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Answer:

405mm^3

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Answer:

405

Step-by-step explanation:

There are 17 one-dollar coins and 19 two-dollar coins in the machine.

4.3.1 Model the statement into two linear equations by letting the number of one-dollar coins to be x and the number of two-dollar coins to be y:

Let x be the number of one-dollar coins and y be the number of two-dollar coins in the machine. Then we can form the following two linear equations:

Equation 1: x + y = 36 (total number of coins)

Equation 2: 1x + 2y = 55 (total value of coins)

4.3.2 Solve the two equations you formed in 4.3.1 using Cramer’s rule to find the number of coins of each value:

To solve the two equations using Cramer's rule, we need to write them in matrix form:

| 1 1 | | x | | 36 |

| | x | | |

| 1 2 | | y | | 55 |

Using Cramer's rule, we first calculate the determinant of the coefficient matrix:

D = | 1 1 |

| 1 2 |

D = (1 x 2) - (1 x 1) = 1

Then we replace the first column of the coefficient matrix with the constants from the right-hand side of the equations:

Dx = | 36 1 |

| 55 2 |

And calculate the determinant of this matrix:

Dx = (36 x 2) - (55 x 1) = 17

Similarly, we replace the second column of the coefficient matrix with the constants from the right-hand side of the equations:

Dy = | 1 36 |

| 1 55 |

And calculate the determinant of this matrix:

Dy = (1 x 55) - (1 x 36) = 19

Finally, we can calculate the values of x and y using the formulas:

x = Dx / D = 17 / 1 = 17

y = Dy / D = 19 / 1 = 19

Therefore, there are 17 one-dollar coins and 19 two-dollar coins in the machine.

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The price of an item that is normally £120 after a 20% discount is £96.

To find the price of an item that is normally £120 after a 20% discount,

Calculate the discount amount: To find the discount amount, multiply the original price (£120) by the discount rate ( 20% ) in decimal form:

Discount amount = Original price x Discount rate

= £120 x 0.2

= £24

Calculate the sale price: To find the sale price, subtract the discount amount from the original price:

Sale price = Original price - Discount amount

= £120 - £24

= £96

Therefore, the sale price is £96

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Option (d) is correct i.e., y | −5 ≤ y ≤ −1 , for this we have to know the concept of range and coordinates.

In mathematics, a function's range can refer to one of two closely related ideas: The function's codomain a    representation of the action A binary relation f between two sets P and Q is a function if there is exactly one y in Q such that f connects x to y for every x in P .

In geometry, a coordinate     system is a method for determining how to place points or other geometrical     objects on a manifold, such Euclidean space, uniquely using one or more numbers, or coordinates.

The range of a function is the    set of all values that f can produce for all the x-axis in the domain.

If we are given the graph, in order to find     the range, we project the graph into the y-axis.     Informally, we draw the "shadow" of the graph into the y axis as in the FIGURE attached.

Option (d) is   correct i.e., y | −5 ≤ y ≤ −1 .

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Answer:

B AND C

Step-by-step explanation:

B AND C ARE THE CORRECT MULTIPLES 40

Answer:

2 and 6

Step-by-step explanation:

2 and 6 is the correct option

i.    π/4

ii.  -0.529

1. Evaluate each expression. Give your answer in radians:

i. Without using a calculator: cos⁻¹(−√2/2)Firstly, let us discuss the meaning of the inverse cosine function. The inverse cosine function is the angle (in radians) that corresponds to the cosine value of the input angle. The inverse cosine function returns values in the range [0, pi].cos⁻¹(−√2/2) can be read as "what angle has a cosine of -√2/2?"In a right-angled triangle with angle θ, adjacent is -1, hypotenuse is √2, and opposite is -1. Therefore, we can write the cosine ratio as adjacent over hypotenuse or -1/√2. Let us now solve for θ using the formula for cosine:cosθ = adjacent/hypotenusecosθ = -1/√2θ = cos⁻¹(-1/√2)The exact value of cos⁻¹(-1/√2) is π/4. Therefore, cos⁻¹(-√2/2) = π/4.

ii. Use a calculator: sin^-1(-0.512)As previously mentioned, the inverse sine function is the angle (in radians) that corresponds to the sine value of the input angle. The inverse sine function returns values in the range [-π/2, π/2].sin⁻¹(-0.512) can be read as "what angle has a sine of -0.512?" To find this value, we use a calculator. First, we press the "sin⁻¹" button or "2nd" + "sin" button. Then, we enter the value we want to find, which is -0.512. The final answer is -0.529. Therefore, sin⁻¹(-0.512) = -0.529.

