which direction does the gradient v point in the direction of maximum increase or maximum decrease in v

Answer:

\(Estimated\ Commission = \$618\)

\(Exact\ Commission = \$592.25\)

Step-by-step explanation:

Given

\(Commission = \$5.75\)

\(Items = 103\)

Required

Find the estimate and exact commission

Estimate Commission

First, we need to approximate the given commission

\(Commission = \$6\)

\(Estimated\ Commission = Commission * Items\)

\(Estimated\ Commission = \$6 * 103\)

\(Estimated\ Commission = \$618\)

Exact Commission

\(Exact\ Commission = Actual\ Commission * Items\)

\(Exact\ Commission = \$5.75 * 103\)

\(Exact\ Commission = \$592.25\)

Answer:

12x+10

Step-by-step explanation:

10x+2(x+5)

10x+2x+10

12x+10

Answer:

10b/y^2

Step-by-step explanation:

Hope this helps! :)

The remaining credit after 63 minutes of calls is $19.92.

From the information illustrated, the remaining credit after 36 minutes of calls is $24.24, and the remaining credit after 55 minutes of calls is $21.20.

The rate will be:

= (24.24 - 21.20) / (55 - 36)

= 3.04 / 19

= 0.16

The remaining credit after 63 minutes of calls will be:

= $21.20 - ((63 - 55) × $0.16)

= $21.20 - $1.28

= $19.92

The credit is $19.92.

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The algebric expression -1/4 + 3/5 is equal to 7/20 when simplified.

To solve the expression -1/4 + 3/5, we need to find a common denominator for the fractions and then perform the addition.

The common denominator for 4 and 5 is 20. We can rewrite the fractions with this denominator:

-1/4 = -5/20

3/5 = 12/20

Now that the fractions have the same denominator, we can add them:

-5/20 + 12/20 = (-5 + 12)/20 = 7/20

Therefore, -1/4 + 3/5 is equal to 7/20.

To further simplify the fraction, we can check if there is a common factor between the numerator and denominator. In this case, 7 and 20 have no common factors other than 1, so the fraction is already in its simplest form.

Thus, the final answer is 7/20.

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By using the facts given, 60.5 cm is 0.605 m or 0.605 meters.

Given: Convert 60.5 cm to meters

And the facts are as follows:

1000 milli-meters (mm) - 1 meter (m)

100 centimeters (cm) - 1 meter (m)

10 decimeters (dm) - 1 meter (m)

1 deka-meter (dam) -10 meters (m)

1 hectometer (hm) - 100 meters (m)

1 kilometer (km) - 1000 meters (m)

What is the length?

Length is the measurement of something from one point to another point.

Length can also be the distance between two points.

The shortest length between two times is known as displacement.

There are different ways to measure the length between two points or objects.

The SI unit of length is metered (m)

Also, kilometers or miles are used to measure large distances.

How to convert from centimeters (cm) to meters (m)?

1 meter or 1 m is equivalent to 100 centimeters or 100 cm. So let us apply the unitary method.

100 cm = 1 m

So 1 cm = 1 / 100 m

Therefore, x cm will be x / 100 m

Let’s solve the problem.

Given 60.5 cm to show in meters

So 100 cm = 1 m

1 cm = 1 / 100 m

60.5 cm = 60.5 / 100 m

60.5 cm = 0.605 m

Hence by using the facts given 60.5 cm is 0.605 m or 0.605 meters.

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Answer:

  MN = 56

Step-by-step explanation:

This can only be solved if we know the relation of MN to other dimensions of the trapezoid. If we assume MN is a midline (AM=MD, BN=NC), then MN is the average of the base lengths:

  MN = (AB +CD)/2

  2MN = AB +CD . . . . . multiply by 2

  2(12x -4) = 8x +72 . . . fill in the given values for the segment lengths

  24x -8 = 8x +72 . . . . . eliminate parentheses

  16x = 80 . . . . . . . . . . . add 8-8x

  x = 5 . . . . . . . . . . . . . . divide by 16

  MN = 12(5) -4 = 56 . . . find the length of MN using its formula

Option C is correct. probability of choosing man and non drinker is given s 0.932

Probability is a branch of mathematics that deals with the study of random events or experiments, and the likelihood or chance of certain outcomes occurring. It is concerned with quantifying the uncertainty of events and helps us make predictions or informed decisions in situations where the outcome is not certain.

probability of choosing man and non drinker= 209 / 425 + 322 / 425 - 135 / 425

= 0.4917 +0.7576 - 0.3176

= 0.9317

this is approximately 0.932

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Using the Green's Theorem, the one along which the work done by the force is 11π/16.

