Find the absolute extrema of the function on the closed interval. Use a graphing utility to verify your results. (If an answer does not exist, enter DNE.) h(t) = t t ? 6 , [7, 13] absolute maximum (t, y) = absolute minimum (t, y) =

Using Green's theorem the line integral H C(4x2 y3)dx+ ( x3 + y2)dy is 70.6858.

Step: 1

Given

[tex]\int\limi {4x2 - y3} \, dx + (x3+y2) dy[/tex]

Formula for Greens theorem

δQ/δx = 3x2

Explanation:

partial derivative w.r.t x i . e y is constant

partial derivative w.r.t y i. e x is constant

power rule of derivative is

d/dx Xn = nXⁿ⁻¹

Step: 2

[tex]\int\limits\int\li {dQ/dy + dP/dx dA} \, dx = \int \int {3(x2+y2)} \, dx[/tex]

Explanation:

in polar coordinates x2 + y2 = r2 and dA = radθ

Step: 3

given

C1 = r1 = 2

C2 = r2 = 1

the limits for r is 1 ≤ r ≤ 2

since it is a circle the limits for θ

0 ≤ θ ≤ 2π

Explanation: Please refer to solution,

now integrate w.rt θ

= 45/4[θ] 2π

= 45/4[2π - 0]

= 45/4(2π)

= 45/2(π)

= 45π/2 ≈ 70.6858.

by greens theorem,

[tex]\int 4x2 y3)dx+ ( x3 + y2)dy \, dx[/tex] is 70.6858.

Green’s theorem is substantially used for the integration of the line combined with a twisted aeroplane . This theorem shows the relationship between a line integral and a face integral. It's related to numerous theorems similar as Gauss theorem, Stokes theorem.

Green’s theorem is used to integrate the derivations in a particular plane. However, it's converted into a face integral or the double integral or vice versa using this theorem, If a line integral is given.

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Answer:

Expected value E(x)

= 2 x 0.11 + 11 x 0.09 + 12 x 0.08 + 13 x 0.58 + 19 x 0.14

= 12.37

Variance

= E( X^2 ) - (E(X))^2

= (2^2 x 0.11 + 11^2 x 0.09 + 12^2 x 0.08 + 13^2 x 0.58 + 19^2 x 0.14) - (12.37)^2

= 171.41 - 153.0169

= 18.393 (cor to 3 dp)

Standard deviation

= [tex]\sqrt{variance}[/tex]

=[tex]\sqrt{18.3931}[/tex]

= 4.289 (cor to 3 dp)

Mean should be ( [tex]\frac{2+11+12+13+19}{5}[/tex] ) = 11.4 but i am not very sure

Mean, variance and the standard deviation of the discrete random variable are 12.37, 18.3931 and 4.2887 respectively.

Expected value in probability is defined as the sum of the product of each of the variable and probability corresponding to the variable.

Expected value is same as the mean of a discrete random variable.

Mean, μ = Σ x. P(x)

              = (2 × 0.11) + (11 × 0.09) + (12 × 0.08) + (13 × 0.58) + (19 × 0.14)

              = 12.37

Variance, σ² = Σx² P(x) - μ²

                     = [(2² × 0.11) + (11² × 0.09) + (12² × 0.08) + (13² × 0.58) + (19² ×

                         0.14)]- [ 12.37²]

                     = 18.3931

Standard Deviation, σ = √Variance

                                    = 4.2887

Hence the mean is 12.37, Variance is 18.3931 and Standard deviation is 4.2887.

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Answer:

120°

Step-by-step explanation:

AB //CD and EF is transversal. When two parallel lines are cut by a transversal, the alternate exterior angles are congruent.

      ∠CHF = ∠BGE

                = 120°

Answer:

Assuming that Peter travels at a constant speed, then he would have travelled a total distance of (98 * 3) + (105 * 2) = 531 km.

So, Katie made 1 19/40 number cups of trail mix.

In mathematics, the denominator is the bottom number in a fraction, and it represents the total number of equal parts into which the whole has been divided. The denominator is written below the numerator, which is the top number in a fraction, and it indicates the number of those equal parts that are being considered or used in the fraction.

given by the question.

