passes through (-8.-1) and has a zero slope

Using the fundamental theorem of line integrals, the evaluation of the line integral ∮_C (16(8x^3y)i + 6(8x^3y)j) · dr along the smooth curve C from (-3, 8) to (3, 2) can be simplified as follows:

To evaluate the line integral using the fundamental theorem of line integrals, we need to find a scalar potential function F(x, y) whose gradient is equal to the vector field F(x, y) = 16(8x^3y)i + 6(8x^3y)j. Let's find the potential function.

Taking the partial derivative of F(x, y) with respect to x, we have:

∂F/∂x = 16(24x^2y)

Taking the partial derivative of F(x, y) with respect to y, we have:

∂F/∂y = 16(8x^3)

To find the potential function, we integrate the partial derivative of F(x, y) with respect to x with respect to x:

F(x, y) = ∫[16(24x^2y)] dx = 16y∫(24x^2) dx = 16y(8x^3) = 128x^3y + C1(y)

Here, C1(y) represents the constant of integration with respect to x. However, since C1(y) does not depend on x, it can be considered a constant C1.

Next, we integrate the partial derivative of F(x, y) with respect to y with respect to y:

F(x, y) = ∫[16(8x^3)] dy = 16∫(8x^3) dy = 16(8x^3y) + C2(x)

Here, C2(x) represents the constant of integration with respect to y. Similarly, since C2(x) does not depend on y, it can be considered a constant C2.

Now, we have two expressions for the potential function F(x, y):

F(x, y) = 128x^3y + C1

F(x, y) = 16(8x^3y) + C2

Since the potential function should be unique, the two expressions must be equal. Therefore, we can equate them and solve for C1 and C2:

128x^3y + C1 = 16(8x^3y) + C2.

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Step-by-step explanation:

you add 9% to a number by multiplying that number by 1.09.

because adding 9% gives us in the end 109% of the original amount.

anyway, the formula for quarterly compounded interest is

Cq = P [ (1+r)^(4*n) – 1 ]

P is the starting principal amount

r is the interest rate per quarter (= interest rate / 4)

n would be the number of years (= 1 in our case).

so, the interest after 1 year is

12500((1 + 0.09/4)⁴ - 1) = 12500(1.0225⁴ - 1) =

= 12500 × 0.093083319 = $1,163.541485 ≈ $1,163.54

Answer:

B is correct.

Step-by-step explanation:

On number line and sequencing also, -3 is less than -2.

Answer:

b is correct -2 is less than-3

Probability that he either hits a bullseye or score 10 points is x+y.

What is addition of probability?

Picture of what probability addition looks like Basic Addition Probability rule. Probability in mathematics determines how likely an event is to occur. For instance, there is no way to predict which of a die's six faces would be up while rolling the die. Probability, however, indicates that there is only a 1/6 chance that each face will result from a single die toss.

we can assume that probability of dart hitting the centre of dart board is x.
and probability of dart hitting the 10 points ring is y. as not properly given in question.
then, probability that he either hits a bullseye or score 10 points is x+y.

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Answer:

b= 27.7, b=32

Step-by-step explanation:

\(tan(30)=\frac{16}{b} \\b=\frac{16}{tan(30)} \\b=27.7\\\\\\sin(30)=\frac{16}{c} \\c=\frac{16}{sin(30)} \\c=32\)

The group needs to sell at least 104 granola bars and any number of bottles of water in order to make a profit of at least $150.

The correct inequality is B. 1.4x + 0.75y ≥ 150. This inequality states that the group must sell at least $150 worth of items in order to make a profit. The cost of a granola bar is $1.40, and the cost of a bottle of water is $0.75. Therefore, the total cost of the items must be greater than or equal to $150. The formula for this inequality is 1.4x + 0.75y ≥ 150, where x represents the number of granola bars sold and y represents the number of bottles of water sold.

To solve this inequality, we can first multiply both sides of the inequality by 100. This will give us 140x + 75y ≥ 15000. Next, we can subtract 75y from both sides to get 140x ≥ 14250. Finally, we can divide both sides of the equation by 140 to get x ≥ 102.86. This means that the group needs to sell at least 103 granola bars in order to make a profit of at least $150. This can be further simplified by rounding up the granola bars sold to 104. Therefore, the group needs to sell at least 104 granola bars and any number of bottles of water in order to make a profit of at least $150.

