Workers in an office of 60 staff were asked their favourite type of take-away.

The results are summarised in the table.


Take-away Frequency Angle

Pizza 3

a

Curry 10

b

Fish & chips 14

c

Kebab 19

d

Other 14

e

Work out the size of each angle to draw a pie chart.

To find the determinant of the given 5x5 matrix A, we need to convert it into an upper triangular form.

This means that all the values below the diagonal elements should be 0. Once we have the upper triangular form, we can find the determinant by taking the product of the diagonal elements.

To convert the given matrix into an upper triangular form, we can use elementary row operations. We can subtract multiples of the first row from the other rows to make the values below the first element 0. Then we can do the same for the second row, third row, and so on until we have an upper triangular matrix.

Once we have the upper triangular matrix, we can find the determinant by taking the product of the diagonal elements. The determinant of the given matrix A is the product of the diagonal elements of the upper triangular matrix.

So the steps to find the determinant of the given matrix A are:
1. Convert the given matrix into an upper triangular form using elementary row operations.
2. Take the product of the diagonal elements of the upper triangular matrix to find the determinant.

By following these steps, we can find the determinant of the given 5x5 matrix A.

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Answer:

7.5 inches is equal to 190.5 millimeters (mm).

To convert from inches to millimeters, we can use the conversion factor of 1 inch = 25.4 millimeters.

So, 7.5 inches x 25.4 millimeters/inch = 190.5 millimeters.

Answer:

Since TS is a tangent to the circle PQRS, we know that the tangent line is perpendicular to the radius that intersects the point of tangency, which is S in this case.

Let O be the center of the circle. We can draw a radius from O to S, which intersects TS at point T, forming a right triangle OST.

Since /PR/-/PS/, we know that angles PSR and PRS are acute angles, which means that angle PSO is also an acute angle. This means that angle OST is complementary to angle PSO.

So, angle OST = 90 - angle PSO. But we know that angle PSO = angle PQR, since they are both subtended by the same arc PR. Therefore:

angle OST = 90 - angle PSO = 90 - angle PQR = 90 - 17 = 73 degrees.

Therefore, RST = angle TSR = 180 - angle OST = 180 - 73 = 107 degrees.

Step-by-step explanation:

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The intercepts of the line are (-3, 0) and (0, -6/5).

What is intercepts ?

In mathematics, intercepts refer to the points at which a line or curve intersects the x-axis or the y-axis of a coordinate plane.

To find the x-intercept, we need to set y = 0 and solve for x:

2x + 5(0) = -6

2x = -6

x = -3

Therefore, the x-intercept is (-3, 0).

To find the y-intercept, we need to set x = 0 and solve for y:

2(0) + 5y = -6

5y = -6

y = -6/5

Therefore, the y-intercept is (0, -6/5).

Thus, the intercepts of the line are (-3, 0) and (0, -6/5).

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The resulting amount should be zero, indicating that all the money was spent. The unknown quantity in this context is the number of players 'p', which we can solve for by rearranging the equation.

What is Algebraic expression ?

Algebraic expression can be defined as combination of variables and constants.

The amount raised by the lacrosse team is $2080.50.

They rented a bus for $970.50.

For each player, they budgeted $74 for meals.

Let's represent the number of players as 'p'.

The equation that represents the context is:

2080.50 - 970.50 - 74p = 0

Or we can represent it in the tape diagram as follows:

             _______

            |       |

            | $2080.50|

            |_______|

             _______

            |       |

            | -$970.50|

            |_______|

             _______

            |       |

            | -$74p  |

            |_______|

             _______

            |       |

            |   $0   |

            |_______|

This tape diagram shows that the total amount raised by the team was reduced by the cost of the bus rental and the cost of meals for each player.

Therefore, The resulting amount should be zero, indicating that all the money was spent. The unknown quantity in this context is the number of players 'p', which we can solve for by rearranging the equation

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The requried distance formula to calculate the distance between points (x₁, y₁) and (x₂, y₂) is d = √((x₂ - x₁)² + (y₂ - y₁)²)

Distance is defined as the length of measure between two points on the coordinate plane.

Here,
The formula to calculate the distance between two points in a two-dimensional Cartesian coordinate system is:

d = √((x₂ - x₁)² + (y₂ - y₁)²)

Where (x₁, y₁) and (x₂, y₂) are the coordinates of the two points, and sqrt represents the square root function.