To find the total amount of trail mix Katie made, we need to add up the amounts of each ingredient:

1/2 cup of raisins +

3/5 cup of banana chips +

3/8 cup of peanuts

To add these fractions, we need to find a common denominator. The smallest number that all the denominators (2, 5, and 8) divide into evenly is 40. We can convert each fraction to have a denominator of 40:

1/2 cup of raisins = 20/40 cup

3/5 cup of banana chips = 24/40 cup

3/8 cup of peanuts = 15/40 cup

Now we can add them up:

20/40 cup + 24/40 cup + 15/40 cup = 59/40 cup

So, Katie made 59/40 cup of trail mix. However, we can simplify this fraction:

59/40 cup = 1 19/40 cup

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a) Either 3 or 4 questions did Mike answer correctly.

b) Either 7 or 8 questions did Sheila answer correctly.

In its simplest form in algebra, the definition of an equation is a mathematical statement that shows that two mathematical expressions are equal. For instance, 3x + 5 = 14 is an equation, in which 3x + 5 and 14 are two expressions separated by an 'equal' sign.

a) Let mike did x correct

then, incorrect will be (10- x)

The equation is:

Now, 5x + (10 - x) (-3) = 0

=> 5x - 30 + 3x = 0

=> 8x = 30

=> x = 30/8

=> x > 3 and x < 4

b) Let Sheila did y correct

then, incorrect = (10 - y)

Now, 5y + (10 - y) (-3) = 32

=> 5y - 30 + 3y = 32

=> 8y = 62

=> y > 7 and y< 8

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The given question is incomplete, complete question is:

In a school test consisting of 10 questions, 5 points are awarded for a correct answer but 3 points are deducted for an incorrect answer.

A blank answer scores (). Mike scored a total of () and he did not leave all of the answers blank. (a) How many questions did Mike answer correctly? _ _ _ _ _ _ _ _ Sheila scored a total of 32. (b) How many questions did Sheila answer correctly?

Answer: The average cost per item is given by the equation C = (a/q) + b. To find the rate of change of C as q increases, we need to take the derivative of this equation with respect to q.

dC/dq = -(a/q^2)

So, the rate of change of C with respect to q is proportional to -1/q^2.

If production increases at a rate of 100 cell phones per week, the rate of change of q is 100. But we need to convert this to units of items per hour or per second, depending on the context.

Let's assume the rate of increase of q is in items per hour. Then the rate of change of C with respect to time t (in hours) is given by:

dC/dt = (dC/dq) * (dq/dt) = (-(a/q^2)) * (100) = -100a/q^2

So, the rate at which the average cost is changing depends on the value of a and q. If we knew the values of a and q, we could calculate the specific rate at which the average cost is changing.

Step-by-step explanation:

(97x/100) represents the total number of cleaner automobiles.

In mathematics, an expression or mathematical expression is a finite combination of symbols that is well-formed according to rules that depend on the context.

Given is that automobiles are 97% cleaner than they were 30 years ago.

Assume that the total number of automobiles 30 years ago were {x}. Then, the total number of clean automobiles will be -

97% of {x} = 97x/100

Therefore, (97x/100) represents the total number of cleaner automobiles.

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The probability that a randomly selected medical student who took the test had a total score that was less than 480 is 0.49, which means that approximately 49% of medical students had a score lower than 480.

Probability can be defined as the ratio of the number of favorable outcomes to the total number of outcomes of an event.

here, we have,

To calculate the probability that a randomly selected medical student who took the test had a total score that was less than 480, we need to start by looking at the data given.

In this case, the data tells us that the mean score was 500 and the standard deviation was 50.

This means that the scores are normally distributed, which means that the probability of finding a score lower than 480 can be calculated using the normal distribution formula.

We can use this formula to calculate the area under the curve (or probability) below the score of 480.

The result of this calculation is 0.49, which means that approximately 49% of medical students had a score lower than 480.

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The total number of wheelbarrow loads required to complete both the projects 25.

What are Fractions?

Any number of equal parts is represented by a fraction, which also represents a portion of a whole. In ordinary English, a fraction refers to the number of parts of a specific size.