In the given question we have to find the one along which the work done by the force is the greatest.

The given closed curves in the plane is

\(F(x,y)=\left(\frac{x^{2}y}{4} + \frac{y^3}{3}\right)\hat{i}+x\hat{j}\)

Suppose C be a simple smooth closed curve in the plane. It is also oriented counterclockwise.

Let S be the interior of C.

Let P = \(\frac{x^{2}y}{4} + \frac{y^3}{3}\) and Q = x

So the partial differentiation is

\(\frac{\partial P}{\partial y}=\frac{x^2}{4}+y^2\) and  \(\frac{\partial Q}{\partial x}\) = 1

By the Green's Theorem, work done by F is given as

W= \(\oint \vec{F}d\vec{r}\)

W= \(\iint_{S}\left ( \frac{\partial Q}{\partial x}-\frac{\partial P}{\partial y} \right )dxdy\)

W= \(\iint_{S}\left ( 1-\frac{x^2}{y}-y^2 \right )dxdy\)

Let C = x^2+y^2 = 1 and

x = rcosθ, y = rsinθ

0≤r≤1; 0≤θ≤2π

There;

W = \(\int_{r=0}^{1}\int_{\theta=0}^{2\pi}\left ( 1-\frac{r^2\cos^2\theta}{4}-r^2\sin^2\theta \right )\left|\frac{\partial(x,y)}{\partial{r,\theta}}\right|d\theta dr\)

and \(\frac{\partial (x,y)}{\partial(r, \theta)}=\left|\begin{matrix}\cos\theta &-r\sin\theta \\ \sin\theta & r\cos\theta\end{matrix} \right |\) = r

Thus;

W = \(\int_{r=0}^{1}\int_{\theta=0}^{2\pi}\left ( 1-\frac{r^2\cos^2\theta}{4}-r^2\sin^2\theta \right )rd\theta dr\)

After solving

W = 11π/16

Hence, the one along which the work done by the force is 11π/16.

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The right question is:

Among all simple smooth closed curves in the plane, oriented counterclockwise, find the one along which the work done by the force:

\(F(x,y)=\left(\frac{x^{2}y}{4} + \frac{y^3}{3}\right)\hat{i}+x\hat{j}\)

is the greatest. (Hint: First, use Green’s theorem to obtain an area integral—you will get partial credit if you only manage to complete this step.)

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

To find the quotient of z₁ by z₂ in trigonometric form, we'll express both complex numbers in trigonometric form and then divide them.

Let's represent z₁ in trigonometric form as z₁ = r₁(cosθ₁ + isinθ₁), where r₁ is the magnitude of z₁ and θ₁ is the argument of z₁.

We have:

z₁ = 7(cos(577°) + i sin(577°))

Now, let's represent z₂ in trigonometric form as z₂ = r₂(cosθ₂ + isinθ₂), where r₂ is the magnitude of z₂ and θ₂ is the argument of z₂.

From the given information, we have:

z₂ = 21(cos(-7°) + i sin(-77°))

To find the quotient, we divide z₁ by z₂:

z₁ / z₂ = (r₁/r₂) * [cos(θ₁ - θ₂) + i sin(θ₁ - θ₂)]

Substituting the given values, we have:

z₁ / z₂ = (7/21) * [cos(577° - (-7°)) + i sin(577° - (-7°))]

= (7/21) * [cos(584°) + i sin(584°)]

The quotient of z₁ by z₂ in trigonometric form is:

7/21 * (cos(584°) + i sin(584°))

Option C, 21(cos(-7°) + i sin(-77°)), is not the correct answer as it does not represent the quotient of z₁ by z₂.

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The compound interest model has a quarterly interest rate is approximately 1.3 %.

Herein we find the case of an amount of money deposited that is increased by means of compound interest, whose model is described below:

C' = C · (1 + r / 100)ⁿ

Where:

First, clear the interest rate in compound interest model:

C' = C · (1 + r / 100)ⁿ

C' / C = (1 + r / 100)ⁿ

\(r = 100\cdot \left(\sqrt [n] {\frac {C'} {C}} - 1\right)\)

Second, substitute all known variables and make all calculations: (n = 72, C = 120, C' = 300)

\(n = 100 \cdot \left(\sqrt[72]{\frac{300}{120} } - 1\right)\)

n ≈ 1.281

The quarterly interst rate for the compound interest model is approximately 1.3 %.

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Answer:5.1%

Step-by-step explanation:

Answer:

None of the options are correct, but I got g(x)=1/2x+2.

