Question 1 < Σ Use integration by parts to evaluate the definite integral: 2t sin( – 9t)dt = 5.25л ба

Answer: 8

Step-by-step explanation:

okay so do 17 x 17 - 15 x 15

then to that result do :

squared root.

The dealer bought 42 radios.

Let x be the number of radios the dealer bought.

Let y be the price the dealer paid for each radio.

We know that the dealer bought x radios for a total of $1,008, so:

x * y = 1008

We also know that the dealer gave away 6 radios and sold the rest for $14 more than she paid for each radio, breaking even. This means that the total revenue from selling the remaining radios is equal to the total cost of buying them:

(x - 6) * (y + 14) = x * y

Simplifying this equation, we get:

xy + 14x - 6y - 84 = xy

14x - 6y = 84

7x - 3y = 42 (dividing by 2 on both sides)

Now we have two equations:

x * y = 1008

7x - 3y = 42

We can use substitution or elimination to solve for x and y. Let's use elimination by multiplying the second equation by y/3 and adding it to the first equation:

x * y + (7x - 3y) * (y/3) = 1008 + 42 * (y/3)

xy + 7xy/3 - y²/3 = 1008 + 14y

10xy/3 - y²/3 - 14y - 1008 = 0

Multiplying both sides by 3, we get:

10xy - y² - 42y - 3024 = 0

Now we can use the quadratic formula to solve for y:

y = (-b ± sqrt(b² - 4ac)) / 2a

where a = -1, b = -42, and c = -3024:

y = (-(-42) ± sqrt((-42)² - 4(-1)(-3024))) / 2(-1)

y = (42 ± sqrt(42² - 4*3024)) / 2

y = (42 ± 126) / 2

y = 84 or y = -42

Since the price of a radio cannot be negative, we can discard the second solution and conclude that y = 84.

Now we can solve for x using the first equation:

x * y = 1008

x * 84 = 1008

x = 12

Therefore, the dealer bought 12 radios.

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Answer: x + 4.8 = 14.3

Step-by-step explanation:

Let x be the initial amount of water that was already in the bucket before the additional 4.8 liters of water was poured in.

Then the total amount of water in the bucket after pouring in the 4.8 liters is the sum of the initial amount x and the amount of water poured in, which is 4.8 liters. This can be represented by the equation:

x + 4.8 = 14.3

We can simplify this equation by solving for x:

x = 14.3 - 4.8

x = 9.5

Therefore, the initial amount of water in the bucket was 9.5 liters, and after pouring in 4.8 liters, the bucket contained a total of 14.3 liters.

The solution to the equation 4x + 17 = 23 is x = 3/2.

It should be noted that to solve this equation, we need to isolate the variable x on one side of the equation.

First, we can subtract 17 from both sides of the equation:

4x + 17 - 17 = 23 - 17

Simplifying the left side of the equation:

4x = 6

Next, we can divide both sides of the equation by 4:

4x/4 = 6/4

Simplifying:

x = 3/2

Therefore, the solution to the equation 4x + 17 = 23 is x = 3/2.

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The average cost per day for the four service is $3.23 per day

Average cost refers to the per-unit cost of production, which is calculated by dividing the total cost of production by the total number of units produced.

Therefore average cost = total cost/ number of unit

total cost = $108

average cost for the three services = $108/3

= $36

total average cost = $36+$54.30

= $90.30

therefore average cost for a day will be average cost for a month over 28day i.e 7days ×4

= 90.30/28

= $3.23 per day

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Statement 5 is True

Statement 1: (M ∧ ~R) ∨ (~S ∧ L)
T or F: T
Main Operator: ∨
Assuming the given truth values, Statement 1 is True.

Statement 2: (~S ↔ M) ∧ (L ∧ ~K)
T or F: F
Main Operator: ∧
Assuming the given truth values, Statement 2 is False.

Statement 3: ~(R ∨ ~L) ∧ (~S ∨ S)
T or F: F
Main Operator: ∧
Assuming the given truth values, Statement 3 is False.

Statement 4: ~ [(Q ∨ ~S) ∧ ~(R ↔ ~S)]
T or F: T
Main Operator: ~
Assuming the given truth values, Statement 4 is True.

Statement 5: (S ↔ Q) ↔ [(K ∧ ~M) ∨ ~(R ∧ ~L)]
T or F: T
Main Operator: ↔
Assuming the given truth values, Statement 5 is True.

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Lara sold 3/5 of a box of candy, which is the same as 0.6 boxes of candy.