The combined volume of concrete needed for the patio and walkway is 1 3/4 + 2 1/3 = 7/4 + 7/3 = 21/12 + 28/12 = 49/12 cubic yards

The entire volume of concrete can be divided by the capacity of a wheelbarrow to determine the necessary number of wheelbarrow loads: (49/12 )/( 1/6) = 49/12* 6/1 = 49/2 = 24.5

We round up to 25 because we can't have half a wheelbarrow load. The homeowner will therefore require 25 wheelbarrow loads to finish both projects.

Hence, The total number of wheelbarrow loads required to complete both the projects 25.

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Step-by-step explanation:

-2x + 11(y+x) = 2

-2x + 11y + 11x = 2

-2x + 11x +11y = 2

9x + 11y = 2

where a = 9, b= 11 and c= 2

M is not on the list, and thus the list cannot be a complete listing of all real numbers between 0 and 1.

Inductive reasoning is defined as, tempting judgments by moving from the details to the fact. It's usually determined with inferential reasoning, where you move from known information to precise conclusions.

Here,
Georg Cantor's diagonal argument is proof by contradiction that shows that there are more real numbers than natural numbers. Here's how the proof can be reworked with the given modification:

Suppose that we have a list of all real numbers between 0 and 1, written in decimal form. We will show that this list cannot be a complete listing of all real numbers between 0 and 1.

Let M be a new real number whose decimal expansion is obtained by following the following rule: if the nth digit of the nth number on the list is 4, then the nth digit of M is 8; if the nth digit of the nth number on the list is not 4, then the nth digit of M is 4.

Since each number on the list has a unique decimal expansion, M is a real number between 0 and 1, and its decimal expansion is different from the nth number on the list in the nth digit for all n.

Therefore, M is not on the list, and thus the list cannot be a complete listing of all real numbers between 0 and 1.

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Answer: 0.0628

Step-by-step explanation:

The closest answer to the p-value for a test statistic of z = -1.86 is 0.0614.

To calculate the p-value for a one-sample two-sided z-test on a population proportion, we must first calculate the area under the standard normal distribution curve that corresponds to the test statistic z = -1.86.

Because this is a two-sided test, we must find the area of the distribution in both tails that is more extreme than the test statistic. We can do this by using a standard normal distribution table or calculator, or by exploiting the distribution's symmetry.

We can calculate the area to the left of z = -1.86 using a standard normal distribution table or calculator. Because this is a two-sided test, the area in the distribution's right tail is also 0.0307.As a result, the p-value for this test statistic is as follows:

2(0.0307) = 0.0614 p-value

So 0.0614 is the closest answer to the p-value for a test statistic of z = -1.86.

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The volume of a solid formed by revolving the region in the first quadrant bounded on the left by the circle , on the right by the line , and above by the line about the x-axis is (47/3)π.

To use the washer method, we need to consider the solid as a stack of thin washers, each with a hole in the center. We will integrate along the axis of revolution (in this case, the x-axis).

First, let's sketch the region we're revolving:

The circle has equation x^2 + y^2 = 1, so its radius is r = 1 when y = 0. The line has equation x = 4, so its distance from the axis of revolution is R = 4. The region we're revolving is bounded by y = 0 and y = √(1 - x^2), which we can rewrite as x = √(1 - y^2).

We can now set up the integral for the volume of the solid:

V = [tex]\int\limits^1_0[/tex] π(R^2 - r^2) dy

 = [tex]\int\limits^1_0[/tex] π(4^2 - x^2) dy

 = π[tex]\int\limits^1_0[/tex] (16 - y^2) dy

 = π [16y - (1/3)y^3] |₀¹

 = π (16 - 1/3)

 = (47/3)π

Therefore, the volume of the solid is (47/3)π cubic units.

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Complete question is:

Using the washer method, determine the volume of a solid formed by revolving the region in the first quadrant bounded on the left by the circle x^2+y^2=1, on the right by the line x = 4, and above by the line x=4 about the x-axis.

Answer:

$1.27

Step-by-step explanation:

We know

The tax is 7.5%

7.5% = 0.075

Which of the following was the sales tax Serena had to pay?

We take

16.99 times 0.075 = $1.27

So, the answer is $1.27

Answer:

8y+2

Step-by-step explanation:

5y+3y=8y

-2+4=2

Since it's positive two we add them together.

8y+2

Answer:

Opposite is = 4

Step-by-step explanation:

Fromthe question Hypotenuse = 5

Adjacent = 3

opposite = ?