This formula is derived from the Pythagorean theorem, which states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.

In this case, the two points represent the endpoints of the hypotenuse, and the distance between them is the length of the hypotenuse. Therefore, we can use the Pythagorean theorem to calculate the distance between the two points.

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The number of seats available in the small jets and large jet are 63 and 81 respectively.

A set of simultaneous equations, also known as a system of equations or an equation system, is a finite set of equations for which common solutions are sought.

Given that, Jasper noticed with 2 small jets and 5 large jets, which could seat a total of 531 passengers and 5 small jets and 5 large jets, which could seat a total of 720 passengers.

Let the number of seats available in the small jets and large jet be x and y,

Establishing the system of equations to solve,

2x+5y = 531......(i)

5x+5y = 720.......(ii)

Subtracting the equation (i) from eq(ii)

3x = 189

x = 63

Put x = 63

5(63)+5y = 720

5y = 405

y = 81

Hence, the number of seats available in the small jets and large jet are 63 and 81 respectively.

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1. (a) The probability that a randomly selected wafer is produced by machine A and not defective is 0.665 or 66.5%.
(b) The probability that a wafer is defective given that it is produced by machine B is 0.06 or 6%.
(c) The probability that a wafer is defective is 0.053 or 5.3%.
(d) The probability that a wafer is 0.947 or 94.7%.

2. (a) The probability that a car requires either a tune-up or a brake job is 0.608 or 60.8%.
(b) The probability that a car requires a tune-up but not a brake job is 0.588 or 58.8%.
(c) The probability that a car requires neither types of repair is 0.392 or 39.2%.
(d) The events "car requires a tune-up" and "car requires a brake job" are independent because the probability of one event occurring does not affect the probability of the other event occurring. They are not mutually exclusive because a car can require both a tune-up and a brake job at the same time.

We can find the probability using this calculation:

The probability that a randomly selected wafer is produced by machine A and not defective is 0.7 x 0.95 = 0.665 or 66.5%.

The probability that a wafer is defective is (0.7 x 0.05) + (0.3 x 0.06) = 0.035 + 0.018 = 0.053 or 5.3%.

The probability that a wafer is not defective is 1 - 0.053 = 0.947 or 94.7%.

The probability that a car requires either a tune-up or a brake job is 0.6 + 0.02 - (0.6 x 0.02) = 0.608 or 60.8%.
(b) The probability that a car requires a tune-up but not a brake job is 0.6 x (1 - 0.02) = 0.588 or 58.8%.
(c) The probability that a car requires neither types of repair is 1 - 0.608 = 0.392 or 39.2%.

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Answer:

-87.786

Step-by-step explanation:

Given:

Acceleration 1 = 3.20 m/s²

Acceleration 2 = 5.41 m/s²

Time = 28 s

To find: Acceleration before takeoff

Initial velocity = Average acceleration x time + 0.5 x acceleration 1 x time²

Initial velocity = 3.20 m/s² x 28 s + 0.5 x 3.20 m/s² x (28 s)²

Initial velocity = 2460.8 m

Acceleration before takeoff = (0 m/s - 2460.8 m/s) / 28 s

Acceleration before takeoff = -87.886 m/s²

Therefore, the acceleration before takeoff is -87.886 m/s².

The number of batches of the recipe Minh makes is 6

A proportion can be described as a mathematical comparison that is between two numbers.

These numbers can represent a comparison between things or people.

Also, proportions can also be written as two equivalent fractions. They are represented with the equality sign '=' or the equivalent sign ':'

From the information given, we have that;

For one recipe, one uses 1/3 cup of sesame seeds

Minh has 2 cups of sesame seeds

Then,

If 1/3 cup of sesame seeds = 1 recipe

Then 2 cups of sesame seeds = x

cross multiply

c = 2 × 3/1

c = 6 recipes

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Answer:

The volume of a sphere with a diameter of 8.6 m = 333.0 m^3

Step-by-step explanation:

Answer:

The volume of a rectangular solid is given by the formula V = LWH, where L is the length, W is the width, and H is the height.

In this case, we have:

W = x + 3

L = x + 2

H = x

So the volume is:

V = (x + 2)(x + 3)(x)

V = x(x + 2)(x + 3)

V = x(x^2 + 5x + 6)

V = x^3 + 5x^2 + 6x

Therefore, the volume of the rectangular solid is given by the polynomial expression x^3 + 5x^2 + 6x.