If Lucy sold 3/5 of a box of candy, then Lara sold 1/5 of 3/5, which is:

(1/5) * (3/5) = 3/25

Therefore, Lara sold 3/25 of a box of candy.

To find the number of boxes Lara sold, we can divide 3/25 by 1/5:

(3/25) ÷ (1/5) = (3/25) * (5/1) = 15/25 = 3/5

So Lara sold 3/5 of a box of candy, which is the same as 0.6 boxes of candy.

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The derivative of the equation g(x) = 8x^2 – 4; h(x) = 1.6^x is f'(x) = 40.96x · 1.6^x - 15.040128 · 1.6^x

To find the derivative of f(x) = g(x) · h(x), we use the product rule of derivatives, which states that if f(x) = u(x) · v(x), then f'(x) = u'(x) · v(x) + u(x) · v'(x).

Using this rule, we can find the derivative of f(x) = g(x) · h(x) as follows:

f(x) = g(x) · h(x) = (8x^2 – 4) · (1.6^x)

f'(x) = g'(x) · h(x) + g(x) · h'(x) [applying the product rule]

To find g'(x), we take the derivative of g(x) = 8x^2 – 4, which is:

g'(x) = 16x

To find h'(x), we take the derivative of h(x) = 1.6^x, which is:

h'(x) = ln(1.6) · 1.6^x [using the chain rule and the fact that the derivative of a^x is ln(a) · a^x]

h'(x) ≈ 0.470004 · 1.6^x

Now we substitute these values into the product rule formula:

f'(x) = (16x) · (1.6^x) + (8x^2 – 4) ·0.470004 · 1.6^x

Simplifying this expression, we get:

f'(x) = 25.6^x + (12.8x^2 – 6.4) ·0.470004 · 1.6^x

f'(x) = 40.96x · 1.6^x - 15.040128 · 1.6^x
Therefore, the derivative of f(x) = g(x) · h(x) is:
f'(x) = 40.96x · 1.6^x - 15.040128 · 1.6^x

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The correct statement comparing their solutions is Charlene correctly graphed the system to find the intersection point at approximately (2.5,5.25).

option C is correct.

Mathematically, an equation can be described as a statement that supports the equality of two expressions, which are connected by the equals sign “=”.

Since Charlene graphed the system and found a solution of x ≈ 2.5 and y ≈ 5.25, the correct statement comparing their solutions is Charlene correctly graphed the system to find the intersection point at approximately (2.5,5.25).

In conclusion, the three major forms of linear equations: are

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The equation x + 4 = -2 + x has no solution for x

From the question, we have the following parameters that can be used in our computation:

x + 4 = -2 + x

Subtract x from both sides of the equation

so, we have the following representation

x - x + 4 = -2 + x - x

When the like terms of the equation are evaluated, we have

4 = -2

The above equation is false

This is because 4 and -2 do not have the same value

Hence, the equation has no solution

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Yes, if there are more concordant pairs in the rank order, it makes sense that the Kendall correlation will be positive, as it suggests a tendency for the two variables to move in the same direction more often.

In Kendall correlation,

Rank values of each observation for the two variables are compared to determine the level of agreement or disagreement between them.

A concordant pair is when the rank order of the two variables is the same both increase or decrease together.

A discordant pair is when the rank order is different one variable increases while the other decreases.

If there are more concordant pairs, it means that the two variables tend to move in the same direction more often.

Which suggests a positive correlation relationship between them.

Conversely, if there are more discordant pairs, it means that the two variables tend to move in opposite directions more often.

Which suggests a negative  relationship between them.

Example ,

two variables, X and Y, that are positively correlated.

If we plot the observations of X and Y on a scatter plot.

Expect to see a pattern where as the values of X increase, the values of Y also tend to increase.

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Answer:

18:19

Step-by-step explanion:
To solve this problem, we need to first calculate the time it takes for the plane to fly from Singapore to Sydney:

Time = Distance ÷ Speed

Time = 6310 km ÷ 757.2 km/h

Time ≈ 8.34 hours

This is the time it takes to fly from Singapore to Sydney in Singapore time. However, we need to convert this time to Sydney time, which is 2 hours ahead of Singapore time. Therefore, the local time when the plane arrives in Sydney is:

Time in Sydney = Singapore time + 2 hours + Flight time

Time in Sydney = 07:45 + 2 hours + 8.34 hours

Time in Sydney = 18:19

Therefore, the local time when the plane arrives in Sydney is 18:19 using the 24-hour clock.