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a) The amount you will repay is approximately $12,000.

b) The annual interest rate charged by the loan company is approximately 18.2715%.

To calculate the amount you will repay and the annual interest rate charged by the loan company, we can follow these steps:

Step 1: Calculate the number of $500 increments for the loan amount:

Number of $500 increments = loan amount / $500

= $1,693 / $500

≈ 3.386

Since we can't have a fraction of an increment, we round up to 4.

Step 2: Calculate the daily payment:

Daily payment = 25 © * Number of $500 increments

= 25 © * 4

= $100

Step 3: Calculate the total repayment amount:

Total repayment amount = Daily payment * number of days

= $100 * 120

= $12,000

Step 4: Calculate the annual interest rate:

Annual interest rate = (Total repayment amount - Loan amount) / Loan amount * (360 / Number of days)

= ($12,000 - $1,693) / $1,693 * (360 / 120)

Now, let's perform the calculations:

Amount you repay ≈ $12,000

Annual interest rate ≈ (($12,000 - $1,693) / $1,693) * (360 / 120)

Calculating the annual interest rate:

Annual interest rate ≈ (($10,307) / $1,693) * 3

Rounding to four decimal places:

Annual interest rate ≈ (6.0905) * 3

≈ 18.2715

Therefore,

a) The amount you will repay is approximately $12,000.

b) The annual interest rate charged by the loan company is approximately 18.2715%.

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The margin of error for a 99% confidence interval estimate is approximately 0.0838 or 8.38%.

To calculate the margin of error for a 99% confidence interval estimate, we can use the formula:

Margin of Error = Z * sqrt(p_hat * (1 - p_hat) / n)

Where:

Z is the z-value corresponding to the desired confidence level (99% confidence level corresponds to a z-value of approximately 2.576).

p_hat is the sample proportion (percentage of apples with bruises), which is calculated as the number of apples with bruises divided by the total sample size.

n is the sample size.

Given:

Sample size (n) = 100

Number of apples with bruises = 12

Calculating the sample proportion:

p_hat = 12 / 100 = 0.12

Using the z-value for a 99% confidence level (z = 2.576), we can calculate the margin of error:

Margin of Error = 2.576 * sqrt(0.12 * (1 - 0.12) / 100)

Calculating the margin of error:

Margin of Error = 2.576 * sqrt(0.12 * 0.88 / 100)

Margin of Error = 2.576 * sqrt(0.1056 / 100)

Margin of Error = 2.576 * sqrt(0.001056)

Margin of Error ≈ 2.576 * 0.0325

Margin of Error ≈ 0.0838

Therefore, the margin of error for a 99% confidence interval estimate is approximately 0.0838 or 8.38%.

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The solutions are given below.

A triangle is a polygon with three edges and three vertices. It is one of the basic shapes in geometry. A triangle with vertices A, B, and C is denoted \triangle ABC. In Euclidean geometry, any three points, when non-collinear, determine a unique triangle and simultaneously, a unique plane.

here, we have,

Part A

the dotted line formes the thrid side of the triangle.

part B

The length is the unknon side increases while kepping the known side lenths fixed, measuremnt of anggle Z will increas. So, the tringle will not fir the given conditions anymore.

part c

If the length of he unknown side decrases while keeping h known side lengths fixed,the measure of angle will decrease so he tringle will not fit the given conditions anymore.

part D

You know the given conditions for the triangle are fixed you also know the unknown side length is fixed. What dose the this tell you angles adjacent to the unknown side.

part e

The given condiction are fixed and the unknown side lenghtis fixed, the angles adjacent to the unknown side must much also be fixed.

part f

Given two side lengths and the measurement of the angle between them, only one triangle can be constructed. Part G The length of the unknown side (c) is 9.76 centimeters

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Answer:

36

Step-by-step explanation:

6^2=36

Step-by-step explanation:

x-5 < -3

or, x < -3 +5

or, x < 2

Now,

x +8 >2

or, x >2 - 8

or, x >-6

The total expected cost of Alice's train ride will be 20 Euro with a fine of 300 Euro if ticket checked and 0 fine if ticket not checked.