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The value of m, n and w are 92, 48 and 88 respectively

A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon( 3sided polygon). The sum of angles In a polygon is 180. i.e A+B +C = 180

In the triangle above, The triangle is divided into two.

42+36+w = 180

88+w = 180

w = 180 - 88

w = 92°

From the law of the law of exterior angle of a triangle which states that; The exterior angle of a triangle is equal to the sum of opposite angles.

Therefore;

92 = n + 44

n = 92-44

n = 48°

w = 180-92( angles on a straight line)

w = 88°

Therefore the value of m, n, w are 92, 48 and 88 respectively

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Answer: 7.33%

Step by step explanation:

CP of 50 glasses = Rs. 1500

4 glasses broken

Glass remaining = 50 - 4 = 46

Selling price of 1 glass = Rs 35

SP of 46 glass = 46 x 35 = Rs 1610

Profit = SP - CP   = 1610 - 1500  = 110

Profit percentage,

= Profit/CP x 100%

= 110/1500 x 100%

= 7.33%

The cost price of 50 glasses = Rs.1500

The remaining glasses = 46

The Selling price of remaining glasses = 46 × 35

=Rs. 1610

Now

Profit = 1610 - 1500

= Rs.110

Now

Profit Percent

[tex] \frac{Profit}{CP} \times 100%[/tex]

[tex] \frac{110}{1500} \times 100%[/tex]

= 7.33%

The stock price of corporation is [tex]45[/tex]%, [tex]34[/tex] and [tex]20[/tex] correspondingly for the absolute change in the dollar and the Ms dollar.

It is the latest trading price for a stock or some other security. Inside an market, the place to start is the current price. It demonstrates the cost that a both parties would be willing to pay for a subsequent deal involving that security.

(a) The absolute change in dollars in the Apple stock price is:

[tex]109 - 75 = 34[/tex]

(b) The absolute change in dollars in the Microsoft stock price is:

[tex]47 - 27 = 20[/tex]

(c) The relative change in the Apple stock price, rounded to the nearest percent is: [tex]((109 - 75)/75) * 100 = 45[/tex]%

(d) The relative change in the Microsoft stock price, rounded to the nearest percent is: [tex]((47 - 27)/27) * 100 = 74[/tex]%

(e) If you invested $[tex]5,000[/tex] in Apple stock on January 1, 2013, and the price per share was $[tex]75[/tex], you could buy: [tex]5,000/75 = 66.67[/tex] shares

Rounded down to the nearest whole number, you would be able to buy [tex]66[/tex] shares.

(f) If you sold all [tex]66[/tex] shares of Apple stock at the price of $[tex]109[/tex] per share at the end of two years, the total amount from the sale would be:

[tex]66 shares * $109/share = 7,194[/tex]

(g) If you invested $[tex]5,000[/tex] in Microsoft stock on January 1, 2013, and the price per share was $[tex]27[/tex], you could buy: [tex]5,000/27 = 185.19[/tex] shares

Rounded down to the nearest whole number, you would be able to buy  [tex]185[/tex] shares.

(h) If you sold all [tex]185[/tex] shares of Microsoft stock at the price of $[tex]47[/tex] per share at the end of two years, the total amount from the sale would be:

[tex]185 shares * 47/share = 8,695[/tex]

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Answer:

Hello, your answer is 10

Step-by-step explanation:

Have a good day UwU

Step-by-step explanation:

A square has all the sides equal

If AD which is a side is 11, all other sides are 1

BC is 11

AC is a diagonal that divides the square and forms a triangle

AD =11

CD =11

Use Pythagoras theorem to find AC which is hypotenuse

AC² = AD² + CD²

= 121 + 121

=242

If AC² = 242, then AC is square root of 242

AC = 15.56 (approximate if required) 15.6 to 1d.p if required

BD = AC = 15.56

EC is half of BD and AC = 15.56/2

EC = 7.78 (check the decimal place required) 7.8 to 1d.p if required

Angle DAB is 90

Angle AEB is 90

Angle CBD is 45

Angle BAC is 45

(Add the units)

Quadrilateral C with 4 congruent sides is a square, all opposite sides are congruent

Quad L is a parallelogram, consecutive angles are supplementary and opposite angles are congruent

Answer: Let's start by using algebra to solve the problem.

Let's call the width of the rectangle "w". Then we know that the length of the rectangle is twice the width, or "2w".

The formula for the perimeter of a rectangle is:

P = 2l + 2w

where P is the perimeter, l is the length, and w is the width.

We know that the perimeter is 18 inches, so we can substitute the values we have:

18 = 2(2w) + 2w

Simplifying:

18 = 4w + 2w

18 = 6w

Dividing both sides by 6:

w = 3

So the width of the rectangle is 3 inches.

To find the length, we can use the fact that it is twice the width:

l = 2w = 2(3) = 6

So the length of the rectangle is 6 inches.

Therefore, the rectangle is 6 inches long and 3 inches wide.

enjoy!

Answer:  A^2 + B^2 = C^2

Step-by-step explanation:

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There is no one definite answer.

Given information: If 3 −2√5 and 6 + ???? are roots of P(x), what other numbers must also be roots?To find out the other roots of P(x), we have to make use of the Fundamental theorem of algebra which states that every polynomial of degree n has n roots, both real and complex.In order to find out the other roots, we have to divide the polynomial P(x) by its given roots i.e (x-(3-2√5))(x-(6+????)) = 0Let's begin by solving the first root:Since, If 3 −2√5 is the root, thus we can write, x - (3 - 2√5) = 0Or, x - 3 + 2√5 = 0Or, x = 3 - 2√5Similarly, for the second root, 6 + ???? ,

we can write: x - (6 + ???? ) = 0Or, x = 6 + ????Now, Let's combine these two roots and write the polynomial in factored form. Using these two roots, we can write the equation as below: Thus, P(x) = (x - 3 + 2√5)(x - 6 - ???? ) = 0We have found the other roots to be: Other roots = (x - 3 + 2√5)(x - 6 - ???? ) = 0Where ???? can be any value. Therefore, there is no one definite answer.

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In a case whereby Filipe bought a classic car, originally valued at $60,000, in 2012. whee  the value of the car depreciates exponentially at a rate of 4% the expected value of Filipe's car after 6 years is $46970

Based on the given information, the future value when there is a depreciation can be calculated using the formular below:

FV =[ P (1 - r)^n]

where the

R  represent the rate of depreciation =4%  = 0.04

N represent the number of years =  6 years

FV represent the Future value

P represent the Present value

From the formula we can input the values as :

$60,000 x ( 1 - 0.04)^6 = $42,890

=$46965.5

=$46970 (rounded up)

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The confidence interval would increase because with fewer people, the margin of error would be larger.

The confidence interval found in part c would increase if fewer than 95 people were surveyed. This is because the margin of error is calculated using the sample size; the smaller the sample size, the larger the margin of error. The margin of error dictates the range of values that the population parameter is likely to fall within. Therefore, if fewer people are surveyed, the margin of error would increase, resulting in a wider confidence interval. This means that the interval from part c would no longer be valid if the sample size decreased, and a new interval with a larger range would need to be calculated.

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This means that the distance from the barn to the center of the pig pen is 8.75 yards.

Distance is the amount of space between two points or objects. It is commonly measured in linear units such as meters, feet, or miles. Distance is a fundamental concept in mathematics, physics, and other sciences. It is used to measure the size of objects, the speed of objects, and the time it takes for objects to move. Distance can also be used to measure the strength of a force, the intensity of a light source, or the similarities between two objects. Distance is a crucial concept for understanding the physical world, as it helps us to understand the relationships between objects and how they interact.

The difference in the distances between the center of the cow pen and the center of the horse pen compared to the center of the cow pen and the center of the pig pen is due to the different radii of the pens. Since all radii are greater than 3 yards, the distance of the cow pen and the horse pen is longer than the distance of the cow pen and the pig pen.

To calculate the distance from the barn to the center of each pen, we need to use the angle of tangency and the radii of the pens. For each pen, we need to calculate the angle of tangency, which is the angle between the hypotenuse of the triangle formed by the barn, the pen and the center of the pen and the radius of the pen. This can be calculated by either the Law of Cosines or the Law of Sines.

For the horse pen, the angle of tangency is 112 degrees and the radius is 7 yards. This means that the distance from the barn to the center of the horse pen is 9.5 yards. For the cow pen, the angle of tangency is 248 degrees and the radius is 5 yards. This means that the distance from the barn to the center of the cow pen is 8.75 yards. Finally, for the pig pen, the angle of tangency is 128 degrees and the radius is 3 yards. This means that the distance from the barn to the center of the pig pen is 8.75 yards.

Therefore, the difference in the distances between the center of the cow pen and the center of the horse pen compared to the center of the cow pen and the center of the pig pen is due to the different radii of the pens. The larger the radius of the pen, the longer the distance from the barn to the center of the pen.

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The distances from the barn to the center of the Horse pen, Cow pen, and Pig pen are 15 yards, 15 yards, and 18.35 yards respectively.

Distance is the amount of space between two points or objects. It is commonly measured in linear units such as meters, feet, or miles. Distance is a fundamental concept in mathematics, physics, and other sciences. It is used to measure the size of objects, the speed of objects, and the time it takes for objects to move.

First, let's start with the Horse pen. To find the distance from the barn to the center of the Horse pen, we'll use the law of cosines. The law of cosines states that for a triangle ABC, with angle A being 90°, the following equation can be used to find the length of side a:

a² = b²+ c² - 2bc cosA

Therefore, for our triangle, with angle A being 90°, we have:

a²= 15² + 10² - 2(15)(10)cos90

a²= 225 + 100 - 300

a²= 25

a = √25

a = 5

Now, we can find the distance from the barn to the center of the Horse pen by adding the distance from the center of the pen to the barn, which is 10 yards, to 5 yards, which is the distance from the barn to the center of the Horse pen.

Therefore, the distance from the barn to the center of the Horse pen is 10 + 5 = 15 yards.

Now, let's find the distance from the barn to the center of the Cow pen. Again, we'll use the law of cosines. The law of cosines states that for a triangle ABC, with angle A being 90°, the following equation can be used to find the length of side a:

a² = b²+ c² - 2bc cosA

Therefore, for our triangle, with angle A being 90°, we have:

a²= 15² + 9.5² - 2(15)(9.5)cos90

a²= 225 + 90.25 - 285.75

a²= 30.25

a = √30.25

a = 5.5

Now, we can find the distance from the barn to the center of the Cow pen by adding the distance from the center of the pen to the barn, which is 9.5 yards, to 5.5 yards, which is the distance from the barn to the center of the Cow pen.

a²= b²+ c²- 2bc cosA

Therefore, for our triangle, with angle A being 90°, we have:

a²= 16² + 8.75² - 2(16)(8.75)cos90

a²= 256 + 76.5625 - 240

a² = 92.5625

a = √92.5625

a = 9.6

Now, we can find the distance from the barn to the center of the Pig pen by adding the distance from the center of the pen to the barn, which is 8.75 yards, to 9.6 yards, which is the distance from the barn to the center of the Pig pen.

Therefore, the distance from the barn to the center of the Pig pen is 8.75 + 9.6 = 18.35 yards.