The four possible decodings of the ciphertext c = 823 845 737 are 156276219, 561472502, 1188260592, and 197895457.

To encode the plaintext m = 414 892 055, we first need to compute the corresponding ciphertext c using the Rabin cryptosystem.

The Rabin cryptosystem involves four steps: key generation, message encoding, message decoding, and key decryption. Since we already have the key n, we can skip the key generation step.

To encode the message m, we compute:

c ≡ m^2 (mod n)

Substituting the given values, we get:

c ≡ 414892055^2 (mod 1359692821)

c ≡ 1105307085 (mod 1359692821)

Therefore, the encoded ciphertext is c = 1105307085.

(b) To find the four decodings of the ciphertext c = 823 845 737, we need to use the Rabin cryptosystem to compute the four possible square roots of c modulo n.

First, we need to factorize n as n = 32359 · 42019. Then we compute the two square roots of c modulo each of the two prime factors, using the following formula:

x ≡ ± [tex]y^((p+1)/4) (mod p)[/tex]

where x is the square root of c modulo p, y is a solution to the congruence y^2 ≡ c (mod p), and p is one of the prime factors of n.

For the first prime factor p = 32359, we can use the following values:

y ≡ 3527^2 (mod 32359) ≡ 15467 (mod 32359)

x ≡ ± y^((p+1)/4) (mod p) ≡ ± 6692 (mod 32359)

Therefore, the two possible square roots of c modulo 32359 are 6692 and 25667.

For the second prime factor p = 42019, we can use the following values:

y ≡ 3527^2 (mod 42019) ≡ 25058 (mod 42019)

x ≡ ± y^((p+1)/4) (mod p) ≡ ± 1816 (mod 42019)

Therefore, the two possible square roots of c modulo 42019 are 1816 and 40203.

To find the four possible decodings of the ciphertext c = 823 845 737, we combine each of the two possible square roots modulo 32359 with each of the two possible square roots modulo 42019, using the Chinese Remainder Theorem:

x ≡ a (mod 32359)

x ≡ b (mod 42019)

where a and b are the two possible square roots modulo 32359 and 42019, respectively.

The four possible values of x are:

x ≡ 156276219 (mod 1359692821)

x ≡ 561472502 (mod 1359692821)

x ≡ 1188260592 (mod 1359692821)

x ≡ 197895457 (mod 1359692821)

Therefore, the four possible decodings of the ciphertext c = 823 845 737 are 156276219, 561472502, 1188260592, and 197895457.

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Answer: To find the vertex of the graph of the equation Y=3x^2+6x+1, we can use the formula:

x = -b/2a

where a = 3 and b = 6, which are the coefficients of the x^2 and x terms, respectively.

x = -6/(2 x 3) = -1

Substituting x = -1 into the equation, we get:

Y = 3(-1)^2 + 6(-1) + 1 = -2

Therefore, the vertex of the graph is (-1, -2), so the answer is A. (-1,-2).

Step-by-step explanation:

Both Nori and her brother Sean made the same amount in interest, $100, assuming that their investments lasted 1 year.

The interest refers to the income or payment received or made for giving or taking credit from a lender.

The interest is usually depicted using a rate, which is expressed over 100.

Nori's Investment = $5,000

Interest rate = 2%

Interest amount = $100 ($5,000 x 2%)

Sean's investment = $10,000

Interest rate = 1%

Interest amount = $100 ($10,000 x 1%)

Thus, Nori and Sean equally made $100 in interest from their investments.

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Answer:

the diameter is 14 and the perimeter is 43.97

The woman bought 21 cards that play a song when they are opened, and 79 cards that do not play music.

Let's assume that the woman bought x cards that play a song when they are opened, and 100-x cards that do not play music.

We know the cost of the cards that play a song is 30 cents each, so the cost of x of these cards is 0.3x dollars.

Similarly, the cost of the cards that do not play music is 5 cents each, so the cost of 100-x of these cards is 0.05(100-x) dollars.

The total cost of all the cards is $10.25, so we can set up the following equation

0.3x + 0.05(100-x) = 10.25

Simplifying the equation, we get

0.3x + 5 - 0.05x = 10.25

0.25x = 5.25

x = 21

Therefore, the woman bought 21 cards that play a song when they are opened, and 100-21 = 79 cards that do not play music.

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The value of the segment IH for the circle with secant through H which intersect the circle at points I and J is (6 + 2i√7) or (6 - 2i√7)

Circle theorems are a set of rules that apply to circles and their constituent parts, such as chords, tangents, secants, and arcs. These rules describe the relationships between the different parts of a circle and can be used to solve problems involving circles.