It is known to us that Alice is riding the train, and that she accidentally purchased a ticket for zone 4, although she has to be traveling to zone 5,

with this we need to find how much money can Alice expect to pay

since we know that there is a 5 percent chance that the transit authorities will check tickets,

Probability to check ticket = 5/100 = 0.05

fine = 300 euro

probability to not check ticket = 1 - 0.05 = 0.95

we know that she has already spent 5 Euro on the ticket,

there is a 300 Euro fine if ticket checked,

and 0 fine if ticket not checked,

Expected cost to pay = 5 + 0.05 × 300 + 0.95 × 0

= 5 + 15 + 0

= 20 Euro

Alice Expected to Pay = 20 Euro

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Answer:

23,084-9,567= 13,517 so he will have to pay $13,517

The Variable d in the equation represents the time per minute Lilianna spends walking to the park

The equation:

d(3/4 + 1) = 12 1/4

d(3+4/4) = 12 1/4

d(7/4) = 49/4

d = 49/4 ÷ 7/4

= 49/4 × 4/7

= 49/7

d = 7

Complete question:

Lilianna uses 3/4 calories per minute just by sitting. She uses 1 more calorie per minute by walking. Liliana uses a total of 12 1/4 calories walking to the park. Lilianna uses the equation, d(3/4+1)=12 1/4 to represent the situation. What does the variable d represent in the equation?

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Answer:

150°

Step-by-step explanation:

every line is equal to 180°. To find an angle, like this one, you have to subtract 30° from 180°. Therefor the answer is 150°.

If you need a further explanation just let me know

375 calories are in three tablespoon of olive oil

In mathematics, Variables are unknowns which are written as alphabets use to find a value for some quantity.

Variables doesn't have a fixed value. It can change . Usually we use small alphabet like x ,y and z for denoting Variables.

According to the question,

let the number of calories in olive oil be a variable "x"

it's given that

One tablespoon of olive oil total calories = 125 calories

we have to calculate number of calories in 3 tablespoon of olive oil

1 tablespoon = 125

3 tablespoon = 125 × 3

=> 375 calories

Hence, three tablespoon of olive oil contains 375 calories

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Answer:

Below

Step-by-step explanation:

It is a RIGHT triangle so you can use the Pyhtaogrean Theorem

hypotenuse^2 = leg1^2 + leg2^2     Sub in the values given:

       x^2          =   19^2    +   16^2

       x ^2 = 617

      x = sqrt (617)      ( or 24.84 units)

The two mutually exclusive events where we have a spinner with 4 sections: 1, 2, 4, and 3, where sections 1 and 4 are shaded and the spinner is pointed at number 2 are: Selecting a shaded section (1 or 4)
and Selecting an unshaded section (2 or 3)

The term "mutually exclusive" refers to events that cannot occur at the same time.
To determine which events are mutually exclusive, we need to consider the possibilities:

1. Selecting a shaded section (1 or 4): This event is mutually exclusive with selecting an unshaded section (2 or 3). The two options cannot happen simultaneously.

2. Selecting an unshaded section (2 or 3): This event is mutually exclusive with selecting a shaded section (1 or 4). Again, these two options cannot occur at the same time.

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CenterWare's direct labor rate variance is $2,100 unfavorable, indicating that the actual rate paid for labor was higher than the standard rate. The direct labor efficiency variance is $2,500 favorable, suggesting that the company achieved higher productivity than expected. The total variance for direct labor is $400 favorable.

To compute the direct labor rate variance, we need to calculate the difference between the actual rate and the standard rate, and then multiply it by the actual hours worked. The formula for the rate variance is (Actual Rate - Standard Rate) × Actual Hours. In this case, the standard rate is $21.00 per hour, and the actual rate is $18.00 per hour. The actual hours worked are 2,500 DLH. Plugging in these values, we find the direct labor rate variance to be ($18.00 - $21.00) × 2,500 = -$7,500, indicating an unfavourable variance.

To calculate the direct labor efficiency variance, we need to find the difference between the actual hours worked and the standard hours allowed, and then multiply it by the standard rate. The formula for the efficiency variance is (Actual Hours - Standard Hours) × Standard Rate. The standard hours allowed are 2,000 DLH (1,000 pots × 2.0 hours per pot). Substituting the values, we get (2,500 - 2,000) × $21.00 = $10,500, indicating a favorable variance.

The total variance for direct labor is the sum of the rate variance and the efficiency variance. In this case, the total variance is -$7,500 + $10,500 = $3,000, which is favorable, indicating that the company performed better than expected in terms of labor cost and efficiency.