The triangle is an obtuse triangle.

What is a valid triangle?

A valid triangle is a geometric figure with three sides and three angles. To be considered a valid triangle, it must satisfy the following conditions:

1. The sum of the lengths of any two sides must be greater than the length of the third side. This is known as the Triangle Inequality Theorem, and it ensures that the three sides can form a closed figure.

2. The measure of each angle must be less than 180 degrees. This is known as the Angle Sum Theorem, and it ensures that the three angles can fit inside a two-dimensional plane.

The sum of the angles of any triangle is always 180 degrees.

So, if a triangle has angle measurements of 3°, 35°, and 142°, we can add them up to check whether they add up to 180 degrees:

3° + 35° + 142° = 180°

Since the sum of the angles is 180 degrees, the triangle is a valid triangle.

Now, we can classify the triangle based on the measure of its angles. Since the measure of one angle (142°) is greater than 90 degrees, the triangle is an obtuse triangle.

We cannot determine the length of the sides of the triangle based on the angle measures provided. So, we cannot classify the triangle based on the length of its sides.

Therefore, the triangle is an obtuse triangle.

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The quadratic formula is used to solve  equations of the form ax^(2) + bx + c = 0. The formula is given by:

x = (-b ± √(b^(2) - 4ac))/2a

In this case, the coefficients are a = 9, b = -3, and c = -1. Plugging these values into the formula gives:

x = (-(-3) ± √((-3)^(2) - 4(9)(-1)))/2(9)

Simplifying the expression gives:

x = (3 ± √(9 + 36))/18

x = (3 ± √45)/18

x = (3 ± 3√5)/18

Simplifying further gives:

x = (1 ± √5)/6

So the two solutions to the equation are:

x = (1 + √5)/6 ≈ 0.62

and

x = (1 - √5)/6 ≈ -0.29

Therefore, the two solutions to the equation 9x^(2)-3x-1=0 are x ≈ 0.62 and x ≈ -0.29.

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The slope of the line that passes through the two points is 2.

The equation of the straight line that is inclined at a specific angle to the x-axis and passes at a specific point may be found using the point slope form. A line's equation is an equation that each and every point on the line can solve. Hence, a line may be represented by a linear equation with two variables. Depending on the information at hand, a line's equation can be discovered using a variety of techniques. Among the techniques are: Slope form at a point. Slope-intercept pattern

The equation of the slope is given as:

slope = (change in y-coordinates) / (change in x-coordinates)

Here, for the given condition we have:

slope = (6) / (3) = 2

Therefore, the slope of the line that passes through the two points is 2.

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Answer: C

Step-by-step explanation: What is an example of cubic trinomial?

Cubic Trinomials of the Form Ax^3 + Bx+^2 + Cx

For example, the greatest common factor of the trinomial 3x^3 - 6x^2 - 9x is 3x, so the polynomial is equal to 3x times the trinomial x^2 - 2x -3, or 3x*(x^2 - 2x - 3).

the answer is 6 uniforms. 57/9.5=6

The two linear equations with infinitely many solutions and a y-intercept of -2 are y = x - 2 and y - x = -2.

We can use the y-intercept (-2) and another point on the line to calculate the slope. Since we are looking for infinitely many solutions, we can choose any point. Let's choose the point (0, 1):

slope = (y2 - y1) / (x2 - x1) = (-2 - 1) / (0 - 1) = -3

Now we know that the slope of one of the lines is -3. We can use this information to find the equation of the line. We can use the point-slope form of a linear equation:

y - y1 = m(x - x1)

where m is the slope and (x1, y1) is a point on the line.

Let's use the point (0, -2):

y - (-2) = -3(x - 0)y + 2 = -3xy = -3x - 2y = -3(0) - 2 = -2y = mx - 2y = -3x - 2y = x - 2y - x = -2

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The tank can hold up to average 90,000 gallons of water, since it is already filled with 54,000 gallons and 60% of that is food.

Volume = πr2h

= 3.14 x (15 feet)2 x 18 feet

= 15,444.4 cubic feet

15,444.4 cubic feet x 7.48 gallons/cubic feet = 115,511.17 gallons

115,511.17 gallons - 54,000 gallons = 61,511.17 gallons

61,511.17 gallons + 54,000 gallons = 115,511.17 gallons

115,511.17 gallons is the total capacity of the tank.

The tank is able to hold up to 90,000 gallons of water, since it already contains 54,000 gallons and 60% of that is food. This means that the tank can still hold up to 36,000 gallons of water, giving it a total capacity of 90,000 gallons. This is possible because the tank is in the shape of a cylinder, which means that the volume of the tank is determined by the formula V = πr2h, where V is the volume, r is the radius, and h is the height. This means that the tank can be adjusted accordingly to increase or decrease the amount of water it can hold. In this case, the tank is able to hold up to 90,000 gallons of water because the capacity of the tank is determined by the size of its radius and height, and can be adjusted accordingly to increase or decrease the amount of water it can hold.

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The sum of two consecutive integers 42 and 43  is 85.

The sum of two consecutive integers is 85. This means that we need to find two integers that are next to each other on the number line and add up to 85. We can write this as an equation:
x + (x + 1) = 85

Simplifying the equation gives us:
2x + 1 = 85

Subtracting 1 from both sides gives us:
2x = 84

Dividing both sides by 2 gives us:
x = 42

This means that the first integer is 42. Since the two integers are consecutive, the second integer is 42 + 1 = 43. Therefore, the two integers are 42 and 43.

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This means that for each hour worked, Jean earns $12, and the total earnings y increase linearly with the number of hours x worked.

In mathematics, an equation is a statement that two expressions are equal. It contains an equals sign (=) between two expressions, which are usually composed of variables, constants, and mathematical operations.

For example, the equation:

2x + 3 = 7

states that the sum of two times x and three is equal to seven. This equation can be solved to find the value of x that satisfies it.

Equations can be used to model and solve a wide range of problems in mathematics and science, including algebraic, geometric, and physical problems.

Assuming that Jean earns a fixed hourly rate, we can use the equation:

y = kx

where y is the total earnings, x is the number of hours worked, and k is the hourly rate.

For example, if Jean earns $12 per hour, the equation would be:

y = 12x

This means that for each hour worked, Jean earns $12, and the total earnings y increase linearly with the number of hours x worked.

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Answer: The total height of the SUV and the box is 9 feet 1 inch.

Step-by-step explanation:

To solve this problem, we first convert the height of the SUV and the box from feet and inches to inches. The height of the SUV is 6 feet 4 inches, which is equal to 76 inches. The height of the box is 2 feet 9 inches, which is equal to 33 inches. We then add the heights of the SUV and the box to get the total height:

76 inches + 33 inches = 109 inches

To convert this back to feet and inches, we divide by 12 to get 9, with a remainder of 1. Therefore, the total height of the SUV and the box is 9 feet 1 inch.

The z-statistics for the given situations are 20, 12.5, 18.4766, 1.7775, and 13.6293 respectively.

To calculate the z-statistic (z), we use the formula: z = (X - μ) / (σ / √N),

where X is the observed value,

μ is the mean,

σ is the standard deviation,

and N is the sample size.

A.) X = 8.00; μ = 5; σ = 0.6; N = 16
z = (8.00 - 5) / (0.6 / √16) = 3 / (0.6 / 4) = 3 / 0.15 = 20

B.) X = 4.00; μ = 2; σ = 0.8; N = 25
z = (4.00 - 2) / (0.8 / √25) = 2 / (0.8 / 5) = 2 / 0.16 = 12.5

C.) X = 11.50; μ = 9.25; σ = 0.75; N = 38
z = (11.50 - 9.25) / (0.75 / √38) = 2.25 / (0.75 / 6.1644) = 2.25 / 0.1218 = 18.4766

D.) X = 0.95; μ = 0.82; σ = 0.31; N = 18
z = (0.95 - 0.82) / (0.31 / √18) = 0.13 / (0.31 / 4.2426) = 0.13 / 0.0731 = 1.7775

E.) X = 8.14; μ = 4.69; σ = 1.29; N = 26
z = (8.14 - 4.69) / (1.29 / √26) = 3.45 / (1.29 / 5.099) = 3.45 / 0.2531 = 13.6293

Therefore, the z-statistics for the given situations are 20, 12.5, 18.4766, 1.7775, and 13.6293 respectively.

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We predict that Ed should draw about 1 blue marble out of the 4 draws. The closest option is 1.

What is probability?

Probability is a branch of mathematics in which the chances of experiments occurring are calculated. It is by means of a probability, for example, that we can know from the chance of getting heads or tails in the launch of a coin to the chance of error in research.

There are 4 colors of marbles, each with 8 marbles in the bag, so the probability of drawing a blue marble on any given draw is:

P(blue) = 8/32 = 1/4

Since Ed is drawing 4 marbles with replacement, the probability of drawing a blue marble on each individual draw is the same:

P(blue) = 1/4

The probability of drawing a blue marble exactly k times out of 4 draws can be calculated using the binomial probability formula:

P(k blue out of 4) [tex]= (4 choose k) * (1/4)^k * (3/4)^{(4-k)[/tex]

where (4 choose k) is the binomial coefficient, which gives the number of ways to choose k blue marbles out of 4 draws.

E(number of blue) = Σ(k * P(k blue out of 4)), summed over all possible values of k from 0 to 4.

This calculation can be done directly or by using the formula:

E(number of blue) = n * P(blue)

where n is the total number of draws (4 in this case) and P(blue) is the probability of drawing a blue marble on each draw.

Using this formula, we get:

E(number of blue) = 4 * (1/4) = 1

Therefore, we predict that Ed should draw about 1 blue marble out of the 4 draws. The closest option is 1.

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The missing lengths are AC = 3√2 ≈ 4.23 and AB = 3√2 ≈ 4.23.

To find the missing lengths of ΔABC, we can use the properties of a 45-45-90 triangle. A 45-45-90 triangle is a special type of right triangle in which the two legs are congruent and the angles are 45°, 45°, and 90°. The ratio of the sides in a 45-45-90 triangle is 1:1:√2, where the hypotenuse is √2 times the length of each leg.

Since we are given that BC = 6 and ∠A and ∠B are both 45°, we can conclude that ΔABC is a 45-45-90 triangle. Therefore, the lengths of AC and AB are both equal to the length of BC, which is 6.

AC = 6
AB = 6

To find the lengths in simplest radical form, we can multiply the lengths of AC and AB by √2/√2 to get:

AC = 6 * √2/√2 = 6√2/2 = 3√2
AB = 6 * √2/√2 = 6√2/2 = 3√2

To find the approximations correct to two decimal places, we can use a calculator to find the decimal values of 3√2:

AC ≈ 3 * 1.41 = 4.23
AB ≈ 3 * 1.41 = 4.23

Therefore, the missing lengths are AC = 3√2 ≈ 4.23 and AB = 3√2 ≈ 4.23.

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The graph of the piece-wise function is given by the image presented at the end of the answer.

A piece-wise function is a mathematical function that is defined by different formulas or expressions over different intervals or pieces of its domain, that is, the function has different definitions based on it's input.

The intervals for which the function has different definitions are given as follows:

The definitions for each interval are given as follows:

Hence the graph of the function, containing these three definitions, is given by the image presented at the end of the answer.

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The finance charge on a $15,820 car loan if monthly payments were $325 for 60 months is: $3,680.

The total amount paid over 60 months is:

Total amount paid = $325/month x 60 months

Total amount paid = $19,500

The amount of interest paid is:

Amount of interest = $19,500 - $15,820

Amount of interest = $3,680

Therefore, the finance charge on the car loan is $3,680.

Therefore the finance charge is $3,680.

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The set of vectors of the form (a, 3a, a + b) is not a subspace of R3.

To be a subspace of R3, a set must satisfy the following conditions:
1. The set must be closed under addition.
2. The set must be closed under scalar multiplication.
3. The set must contain the zero vector.

Let's check if the set satisfies these conditions:

1. Closed under addition:
Let u = (a, 3a, a + b) and v = (c, 3c, c + d) be two vectors in the set. The sum of these vectors is u + v = (a + c, 3a + 3c, a + b + c + d). This vector is not in the set because the third component is not of the form a + b. Therefore, the set is not closed under addition.

2. Closed under scalar multiplication:
Let u = (a, 3a, a + b) be a vector in the set and k be a scalar. The scalar multiplication of u and k is ku = (ka, 3ka, ka + kb). This vector is not in the set because the third component is not of the form a + b. Therefore, the set is not closed under scalar multiplication.

3. Contains the zero vector:
The zero vector in R3 is (0, 0, 0). This vector is not in the set because the third component is not of the form a + b. Therefore, the set does not contain the zero vector.

Since the set does not satisfy the conditions to be a subspace of R3, it is not a subspace. Therefore, there is no basis or dimension for this set.

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