GH² = IH × JI {secant tangent segments}

JI = 12 - IH, we shall represent IH with x so that;

8² = x(12 - x)

64 = 12x - x²

x² - 12x + 64 = 0 {rearrange to get a quadratic equation}

with the quadratic formula;

x = [12 + √(-112)]/2 or x = = [12 - √(-112)]/2

√(-112) = 4i√7 {where i = √(-1)}

so;

x = (6 + 2i√7) or x = (6 - 2i√7)

Therefore, the value of the segment IH for the circle with secant through H which intersect the circle at points I and J is (6 + 2i√7) or (6 - 2i√7)

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We can use the given point P(3, 4) to find the values of sin(theta) and cos(theta) as follows:

[tex]sin(theta) = opposite/hypotenuse = 4/5[/tex]

[tex]cos(theta) = adjacent/hypotenuse = 3/5[/tex]

Since theta is a first-quadrant angle, we know that tan(theta) = sin(theta)/cos(theta).

Using the half-angle formula for tangent, we have:

[tex]tan(1/2 * theta) = ±√((1 - cos(theta))/2) / (1 + √((1 - cos(theta))/2))[/tex]

We can substitute the values of sin(theta) and cos(theta) that we found earlier:

[tex]tan(1/2 * theta) = ±√((1 - 3/5)/2) / (1 + √((1 - 3/5)/2))[/tex]

[tex]tan(1/2 * theta) = ±√(1/5) / (1 + √(1/5))[/tex]

[tex]tan(1/2 * theta) = ±√5 - 1[/tex]

Since theta is in the first quadrant, tan(1/2 * theta) is positive. Therefore:

[tex]tan(1/2 * theta) = √5 - 1[/tex]

We can simplify this expression by rationalizing the denominator:

[tex]tan(1/2 * theta) = (√5 - 1) / (√5 + 1) * (√5 - 1) / (√5 - 1)[/tex]

[tex]tan(1/2 * theta) = (5 - 2√5)[/tex]

So the answer is (5 - 2√5), which is approximately 0.382. Therefore, the answer is not one of the choices given.

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56 members will weigh 166 pounds or more. The closest answer choice is: A. 67

We'll use the concepts of normal distribution, z-scores, and a z-table. Follow these steps:

1. Calculate the z-score for 166 pounds using the formula: z = (X - μ) / σ
  where X = 166 pounds, μ = mean (176 pounds), and σ = standard deviation (114 pounds)

  z = (166 - 176) / 114 = -10 / 114 ≈ -0.088

2. Look up the corresponding probability for the z-score in a z-table.
  For a z-score of -0.088, the probability is approximately 0.535.

3. Since we want to know how many members weigh 166 pounds or more, we need to find the proportion of members in the upper tail of the distribution. To do this, subtract the probability found in the z-table from 1:

  1 - 0.535 = 0.465

4. Multiply the proportion by the total number of members (120) to find the number of members weighing 166 pounds or more:

  0.465 * 120 ≈ 56

However, none of the provided answer choices matches this result. Please check the question for any typos or errors. If the question's parameters are correct, the closest answer choice is: A. 67

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The solutions of the quadratic equation are:

x = - 3 ±√14

Here we want to solve the equation:

[tex]x^2 + 6x = 5[/tex]

We can rewrite that to standard form:

[tex]x^2 + 6x - 5 = 0[/tex]

Completing squares we will get:

[tex](x^2 + 2*3*x + 3^2 - 3^2) - 5 = 0[/tex]

[tex](x + 3)^2 = 5 + 9[/tex]

x = - 3 ±√14

These are the two solutions of the quadratic equation.

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The correct equation to predict the number of years it would take for the painting to have a value of $10,000 is 15,000(0.85)[tex]^{(t)}[/tex] = 10,000. The correct answer is option (c).

The initial value of the painting is $15,000, and its value is predicted to decay by 15% each year. This means that its value after t years can be represented by the equation:

V(t) = 15,000(0.85)[tex]^{(t)}[/tex]

We want to find the number of years it would take for the value to reach $10,000, so we set V(t) equal to 10,000 and solve for t:

10,000 = 15,000(0.85)[tex]^{(t)}[/tex]

Dividing both sides by 15,000 gives:

0.6667 = 0.85[tex]^{(t)}[/tex]

Taking the natural logarithm of both sides gives:

ln(0.6667) = t ln(0.85)

Solving for t gives:

t = ln(0.6667) / ln(0.85) = 2.294

So it would take approximately 2.294 years for the painting to have a value of $10,000. The right option is (c).