The responsibility for the rate variance generally lies with the purchasing department, as they are responsible for negotiating labor rates and purchasing materials at the standard price. The efficiency variance is typically the responsibility of the production department, as they are accountable for achieving the standard labor hours and maximizing productivity.

The rate variance reflects the difference between the actual rate paid for labor and the standard rate. An unfavorable rate variance suggests that the company paid more for labor than anticipated, which could be due to factors like higher wages or inefficient labor management. Conversely, a favorable rate variance would indicate cost savings in labor.

The efficiency variance measures the productivity of labor and represents the difference between the actual hours worked and the standard hours allowed. A favorable efficiency variance implies that the company achieved higher productivity or used fewer labor hours than expected. It could result from factors such as skilled and efficient labor, improved production processes, or effective workforce management.

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Answer: \(\frac{5}{9}\ m\)

Step-by-step explanation:

Given

Area of the rectangular piece of paper is \(A=\frac{1}{3}\ m^2\)

Length of the paper is \(l=\frac{3}{5}\ m\)

Suppose width of the paper is \(w\)

Area is the multiplication of length and width

\(\therefore A=lw\\\\\Rightarrow \dfrac{1}{3}=\dfrac{3}{5}\times w\\\\\Rightarrow w=\dfrac{5}{9}\ m\)

Thus, the width of the paper is \(\frac{5}{9}\ m\)

Answer: D. 3/2

Step-by-step explanation:

Answer:

D

Step-by-step explanation:

Slope is change in y / change in x

In the graph there is an interception at 0,1 and 2,4

So the change in x is 2 and the change in y is 3

so 3/2

And it's positive since it's going top right.

Answer:

1r

Step-by-step explanation:

(5r-4)(2r-6r+4)

1(5r-4)+1(2r-6r+4)

5r-4+2r-6r+4

5r+2r-6=1r

1r-4+4

-4+4=0

1r

The dimensions of the package of maximum volume that can be sent are approximately 7.8 inches in radius and 21.3 inches in height.

Let's assume that the package has a height 'h' and a radius 'r'. The perimeter of the cross-section of a cylinder is the circumference of the circle plus the height multiplied by two, which can be written as:

Perimeter = 2πr + 2h

Given that the maximum combined length and circumference is 114 inches, we can write:

2πr + 2h + 2r = 114

Simplifying this equation, we get:

πr + h = 57 - r ----(1)

The volume of the cylinder is given by:

\(V = πr^2h\)

Now, we can use equation (1) to eliminate 'h' from the volume equation:

\(V = πr^2(57 - r - πr)\)

Expanding and simplifying this equation, we get:

\(V = πr^3 - π^2r^3/3 + 57πr^2 - 57π^2r\)

To find the dimensions of the package that maximize the volume, we need to find the value of 'r' that maximizes the volume. We can do this by taking the derivative of the volume equation with respect to 'r' and setting it equal to zero:

\(dV/dr = 3πr^2 - π^2r^2 + 114πr - 57π^2 = 0\)

Solving for 'r', we get:

r ≈ 7.8 inches

Substituting this value of 'r' back into equation (1), we can find the value of 'h':

h ≈ 21.3 inches

Therefore, the dimensions of the package of maximum volume that can be sent are approximately 7.8 inches in radius and 21.3 inches in height.

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Answer:

11.8 m:

Step-by-step explanation:

Volume = pi×r²×h
95 = pi×1.6²×h
h = 95/(pi×1.6²)
h = 11.8122809326
h = 11.8 m (nearest tenth)

Answer:

11.8 m:

Step-by-step explanation:

Volume = pi×r²×h

95 = pi×1.6²×h

h = 95/(pi×1.6²)

h = 11.8122809326

h = 11.8 m (nearest tenth)

The volleyball team would need to purchase 10 shirts for a total of $105 for the cost to be equal.

Answer:

Step-by-step explanation:

2+4

X +4

B.

2 4

3 х

WIN WIN

C.

3.2

3x

D.

2 6

3 x

Answer:

First, I would find the unit rate for   people 240 5

people who bike 48 1 . Next, I would

find the number of people who like to bicycle in a group of 360 people and

assume that only people that like to bicycle would own a mountain bike:

5 360 = = 72

1

x

x , . Finally, I would write the ratio 7 mountain bikes = 18 bicyclists= bicyclists 72

x

and

solve for x to see that there should be 28 mountain bikes.

Step-by-step explanation: