Niamh was driving back home following a business trip.
She looked at her Sat Nav at 17:30
Time: 17:30
Distance: 143 miles
Niamh arrived home at 19:42
Work out the average speed of the car, in mph, from 17:30 to 19:42
You need to show all your working
:)​

The function used to model the monthly profit for x trinkets produced are f(x) = -4(x - 50)(x - 250). The maximum profit occurs when 150 trinkets are produced.

The quadratic function that can be used to model the monthly profit for x trinkets produced is:

f(x) = -4(x - 50)(x - 250)

This is because the function is in the form of a quadratic equation, which is y = ax² + bx + c. In this case, a = -4, b = 1200, and c = 0. When we expand and simplify the equation, we get:

f(x) = -4x² + 1200x

This equation represents a parabola with a maximum value at x = 150. Therefore, the maximum profit occurs when 150 trinkets are produced.

The other answer choices are not correct because they are not quadratic functions. For example, f(x) = (x - 50)(x - 250) is a product of linear factors, and f(x) = 28(x - 50)(x + 250) and f(x) = (x + 50)(x + 250) have a coefficient of x² that is not equal to -4.

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The particular solution is [tex]y(t) = (1/2c) (t^2/2 + t/2 + 1/2c) + (2 - 1/(4c))e^(-2ct)[/tex].

[tex]dy/dt + 2cy = t^2 + 1[/tex]

To find the general solution of this differential equation, we can start by finding the integrating factor, which is given by:

I(t) = e^(∫2c dt) = [tex]e^(2ct)[/tex]

Next, we can multiply both sides of the differential equation by the integrating factor I(t):

[tex]e^(2ct) dy/dt + 2ce^(2ct) y = (t^2 + 1) e^(2ct)[/tex]

We can now recognize the left-hand side as the product rule of the derivative of the product of y and I(t):

[tex](d/dt)(y e^(2ct)) = (t^2 + 1) e^(2ct)[/tex]

Integrating both sides with respect to t gives:

[tex]y e^(2ct) = ∫(t^2 + 1) e^(2ct) dt + C[/tex]

The integral on the right-hand side can be solved using integration by parts, and we get:

∫([tex]t^2[/tex] + 1) [tex]e^(2ct) dt = (1/2c) e^(2ct) (t^2/2 + t/2 + 1/2c) + K[/tex]

where K is an arbitrary constant of integration.

Substituting this expression back into the previous equation, we get:

[tex]y e^(2ct) = (1/2c) e^(2ct) (t^2/2 + t/2 + 1/2c) + K[/tex]

Dividing both sides by e^(2ct), we obtain the general solution:

[tex]y(t) = (1/2c) (t^2/2 + t/2 + 1/2c) + Ke^(-2ct)[/tex]

where K is an arbitrary constant.

To find the particular solution that satisfies y(0) = 2, we can substitute t = 0 and y(0) = 2 into the general solution and solve for K:

[tex]y(0) = (1/2c) (0^2/2 + 0/2 + 1/2c) + Ke^(0)[/tex]

2 = 1/(4c) + K

Solving for K, we get:

K = 2 - 1/(4c)

Substituting this value of K back into the general solution, we get the particular solution:

[tex]y(t) = (1/2c) (t^2/2 + t/2 + 1/2c) + (2 - 1/(4c))e^(-2ct)[/tex]

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The value of x is  17.5 when the given diagonals of square ABCD points intersect at M and the measure 0f <MAD = 6x-15.

The diagonals are perpendicular bisectors of each other in a square and they intersect at the center of the square. By using diagonals we can divide the square into four congruent right triangles and assume that diagonals are all right angles (90 degrees).

let us consider the angle MAD as one of these angles. we can find the value of x by using the equation

6x - 15 = 90

6x = 105

x = 105/6

= 17.5.

Therefore, the value of the x is 17.5.

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The complete question is,

Given the diagonals of square ABCD points intersect at M: If the measure 0f <MAD = 6x-15, find the value of x Show the work that justifies your answer: M B Your answer

Answer:

[tex] \sqrt{125 {p}^{2} } = p \sqrt{25} \sqrt{5} = 5p \sqrt{5} [/tex]

D is the correct answer.

The system of inequalities that has a solution set that is a line is [x + y ≥ 3; x + y ≤ 3]; option A

A system of inequalities is a set of two or more inequalities that are solved simultaneously to find the values of variables that satisfy all the inequalities in the system.

Considering the given system of inequalities:

The system of inequalities that has a solution set that is a line is:

[x + y = 3;]

This is because the solution set of this equation is a line with slope -1 passing through the point (3, 0) and (0, 3).

Therefore, the system of inequalities [x + y ≥ 3; x + y ≤ 3] has a solution set that is a line.

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The pool has approximately 258.2 square feet of plastic material. Rounded to the nearest tenth, the answer is 258.2 square feet.+

To calculate the surface area of the pool that is lined with plastic material, we need to find the area of the curved part and the area of the top and bottom circles.

First, let's find the radius of the pool, which is half of the diameter:

radius = 11 feet / 2 = 5.5 feet

The curved part of the pool is a cylinder with a height of 2 feet and a circumference of [tex]2 * π *radius:[/tex]

curved area = height * circumference

[tex]curved area = 2 feet * 2 * 3.14 * 5.5 feet[/tex]

[tex]curved area = 68.2 square feet[/tex]

The top and bottom of the pool are two circles with a radius of 5.5 feet:

circle area = π * radius²

[tex]circle area = 3.14 * 5.5 square feet[/tex]

[tex]circle area = 95.0 square feet[/tex]

To find the total surface area of the pool that is lined with plastic material, we add the area of the curved part and the area of the top and bottom circles:

Total area = curved area + 2 * circle area

Total area = 68.2 square feet + 2 * 95.0 square feet

Total area = 258.2 square feet

The pool has approximately 258.2 square feet of plastic material. Rounded to the nearest tenth, the answer is 258.2 square feet.

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Therefore, the total area of the forest is approximately 43.10 acres.

Area is the measure of the size of a two-dimensional surface or region. It is typically measured in square units, such as square meters (m²) or square feet (ft²). The area of a shape can be calculated by multiplying the length and the width of the shape. Different shapes have different formulas for calculating their area, such as the formula for the area of a rectangle, which is length x width, or the formula for the area of a circle, which is πr², where r is the radius of the circle and π is a mathematical constant approximately equal to 3.14159.

Here,

Let's call the total area of the forest "T".

We know that 25 acres of the forest is covered by coniferous trees. Therefore, the remaining area of the forest is:

T - 25

We also know that the shrubs and bushes constitute 42% of the total area of the forest. This means that:

0.42 x T = area covered by shrubs and bushes

Putting it all together, we can set up the following equation:

T = 25 + (0.42 x T)

Simplifying, we can solve for T:

0.58 x T = 25

T = 25 / 0.58

T = 43.10 acres (rounded to two decimal places)

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The value of the [tex]5000^{th}[/tex] term in the given arithmetic sequence K is 44995.

The sequence that is given in the question is said to be an arithmetic sequence which means the consecutive elements in the series will have common differences.

To find any term in the series first, we need to find the first term and the common difference that the series follows.

Here we know that the first and the second term of the series are 4 and 13 so from this we can find the common difference which is:

13-4=9

so the first term (a) = 4

the common difference (d) = 9

To find the [tex]n^{th}[/tex] term of the series we can use the formula:

[tex]a_n=a_1+(n-1)*d[/tex]

where [tex]a_n[/tex] is the nth term in the sequence, [tex]a_1[/tex] is the first term of the series, n is the no.of term, and d is the common difference.

So to find the 5000th term in the series

[tex]a_{5000}=4+(5000-1)*9\\a_{5000}=4+(4999*9)\\a_{5000}=4+ 44991\\a_{5000}= 44995\\[/tex]

The value of the [tex]5000^{th}[/tex] term is 44995

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The value of (f + g)(−3) given the functions f(x) = x² − 6x − 4 and g(x) = 5x + 3 is 11.

To find (f + g)(-3), we first need to add the functions f(x) and g(x) together, and then evaluate the resulting function at x = -3.

f(x) = x² - 6x - 4
g(x) = 5x + 3

Now, let's add f(x) and g(x):

(f + g)(x) = (x² - 6x - 4) + (5x + 3) = x² - x - 1

Now that we have the combined function, we can evaluate it at x = -3:

(f + g)(-3) = (-3)² - (-3) - 1 = 9 + 3 - 1 = 11

So, (f + g)(-3) = 11.

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The length of chord segment EG = 6 inches and the length of FG = √23 inches.

Given, chord EG = 8 inches and the distance from the center of J to the chord is 3 inches.

We can draw a diagram as follows:

              J

            /   \

           /     \

          /       \

         /         \

        E-----------G

              |

              |

              |

              |

              |

              F

Here, OJ is perpendicular to chord EG at point F.

As per the theorem, the length of the perpendicular from the center of the circle to a chord is half the length of the diameter intersecting the chord.

So, we can find the length of the diameter intersecting chord EG and then use it to find the radius of the circle.

Length of chord EG = 8 inches

Length of OJ = 3 inches

Using Pythagorean theorem in right triangle OFG, we get:

OG² = OF² + FG²

Let x be the length of FG

We know that OF = OJ = 3 inches

OG = radius of the circle

So, we have:

radius of circle = OG = √(OF² + FG²) = √(3² + x²)

The diameter of the circle = 2(radius) = 2√(3² + x²)

Now, using the theorem mentioned above, we can say:

Length of perpendicular from the center of the circle to chord EG = OF = 3 inches

Length of diameter intersecting chord EG = 2√(3² + x²)

So, we get:

Length of chord segment EG = 2 * length of perpendicular

                            = 2 * 3 inches

                           = 6 inches

Now, we know that the chord segment EG divides the diameter intersecting it into two equal parts.

So, we have:

Length of one part of the diameter = (2√(3² + x²))/2 = √(3² + x²)

Using Pythagorean theorem in right triangle OJF, we get:

OJ² + JF² = OF²

3² + JF² = 8²

JF² = 8² - 3² = 55

JF = √55

Using Pythagorean theorem in right triangle JFG, we get:

JG² + FG² = JF²

(√(3² + x²))² + x² = 55

9 + x² + x² = 55

2x² = 46

x² = 23

x = √23

Therefore, the length of chord segment EG = 6 inches and the length of FG = √23 inches.

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Answer:

8 people

Step-by-step explanation:

Tea- 13 people

Coffee- 12 people

Neither- 3 people

20 - 3 = 17

12 + 13 = 25

25 - 17 = 8

Part A:

The definition provided for a circle is actually correct. However, if we change the definition slightly to say that a circle is the set of all points in a plane that are the same distance from a given point, we can find an example that contradicts it.

For instance, consider a cone in three-dimensional space. If we take a cross-section of the cone that is parallel to the base, we get a circle. However, this circle is not the set of all points that are the same distance from one given point, but rather from the axis of the cone.

To make the definition more accurate, we need to specify that the circle exists in a plane.

Part B:

An example of an undefined term related to a circle is the term "point." A circle is defined as the set of all points that are the same distance from a given point, but the term "point" is not defined within this definition.

A point is typically defined as a location in space that has no size or shape. In the context of a circle, a point can be thought of as any location on the circumference of the circle. However, it is important to note that the definition of a point is not dependent on the definition of a circle, and vice versa.

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The probability of choosing randomly with replacement an H or P in either selection is derived to be equal to 0.16 which makes the last option correct.

The probability of an event occurring is the fraction of the number of required outcome divided by the total number of possible outcomes.

The total possible outcome = 5

the event of selecting H = 1

probability of selecting H= 1/5

the event of selecting P = 2

probability of selecting H= 2/5

probability of choosing an H or P in either selection = 1/5 × 2/5 + 2/5 × 1/5

probability of choosing an H or P in either selection = 4/25

probability of choosing an H or P in either selection = 0.16

Therefore, the probability of choosing randomly with replacement an H or P in either selection is derived to be equal to 0.16

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To get a number greater than 5,but less than 0, Peter can use the mathematical symbol of a decimal point (.) to solve this puzzle.

If Peter places decimal point between 5 and 9, he can get a number like 5.1, 5.2, 5.3... up to 8.9, which meets the conditions of being greater than 5 but less than 9.

A decimal point (.) is a mathematical symbol. When this decimal point is placed in between two numbers, suppose x and y, then x.y means x.y is greater than x and less than y.  

So to solve the puzzle, Peter can use decimal point.

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The system of equations is:

Revenue from balcony seats = $10 × B

Revenue from main floor seats = $25 × M

Total revenue = $6250

B = 3M + 20

Let's define the following variables:

B = number of balcony seats sold

M = number of main floor seats sold

We know that the price of a balcony seat is $10 and the price of a main floor seat is $25.

From the given information, we can create the following equations:

The total revenue from balcony seats sold (B) is given by: Revenue from balcony seats = $10 × B

The total revenue from main floor seats sold (M) is given by: Revenue from main floor seats = $25 × M

The total revenue from the afternoon performance is $6250: Total revenue = Revenue from balcony seats + Revenue from main floor seats

The number of balcony seats sold (B) is 20 more than 3 times the number of main floor seats (M): B = 3M + 20

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The containment area is shrinking at a rate of 280π m²/min when the diameter is 80m and the radius is decreasing at a constant rate of 7m/min.

Let's begin by first finding the radius of the containment area when its diameter is 80m.

The diameter of the containment area is 80m, so its radius is half of that:

[tex]r = 80m / 2 = 40m[/tex]

Now, we need to find the rate at which the containment area is shrinking when the radius is decreasing at a constant rate of 7m/min.

We can use the chain rule of differentiation to find this rate:

[tex]dA/dt = dA/dr * dr/dt[/tex]

where A is the area of the containment, t is time, r is the radius of the containment, and dA/dt and dr/dt are the rates of change of A and r with respect to time, respectively.

We know that dr/dt = -7 m/min (negative because the radius is decreasing), and we can find dA/dr by differentiating the formula for the area of a circle with respect to r:

A = π[tex]r^2[/tex]

[tex]dA/dr = 2πr[/tex]

So, when r = 40m, we have:

[tex]dA/dt = dA/dr * dr/dt[/tex]

= (2πr) * (-7)

= -280π [tex]m^2[/tex]/min

Therefore, the containment area is shrinking at a rate of 280π m^2/min when the radius is decreasing at a constant rate of 7m/min and the diameter of the containment area is 80m.

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False. Cultural traits that are diffused from one group are not always changed or adopted over time by the people in the receiving culture.

This is because different cultures have their own unique values, beliefs, and practices that may not align with the diffused cultural trait. Additionally, some cultural traits may be seen as a threat to the receiving culture and therefore not adopted.
Moreover, not all diffused elements of culture are successfully integrated into other cultures. Some may be rejected outright, while others may only be partially integrated or adapted to fit the receiving culture. It's important to note that cultural diffusion is a complex and ongoing process that involves a multitude of factors, including social, economic, and political influences, as well as individual attitudes and beliefs.

Therefore, the success of cultural diffusion and integration can vary greatly from one context to another.

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The number of pillows requiring [tex]\frac{2}{3}[/tex] yards that can be made from [tex]3\frac{1}{3}[/tex] yards is 5. Thus the right answer to the given question is C.

Material required for making one pillow = [tex]\frac{2}{3}[/tex] yards

Total material = [tex]3\frac{1}{3}[/tex] yards

To find the number of pillows made we have to divide the material required for one pillow by the total material available to Kevin for making pillows

Number of pillows = [tex]3\frac{1}{3}[/tex] ÷ [tex]\frac{2}{3}[/tex]

=  [tex]\frac{10}{3}[/tex] ÷ [tex]\frac{2}{3}[/tex]

To divide two fractions, we take the reciprocal of the second number and multiply it by the first number.

=  [tex]\frac{10}{3}[/tex] * [tex]\frac{3}{2}[/tex]

= 5

Thus, the number of pillows made is 5.

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20 questions subtraction and addition of fractions only like this:

A recipe calls for 2/3 cup of flour and 1/4 cup of sugar. What is the total amount of flour and sugar needed in fraction?

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The two values of k that satisfy the given equation are approximately 0.1449/t and 1.096/t.

We have the partial differential equation uₜ = 4uₓₓ. Substituting u(x,t) = e¯³ᵗsin(kt) into this equation, we get:

uₜ = e¯³ᵗ(k cos(kt) - 3k sin(kt))

uₓₓ = e¯³ᵗ(-k² sin(kt))

Now, we can compute uₓₓ and uₜ and substitute these expressions back into the partial differential equation:

uₜ = 4uₓₓ

e¯³ᵗ(k cos(kt) - 3k sin(kt)) = -4k²e¯³ᵗ sin(kt)

Dividing both sides by e¯³ᵗ and sin(kt), we get:

k cos(kt) - 3k sin(kt) = -4k²

Dividing both sides by k and simplifying, we get:

tan(kt) - 1 = -4k

Letting z = kt, we can write this equation as:

tan(z) = 4z + 1

We can graph y = tan(z) and y = 4z + 1 and find their intersection points to find the values of z (and therefore k) that satisfy the equation. The first intersection point is approximately z = 0.1449, which corresponds to k ≈ 0.1449/t. The second intersection point is approximately z = 1.096, which corresponds to k ≈ 1.096/t. Therefore, the two values of k that satisfy the given equation are approximately 0.1449/t and 1.096/t.

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Answer: 2100 square feet

Step-by-step explanation:

To solve this question we must add the areas of the two rectangles.

area = length x width

Rect 1:

a = lw

  = 80 x 15 = 1200 square feet

Rect 2:

a = lw

  = 30 x 30 = 900 square feet

so in total, the driveway is 1200 + 900 = 2100 square feet

Answer:

To find the area of the driveway, we need to find the area of both rectangles and add them together.

The area of the first rectangle is:

80 ft x 15 ft = 1200 sq ft

The area of the second rectangle is:

30 ft x 30 ft = 900 sq ft

To find the total area of the driveway, we add the two areas together:

1200 sq ft + 900 sq ft = 2100 sq ft

Therefore, the area of the driveway is 2100 square feet.

The slope of the line through points (6,3) and (12,7) is 2/3.

To find the slope of a line, we use the formula:

Slope = (y2 - y1) / (x2 - x1)

In this case, we have two points: (6, 3) and (12, 7). We can label them as follows:

x1 = 6
y1 = 3
x2 = 12
y2 = 7

Now we can plug these values into the formula:

Slope = (y2 - y1) / (x2 - x1)
Slope = (7 - 3) / (12 - 6)
Slope = 4 / 6
Slope = 2/3

Therefore, the slope of the line through the points (6, 3) and (12, 7) is 2/3.

The slope of a line tells us how steep it is. A positive slope means the line goes up as you move from left to right, while a negative slope means the line goes down. In this case, since the slope is positive (2/3), we know that the line goes up as we move from left to right.

The slope also tells us how much the y-value changes for every one unit of x-value. In this case, for every one unit we move to the right, the y-value goes up by 2/3.

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The height of the trapezoid is 9 yards. Therefore, the correct answer is option b. 9 yd.

To find the height of the trapezoid with the given area and base lengths, we will use the formula for the area of a trapezoid:

Area = (1/2) * (base1 + base2) * height

Here, the area is given as 126 square yards, base1 is 17 yards, and base2 is 11 yards. We need to find the height.

1. Substitute the given values into the formula:

126 = (1/2) * (17 + 11) * height

2. Simplify the equation:

126 = (1/2) * 28 * height

3. To isolate the height, divide both sides by (1/2) * 28:

height = 126 / ((1/2) * 28)

4. Calculate the result:

height = 126 / 14

height = 9

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To maximize the total weight of bass in the lake, we should stock 3000 smallmouth bass and 4666.67 largemouth bass

To maximize the total weight of bass in the lake, we need to find the optimal values of and that will maximize the total weight of the fish.

Let's start by writing an expression for the total weight of the fish in the lake:

Total weight = (weight of a single smallmouth bass) × (number of smallmouth bass) + (weight of a single largemouth bass) × (number of largemouth bass)

Substituting the given expressions for the weight of a single smallmouth bass and largemouth bass, we get:

Total weight = (0.5 + 0.1) × × + (1.2 + 0.2) ×

Simplifying this expression, we get:

Total weight = (0.6) × × + (1.4) ×

To find the optimal values of and that maximize the total weight, we can take the partial derivatives of this expression with respect to and and set them equal to zero:

[tex]∂ \frac{(Total weight)}{∂} = 0.6-0.0002=0[/tex]

[tex]∂ \frac{(Total weight)}{∂} = 1.4-0.0003=0[/tex]

Solving these equations simultaneously, we get:

= 3000

= 4666.67

Therefore, to maximize the total weight of bass in the lake, we should stock 3000 smallmouth bass and 4666.67 largemouth bass.

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Probability or p-vale that the sample mean would differ from the population mean by less than 221 miles in a sample of 56 tires is equals to zero if the manager is correct.

We have data of an operation manager at a tire manufacturing company.

Mean mileage of a tire, [tex] \mu[/tex]

= 37,014 miles

standard deviation, [tex] \sigma[/tex]

= 4617 miles.

Sample size, n = 56

We have to determine the probability that the sample mean would differ from the population mean by less than 221 miles. Using Z-score formula in normal distribution, [tex]\small z= \frac{ \bar x-\mu }{\frac{\sigma }{\sqrt{n}}},[/tex]

Plugging all known values in above formula, [tex]z = \frac{ 221 - 37,014} {\frac{4617}{ \sqrt{56}}}[/tex]

= 59.634

[tex]P( \bar x < 221) = P ( \frac{ \bar x-\mu }{\frac{\sigma }{\sqrt{n}}} < \frac{ 221 - 37,014} {\frac{4617}{ \sqrt{56}}}) \\ [/tex]

=> P ( z < 59.63) = P( \bar x < 221)

Using the Z-distribution table, probability value is equals to 0. Hence, required probability is zero.

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Answer:

Another vehicle has a mass of 1290 kg and uses diesel fuel. 1 L of petrol has a mass of 737 g. 1L of diesel has a mass of 820g.

The speed of Fred's snowmobile was 30 miles per hour.

This is calculated by dividing the distance traveled by the time taken for each journey, which gives a speed of 30 mph for both the outward and return journeys.

To find Fred's speed, we can use the formula speed = distance/time. We know that Fred traveled a distance of 360 miles in 12 hours on the outward journey, so his speed was 360/12 = 30 mph.

Similarly, on the return journey, he traveled the same distance of 360 miles, but it took him 15 hours, so his speed was again 360/15 = 24 mph.

However, we are asked to find his constant speed, so we take the average of the two speeds, which gives us (30 + 24)/2 = 27 mph. Therefore, Fred's snowmobile was traveling at a constant speed of 30 mph on both journeys.

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Answer:

b=18.7

Step-by-step explanation:

sin112°/37=sin28°/b

b=sin28°/(sin112°/37)

b=18.7

Applying the triangle inequality theorem, the possible length of side AC is: C. 18 inches.

The triangle inequality theorem states that lengths of the two sides of a triangle, when added together must be greater than the third side of any given triangle.

Therefore, to determine the possible length of side AC, we can use the triangle inequality theorem, stated above and applying this to triangle ABC, we have the following:

AC < AB + BC

AC < 12 + 20

AC < 32

This implies that, length of side AC must be less than 32 inches. Thus, the answer is: C. 18 inches.

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The time it will take the flight is C) 5 hours.

To solve this problem, we can use the formula: distance = rate x time. In this case, we know that the distance is 1500 miles and the rate (or speed) is 300 miles per hour. We can rearrange the formula to solve for time: time = distance / rate. Plugging in the values we have, we get:

time = 1500 miles / 300 miles per hour
time = 5 hours

Therefore, the correct answer is C. It will take Penny 5 hours to fly from her starting point to Palawan at an average speed of 300 miles per hour. This calculation assumes that the plane maintains a constant speed throughout the entire flight, which may not be the case due to factors such as wind and turbulence.

Learn more about speed here: https://brainly.com/question/27888149

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