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when running a line, in a right-triangle, from the 90° angle perpendicular to its opposite side, we will end up with three similar triangles, one Small, one Medium and a containing Large one.

Check the picture below.

The required probability 40%

To find the probability that the marble that hits the yard stick between A and D hits it between C and D, we need to find the length of the interval between C and D, and divide it by the length of the interval between A and D.

The length of the interval between C and D is

36 - 26 = 10

The length of the interval between A and D is

36 - 11 = 25

The probability that a marble will strike a yardstick between A and D and C and D is

10/25 × 100 = 40%

Therefore, the probability that a marble will strike a yardstick between A and D and C and D is 40%

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Answer:

Ф  Exponential.                                

Step-by-step explanation:

The most appropriate for tehe data shown is:

Ф  Exponential.                                          

...

The correct expressions are:

A) sin θ = y

B) tan θ = y/x

C) cos θ = x

On a unit circle, the terminal side of Angle 0 intersects the circle at points (x,y). We can use trigonometric ratios to relate the coordinates (x,y) to the angle θ.

A) sin θ = the ratio of y to 1, or simply y.

B) tan θ = the ratio of y to x.

C) cos θ = the ratio of x to 1, or simply x.

Therefore, the correct expressions are:

A) sin θ = y

B) tan θ = y/x

C) cos θ = x

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a) The divergence of F is -4x - 2y,

b) The curl of F is (-2(x+y), 0, -2x).

A) To find the divergence of F, we need to take the dot product of the del operator with F. Therefore, we have:

div(F) = ∇ · F = ∂(yz)/∂x + ∂(-5xz)/∂y + ∂(-4xy)/∂z

= 0 - 5z - 4x

= -5z - 4x

To find the curl of F, we need to take the cross product of the del operator with F. Therefore, we have:

curl(F) = ∇ × F = ( ∂(-4xy)/∂y - ∂(-5xz)/∂z, ∂(yz)/∂z - ∂(4xy)/∂x, ∂(-yz)/∂x - ∂(-5xz)/∂y )

= (-5z, y, -5x)

B) To find the divergence of F, we need to take the dot product of the del operator with F. Therefore, we have:

div(F) = ∇ · F = ∂(-x²)/∂x + ∂(-(x+y)²)/∂y + ∂(0)/∂z

= -2x - 2(x+y)

= -4x - 2y

To find the curl of F, we need to take the cross product of the del operator with F. Therefore, we have:

curl(F) = ∇ × F = ( ∂(0)/∂y - ∂(-(x+y)²)/∂z, ∂(0)/∂z - ∂(-x²)/∂x, ∂(-(x+y))/∂x - ∂(-x²)/∂y )

= (-2(x+y), 0, -2x)

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The volume of a triangular prism in question number 3, obtained from the product of the area of a triangle and the thickness of the prism is 1,728 mi³

A triangular prism consists of two triangular bases and three sides that are rectangular.

The solid in the figure in question number 3 is a triangular prism, with the following dimensions.

Base length = 30 mi.

Thickness (depth of the prism) = 8 mi

Shape of the triangles = Right triangles

Leg lengths of the right triangles = 18 miles and 24 miles

The volume of the triangular prism = Area of the cross section of the triangular prism × Depth of the prism

Area of the triangular cross section of the triangular prism = (1/2) × 18 × 24 = 216 mi²

Volume of the triangular prism = 216 mi² × 8 mi = 1728 mi³

The volume of the triangular prism in the figure is therefore; 1,728 mi³

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Answer:

Step-by-step explanation:

The theorem states that the square on the hypotenuse  (longest side) of a right triangle equal the sum of the squares on the other 2 sides.

Counting the small squares gives us these areas.

We see that

Sum of squares on hypotenuse = 25.

and sum of squares on the other 2 sides = 9 and 16  which equals 25.

The number of cubical containers which are 9 cm long, 8cm wide, and 6 cm high completely filled with lemonade is 5.

volume of lemonade = 2160 cm³

Dimensions of container

L = 9 cm , B = 8 cm , H = 6 cm

Volume of container = L× B × H

Volume of container = 9×8×6

Volume of container = 432 cm³

To find the number of cubical containers filled we use

Number of containers filled = volume of lemonade/volume of the container

putting the value in formula

Number of container filled = 2160/432

Number of container filled = 5

Total number of container filled with lemonade is 5

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