In conclusion, the distances from the barn to the center of the Horse pen, Cow pen, and Pig pen are 15 yards, 15 yards, and 18.35 yards respectively.

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Answer:

-77

Step-by-step explanation:

What is Radical? The radical of a number is the same as the root of a number. The root can be a square root, cube root, or in general, nth root. Thus, any number or expression that uses a root is known as a radical. The term radical is derived from the Latin word Radix which means root.

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Answer: x=9

Step-by-step explanation:

Simplify the expression

Add 777 to both sides

Simplify the expression

Divide both sides by the same factor

Simplify the expression

Answer:

290 feet/minute

Step-by-step explanation:

2320/9 = 290

4350/15 = 290

Answer:

Length - 12 m, width - 8m, height - 4 m

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

The relation between dimensions of the box:

Use volume equation and find the value of l:

Find the width and height:

The length of BC is 6 units.

In geometry, the tangent is commonly used to describe the relationship between a circle and a straight line. A tangent line to a circle is a line that intersects the circle at exactly one point. This point of intersection is called the point of tangency. The tangent line is perpendicular to the radius of the circle at the point of tangency.

By the tangent-secant theorem, we have:

PB^2 = PA(PA + AB)

where AB is the length of the tangent segment from point A to the point of intersection of the secant with the circle.

Substituting the given values, we get:

4^2 = 8(8 + AB)

Simplifying and solving for AB, we get:

16 = 64 + 8AB

8AB = -48

AB = -6

Since AB is a length, it must be positive, so we take the absolute value:

AB = 6

Now we can use the secant-tangent theorem to find the length of BC:

PC(PC + BC) = PB^2

Substituting the given values and using the fact that PC = PA = 8, we get:

8(8 + BC) = 4^2

64 + 8BC = 16

8BC = -48

BC = -6

Again, since BC is a length, it must be positive, so we take the absolute value:

BC = 6

Therefore, the length of BC is 6 units.

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The time it takes for the beanbag to reach the ground is t = 1 second.

What is quadratic equation ?

A quadratic equation is a expression of the form ax^{2} + bx + c = 0, where x is the variable, and a, b, and c are constants. It is a type of second-degree polynomial equation, which can be solved using various methods, including factoring, completing the square, and using the quadratic formula

We know that the beanbag will touch the ground when its height, h, equals zero. Therefore, we can set the equation for h equal to zero and solve for t:

h = -16t² + 14t + 2

0 = -16t²  + 14t + 2 (substitute h=0)

0 = -8t²  + 7t + 1 (divide both sides by 2)

0 = (t-1)(-8t-1) (factor the quadratic)

So, either t - 1 = 0 or -8t - 1 = 0. Solving for t in each case, we get:

t - 1 = 0 => t = 1

-8t - 1 = 0 => t = -1/8

The negative value of t doesn't make sense in this context, since time cannot be negative. Therefore, the time it takes for the beanbag to reach the ground is t = 1 second.

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Answer:

y = 0

Step-by-step explanation:

the 2 points (- 1, 0 ) and (0, 0 ) both have the same y- coordinate.

this indicates the line is horizontal with equation

y = c ( c is the value of the y- coordinates the line passes through )

both points have a y- coordinate of 0 , then

y = 0 ← equation of line

The perimeter of the quarter circle with radius 1 yard is approximately 2.57 yards.

To find the perimeter of a quarter circle, we need to add up the lengths of its curved edge and its straight edge.

In this case, the curved edge is a quarter of a circle with radius 1 yard. The formula for the circumference of a circle is C = 2πr, where r is the radius of the circle. Since we only need a quarter of the circumference, we can divide the formula by 4:

C = (2πr)/4

Substituting r = 1, we get:

C = (2π(1))/4

C = π/2

Therefore, the curved edge of the quarter circle has a length of π/2 yards. The straight edge of the quarter circle is simply the radius, which is also 1 yard.

So the perimeter of the quarter circle is the sum of the curved edge and the straight edge:

Perimeter = (π/2) + 1

Using 3.14 for π and adding the two terms, we get:

Perimeter ≈ 2.57 yards

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