1} \end{array}\)

The total value of a triangle's angles is 180*

so x=180-y-z

x=180-76-41

x=63*

hope it helps

Using it's concept, it is found that the probability that a student chosen at random will play the keyboard is of 0.15.

A probability is given by the number of desired outcomes divided by the number of total outcomes.

In this problem:

Hence:

\(p = \frac{11}{71} = 0.15\)

The probability that a student chosen at random will play the keyboard is of 0.15.

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