Step-by-step explanation:

You start with the equation. You first need to change f(x) to y, and switch the x and y values. After this, your equation would be x=2y-4. Then, you need to icolate the y value, and to do that you first cancel out the four by adding it to both sides, and now your equation should be x+4=2y. The second step in icolating the y value is dividing everything in the equation by two. Now that the y is icolated, you equation should be y=1/2x+2. You then change the y to be g(x), and that's how I got my answer, g(x)=1/2x+2. You should ask your teacher about this, becuase from my calculations, none of the given responses would be correct. Sorry if that doesn't help you at all but yeah

Answer:

D, g(x) = 1/2 x + 2

Step-by-step explanation:

The second answer IS ONE TO ONE

Answer:

Yes

Step-by-step explanation

13/12=1 1/12

Answer:

- Banking Operations salary in India with less than 1 year of experience to 10 years ranges from ₹ 1.4 Lakhs to ₹ 7 Lakhs with an average annual salary of ₹ 3.1 Lakhs based on 261 latest salaries

Answer:

B

Step-by-step explanation:

26 divides by 2 = 13

13+2=14

Answer:

The value is  \(P(X > 3.30) = 0.12405\)

Step-by-step explanation:

From the question we are told that

   The mean GPA is  \(\mu = 3.25\)

   The standard deviation is \(\sigma = 0.75\)

    The sample size is  n  =  300

Generally the standard error of mean is mathematically represented as

     \(\sigma_{\= x} = \frac{\sigma }{\sqrt{n} }\)

=>   \(\sigma_{\= x} = \frac{0.75}{\sqrt{300} }\)

=>   \(\sigma_{\= x} = 0.0433\)

Generally the  probability that a random sample of 300 students will have a mean GPA greater than 3.30 is mathematically represented as

     \(P(X > 3.30) = P(\frac{X - \mu}{\sigma_{\= x}} > \frac{3.30 -3.25}{ 0.0433} )\)

\(\frac{\= X -\mu}{\sigma }  =  Z (The  \ standardized \  value\  of  \ \= X )\)

    \(P(X > 3.30) = P(Z> 1.155 )\)

From the z table the probability of  (Z >  1.155 ) is

     \(P(Z> 1.155 ) = 0.12405\)

   \(P(X > 3.30) = 0.12405\)

Answer:

Step-by-step explanation:

0.0000015

The sketch for slope is attached below.

A line's slope is determined by how its y coordinate changes in relation to how its x coordinate changes. y and x are the net changes in the y and x coordinates, respectively. Therefore, it is possible to write the change in y coordinate with respect to the change in x coordinate as,

m = Δy/Δx where, m is the slope

Given:

Point               Slopes

(1, 1)                     (a) 3

_                        (b) -3

_                        (c) -5/2

_                         (d) Undefined

a) Now, using slope intercept form

y - 1= 3 (x-1)

y- 1= 3x- 3

y= 3x - 2

(b) Equation of a line has a slope -3 is given by

y - 1= (-3) (x-1)

y-1 = 3- 3x

y = -3x + 4

(c) Equation of a line has a slope -5/2 is given by

y - 1= (-5/2) (x-1)

y-1 = -5/2x + 5/2

y= -5/2x + 7/2

(d) The line parallel to y axis and passes through given point : x=1

"undefined" means the line is vertical.

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The inequality value that would be able to show/x/ ≤ 5 is option A

In mathematics, inequality refers to a mathematical statement that expresses a relationship between two quantities, indicating that one quantity is greater than, less than, or not equal to the other.

The symbol that we have  is telling us that the value of the x would be less than  or it would be seen to be equal to five.

We can see that /x/ ≤ 5 would exclude the negative values and this can be seen in the option that is marked option A

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Answer:

0.5 = 0.500

Step-by-step explanation:

Both numbers are five-tenths. The zeros to the right of the 5 are not place holders and do not change the value of the number.

0.5 = 0.500

Answer:

400.64 is your answer

Step-by-step explanation:

I need brainlyest PLZ!!!!

Answer: 21

Step-by-step explanation: Okay but actually its 19 :)

Answer: (A)=10x5−29x4+33x3−18x2−18x+27

Step-by-step explanation:

How i solved it was by simplifying each answer there was available and (A) was the most compatiable answer!

=(2x+−3)(5x4+−7x3+6x2+−9)

=(2x)(5x4)+(2x)(−7x3)+(2x)(6x2)+(2x)(−9)+(−3)(5x4)+(−3)(−7x3)+(−3)(6x2)+(−3)(−9)

=10x5−14x4+12x3−18x−15x4+21x3−18x2+27

=10x5−29x4+33x3−18x2−18x+27

Answer:

=(2x+−3)(5x4+−7x3+6x2+−9)

=(2x)(5x4)+(2x)(−7x3)+(2x)(6x2)+(2x)(−9)+(−3)(5x4)+(−3)(−7x3)+(−3)(6x2)+(−3)(−9)

=10x5−14x4+12x3−18x−15x4+21x3−18x2+27

=10x5−29x4+33x3−18x2−18x+27

Step-by-step explanation:

Answer:

Step-by-step explanation:

Answer:

Yeah. The answer is \(206\frac{2}{25}\).