Let opposite = x

Hypotenuse² = adjacent² + opposite²

5² = 3² + x²

25 = 9 + x²

25 - 9 = x²

16 = x²

[tex] \sqrt{16} = \sqrt{ {x}^{2} } \\ = \sqrt{16} = x \\ = 4 = x [/tex]

Therefore opposite is = 4.

The measure of ER given by the equation ER = 21

Equations are mathematical statements with two algebraic expressions flanking the equals (=) sign on either side.

It demonstrates the equality of the relationship between the expressions printed on the left and right sides.

Coefficients, variables, operators, constants, terms, expressions, and the equal to sign are some of the components of an equation. The "=" sign and terms on both sides must always be present when writing an equation.

Given data ,

Let the equation be represented as A

Now , the value of A is

Substituting the values in the equation , we get

The measure of QE = 8x + 3   be equation (1)

The measure of ER = 4x + 1   be equation (2)

The measure of QR = 64

Now , QR = QE + ER   be equation (3)

Substituting the values of QE and ER in the equation (3) , we get

8x + 3 + 4x + 1 = 64

On simplifying the equation , we get

12x + 4 = 64

Subtracting 4 on both sides of the equation , we get

12x = 60

Divide by 12 on both sides of the equation , we get

x = 5

Substitute the value of x in equation (2) , we get

The measure of ER = 4 ( 5 ) + 1

The measure of ER = 21

Hence , the equation is ER = 21

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Answer: The numerators must be the same for the fractions to be equal.

The denominator of a fraction is the bottom number. Take a look at these two fractions.

¾ & ¾

The numbers at the bottom are the same. If I eat ¾ of an apple and you eat ¾ of an apple, we both eat the same amount.

Now look at these fractions.

⅗ & ¾

They both have the same top number (numerator), but they have different denominators. If I eat ¾ of an apple and you eat ⅗ of an apple, we both do not eat the same amount.

So if both the numerator and denominator are the same they are equal.

This means that the numerators must be the same for the fractions to be equal.

I hope this helps & Good Luck <3 !!!

After reflection, Coordinates of W'X'Y'Z' are

W'(-2, 2), X'(-2 , 4), Y' (-4, 4), and Z' (-4, 2)

A reflection is a mirror image of the shape. An image will reflect through a line, known as the line of reflection. A figure is said to reflect the other figure, and then every point in a figure is equidistant from each corresponding point in another figure. The reflected image should have the same shape and size, but the image faces in the opposite direction.

Given,

Vertices of a polygon WXYZ

W(2, 2), X(2, 4), Y(4, 4), and Z(4, 2)

There is reflection over y-axis

For reflection over y - axis , y=f(-x)

Thomas reflected y coordinate y → -y

but x coordinate should be reflected, then x → -x

W(2, 2) → W'(-2, 2)

X(2, 4) → X'(-2 , 4)

Y(4, 4) → Y' (-4, 4)

Z(4, 2) → Z' (-4, 2)

Hence, W'(-2, 2), X'(-2 , 4), Y' (-4, 4), and Z' (-4, 2) are coordinates of W'X'Y'Z'

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Answer:

y=4

x=3

Step-by-step explanation:

2y-4=y

y=4

4x=x+9

3x=9

x=3

The probability of exactly one paycheck being in the correct envelope is 1 in 5, while the probability of at least one paycheck being in the correct envelope is 4 in 5.

The probability of exactly one paycheck being in the correct envelope can be calculated by taking the number of possible outcomes where one paycheck is in the correct envelope (1) and dividing it by the total number of possible outcomes (5). This yields a probability of 1 in 5. The probability of at least one paycheck being in the correct envelope is calculated by taking the total number of possible outcomes where at least one paycheck is in the correct envelope (4) and dividing it by the total number of possible outcomes (5). This yields a probability of 4 in 5. Thus, the probability of exactly one paycheck being in the correct envelope is 1 in 5, while the probability of at least one paycheck being in the correct envelope is 4 in 5.

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Step-by-step explanation:

the volume of such a cone is

pi×r² × h / 3

r is the radius of the ground circle, h is the straight inner height.

the radius is as always half of the diameter, so in our case

6/2 = 3 units.

so, the volume is

pi×3² × 11 / 3 = pi×9×11/3 = pi×3×11 = 33pi =

= 103.6725576... units³ ≈

≈ 103.7 units³

The grocer ordered approximately 164.3 pounds of raspberries from the local farmer. We can round this to the nearest tenth if needed, which would give us an answer of 164.3 pounds.