Step-by-step explanation:

Answer:

1) \(\sqrt{53}(\cos286^\circ+i\sin286^\circ)\)

2) \(\displaystyle 5,-\frac{5}{2}+\frac{5\sqrt{3}}{2}i,-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

Step-by-step explanation:

Problem 1

\(z=2-7i\\\\r=\sqrt{a^2+b^2}=\sqrt{2^2+(-7)^2}=\sqrt{4+49}=\sqrt{53}\\\\\theta=\tan^{-1}(\frac{y}{x})=\tan^{-1}(\frac{-7}{2})\approx-74^\circ=360^\circ-74^\circ=286^\circ\\\\z=r\,(\cos\theta+i\sin\theta)=\sqrt{53}(\cos286^\circ+i\sin 286^\circ)\)

Problem 2

\(\displaystyle z^\frac{1}{n}=r^\frac{1}{n}\biggr[\text{cis}\biggr(\frac{\theta+2k\pi}{n}\biggr)\biggr]\,\,\,\,\,\,\,k=0,1,2,3,\,...\,,n-1\\\\z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(2)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{4\pi}{3}\biggr)=5\biggr(-\frac{1}{2}-\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}-\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(1)\pi}{3}\biggr)\biggr]=5\,\text{cis}\biggr(\frac{2\pi}{3}\biggr)=5\biggr(-\frac{1}{2}+\frac{\sqrt{3}}{2}i\biggr)=-\frac{5}{2}+\frac{5\sqrt{3}}{2}i\)

\(\displaystyle z^\frac{1}{3}=125^\frac{1}{3}\biggr[\text{cis}\biggr(\frac{0+2(0)\pi}{3}\biggr)\biggr]=5\,\text{cis}(0)=5(1+0i)=5\)

Note that \(\text{cis}\,\theta=\cos\theta+i\sin\theta\) and \(125=125(\cos0^\circ+i\sin0^\circ)\)

Answer:

a. 5.53

b. 1.078

c. 0.126

d. 0.109

e. 0.549

f. 0.834

g.  0.451

Step-by-step explanation:

The percentage of the flights that arrive on time, P(x) = 79%

The number of flights in the sample, n = 7 flights

a. The mean of the probability distribution, μ = ∑x·P(x)

Therefore, we have; μₓ = n·p

μₓ = 7 × 79/100 = 5.53

b. The standard deviation, σₓ = √(n·p·(1 - p))

∴ σₓ = √(7 × 0.79 × (1 - 0.79)) ≈ 1.078

c. We have;

p = 0.79

q = 1 - p = 1 - 0.79 = 0.21

By binomial probability distribution formula, we have;

The probability of exactly four, P(Exactly 4) = ₇C₄·p⁴·q³

P(Exactly 4) = 35 × 0.79⁴×0.21³ ≈ 0.12625

d. The probability of less than 4 is given as follows;

P(Less than 4) = ₇C₀·p⁰·q⁷ + ₇C₁·p¹·q⁶ + ₇C₂·p²·q⁵ + ₇C₃·p³·q⁴

∴ P(Less than 4) = 1×0.79^0 * 0.21^7 + 7 * 0.79^1 × 0.21^6 + 21*0.79^2*0.29^5+ 85×0.79^3*0.21^4 ≈ 0.109

The probability of less than 4 is ≈ 0.109

e. The probability that more than 5 is given as follows;

P(More than 5) = ₇C₆·p⁶·q¹ + ₇C₇·p⁷·q⁰

7×0.79^6 * 0.21 + 1 * 0.79^7 × 0.21^0 ≈ 0.549

f. The probability that at least 5 of the flight were on time is given as follows;

P(At least 5) = ₇C₅·p⁵·q² + ₇C₆·p⁶·q¹ + ₇C₇·p⁷·q⁰

∴ P(At least 5) = 21×0.79^5 * 0.21^2 + 7×0.79^6 * 0.21 + 1 * 0.79^7 × 0.21^0 ≈ 0.834

g.  For the probability that no more than 5 of the flights were on time, e have;

P(At most 5) = 1 - P(More than 5)

∴ P(At most 5) = 1 - 0.549 ≈ 0.451.