What is linear equation ?

Linear equation can be defined as equation in which highest degree is one.

Given,

o determine how many pounds of raspberries the grocer ordered, we can use the formula:

Total cost = Price per pound x Number of pounds

We know that the price per pound is $1.04, and the total cost of the last order was $171.08. Let's use "x" to represent the number of pounds of raspberries the grocer ordered:

$171.08 = $1.04 x

To solve for x, we can divide both sides by $1.04:

x = $171.08 / $1.04

x ≈ 164.3

Therefore, The grocer ordered approximately 164.3 pounds of raspberries from the local farmer. We can round this to the nearest tenth if needed, which would give us an answer of 164.3 pounds.

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Answer:

B. Vertex

Step-by-step explanation:

The midpoint between the two x-intercepts of a parabola will provide the x-coordinate of the vertex. Line of symmetry is drawn along this particular  x-coordinate. This x-coordinate is substituted into the equation of the graph to find its corresponding y-coordinate.

a) C(x) = 0.02x + 2200, b) A straight line with positive slope, c) Slope is 0.02, represents cost per chair, d) Y-intercept is 2200, represents fixed cost.

a) The cost C(x) can be expressed as a linear function of the number of chairs x produced. We can solve for the slope and y-intercept using the two points (100, 2200) and (300, 4800). First, calculate the slope of the line using the formula (y2 - y1)/(x2 - x1). This gives us (4800 - 2200)/(300 - 100) = 0.02. Then, we can use the slope and one of the points to solve for the y-intercept using the equation y = mx + b, where m is the slope and b is the y-intercept. Substituting the values from the first point (100, 2200) into the equation gives us 2200 = 0.02(100) + b, so the y-intercept is 2200. Therefore, the cost function can be expressed as C(x) = 0.02x + 2200.

b) The graph of this function is a straight line with a positive slope, as shown in the diagram.

c) The slope of the graph is 0.02, which represents the cost per chair.

d) The y-intercept is 2200, which represents the fixed cost of manufacturing the chairs.

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The correct equation is option (A): 0.7386x - 15.75 = 41.87 equation can be used to find the quantity of Canadian dollars that Tobias exchanged .

In mathematics, an expression is a combination of numbers, variables, and operations that can be evaluated to obtain a value. An expression can contain constants, variables, and operators such as addition, subtraction, multiplication, division, and exponentiation, as well as functions and parentheses to control the order of operations.

Let x be the quantity of Canadian dollars that Tobias exchanged. According to the problem statement, he received 0.7386 U.S. dollars for each Canadian dollar exchanged, and he gave away $15.75, leaving him with $41.87. We can use this information to set up the equation:

0.7386x - 15.75 = 41.87

Therefore, the correct equation is option (A):

0.7386x - 15.75 = 41.87 equation can be used to find the quantity of Canadian dollars that Tobias exchanged .

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To calculate the monthly payment and total interest for a loan of $89,000 at 5.7% for 30 years, we can use the formula for the monthly payment of a fixed-rate mortgage loan:

P = L[c(1 + c)^n]/[(1 + c)^n - 1]

where P is the monthly payment, L is the loan amount, c is the monthly interest rate (which is the annual interest rate divided by 12), and n is the total number of monthly payments (which is the number of years multiplied by 12).

Plugging in the given values, we have:

L = $89,000

r = 5.7% = 0.057 (monthly interest rate)

n = 30 years * 12 months/year = 360 months

P = ($89,000)[0.057(1 + 0.057)^360]/[(1 + 0.057)^360 - 1]

P = $515.92 (rounded to the nearest cent)

Therefore, the monthly payment is $515.92.

To calculate the total interest, we can subtract the loan amount from the total amount paid over the life of the loan. The total amount paid is equal to the monthly payment times the total number of payments:

Total amount paid = P * n = $515.92 * 360 = $185,731.20

Total interest = Total amount paid - Loan amount = $185,731.20 - $89,000 = $96,731.20

Therefore, the total interest paid over the life of the loan is $96,731.20.