It takes Niamh 3 hours to drive from Ashdown to Bridgeton at an average speed of 50 mph.
She then drives 60 miles from Bridgeton to Carton at an average speed of 40 mph.
Assuming Niamh doesn't stop, what is her average speed from Ashdown to Carton to 1 dp?

Answer:

$96.

Step-by-step explanation:

5/6  costs 80

Multiply both parts by 6/5:

5/6 * 6/5 ( = 1 ) costs 80 * 6/5

= 16 * 6

= $96.

To find the largest rectangle with its base on the x-axis that can be inscribed under the graph of y = xcos(x), we need to maximize the area of the rectangle.

The base of the rectangle will lie on the x-axis, so the height of the rectangle will be determined by the function y = xcos(x).

To find the maximum area, we need to locate the critical points of the function xcos(x). We can do this by finding where the derivative of the function equals zero or does not exist.

Taking the derivative of xcos(x) with respect to x, we have:

d/dx (xcos(x)) = cos(x) - xsin(x)

Setting this derivative equal to zero, we get:

cos(x) - xsin(x) = 0

We need to solve this equation to find the critical points.

Unfortunately, there is no exact algebraic solution for this equation. We can use numerical methods or graphing software to approximate the critical points.

Once we have the critical points, we can evaluate the function y = xcos(x) at these points to find the height of the rectangle.

Finally, we can calculate the area of the rectangle by multiplying the base (x-coordinate of the critical points) with the corresponding height (y = xcos(x)).

Answer

how many people where in the class - 15 girls = boys that played basket ball

Step-by-step explanation:

The equation 3x + 4y = 8 can be expressed in slope-intercept form as y = (-3/4)x + 2.

To express the equation 3x + 4y = 8 in slope-intercept form, we need to isolate y on one side of the equation. The slope-intercept form is given by y = mx + b, where m represents the slope and b represents the y-intercept.

Let's rearrange the given equation:

3x + 4y = 8

First, subtract 3x from both sides to isolate 4y:

4y = -3x + 8

Next, divide both sides by 4 to obtain y alone:

y = (-3/4)x + 2

Now, we have the equation in slope-intercept form, y = (-3/4)x + 2.

From this form, we can identify the slope, which is -3/4, and the y-intercept, which is 2. The slope represents the rate of change of y with respect to x, and the y-intercept represents the point where the line intersects the y-axis.

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Answer:

11.571

Step-by-step explanation:

The linear equations that represents the graphed line is y = (2/3)x + 1

The general form of linear equations is given by:

y = mx + c

where m is the slope and c is the y-intercept

The given graph passes through points (0, 1) and (6, 5). Thus, we can say:

c = 1

By definition, slope is given by:

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

where x1 = 0, y1 = 1 and x2 = 6, y2 = 5

m =  (5 - 1)/(6 - 0)

m = 4/6

m = 2/3

Substitute m and c into y = mx + c:

y = (2/3)x + 1

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Answer:

y=10/7x-1/7

Step-by-step explanation:

m=(-3-7)/(-2-5)

m=-10/-7

m=10/7

y-y1=m(x-x1)

y-7=10/7(x-5)

y=10/7x-50/7+7

y=10/7x-50/7+49/7

y=10/7x-1/7

Answer:

The price was $15 per lesson.

Step-by-step explanation:

We have to isolate the x, the cost per lesson. This is how we do so:

70-25 = 45, which is the cost for 3 lessons. Since she paid for enrollment plus three lessons, this takes care of the enrollment part, leaving just the 3 lessons cost, which is 45.

In order to isolate the cost per lesson, we have to divide 45 dollars by 3 lessons, which is 15 dollars per lesson.

The slope of the line of best fit represents: the expected change in temperature in degrees Fahrenheit for each additional cricket chirp in one minute.

A line of best fit simply refers to a statistical tool that is used in conjunction with a scatter plot, in order to determine whether or not there's any association between data points.

A slope is also referred to as the rate of change and it's typically used to describe both the direction, ratio, and steepness of the function of a straight line based on its coordinates or data points.

In this scenario, the slope for the given data is the change in temperature with respect to a unit change in the number of chirps sold.

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Answer:

the time taken for having 1 million bacteria is 137.68 hours  

Step-by-step explanation:

The computation is shown below:

y = 2 × (1.10)^x

1,000,000 = 2 × (1.10)^x

500,000 = (1.10)^x

x = log (500,000) ÷ log (1.10)

= 137.68 hours

hence the time taken for having 1 million bacteria is 137.68 hours  

The correct answer is: 2.8 is greater than 2.58.

A decimal value is a number expressed in the decimal system, which is based on the number ten. It includes a decimal point that separates the whole number part from the fractional part. The digits to the left of the decimal point represent whole numbers, and the digits to the right of the decimal point represent fractional parts of a whole number, which are expressed in powers of ten (tenths, hundredths, thousandths, etc.). For example, in the decimal value 3.14, the digit 3 represents the whole number part, and the digits 1 and 4 represent the tenths and hundredths parts, respectively. Decimal values are commonly used in mathematics, science, and everyday life to represent quantities that are not whole numbers, such as measurements, percentages, and money values.

Given by the question.

because the digit in the tenths place is larger in 2.8 than in 2.58. In decimal notation, the digit immediately to the right of the decimal point represents tenths, and larger values in this place indicate a larger overall value. In this case, 2.8 has a digit of 8 in the tenths place, while 2.58 has a digit of 5 in the tenths place. Therefore, 2.8 is greater than 2.58. The location of the numbers on a number line is not relevant for comparing decimal values, unless they have the same digit in the tenths.

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Answer:

The answer should be -35y + 13x + 14. As you can clearly see, you can't break it down any further than this. That's because y and x are completely different. Plus, 14 isn't part of a variable.

Answer:

107 concert tickets were bought

Step-by-step explanation:

The Kanizsa triangle illusion helps us understand that our perceptual experiences are not simply the sum of the individual sensory inputs, but rather the result of a complex and variable process of perceptual organization.

Gestalt is a German word meaning "shape" or "form," and in psychology, it refers to a set of principles that describe how people perceive and organize sensory information into meaningful wholes. These principles propose that the whole is greater than the sum of its parts, and that we tend to organize our perceptual experiences into coherent, holistic forms rather than isolated, unrelated sensations.

Experimental examples such as the Necker cube, visual cliff, and others help demonstrate principles of perceptual organization by highlighting how our minds naturally try to impose structure and order on sensory input. For example, the Necker cube is a two-dimensional drawing that can be perceived as a cube that can be viewed from different angles. However, as one stares at the image, it appears to flip back and forth between different possible interpretations. This phenomenon illustrates the Gestalt principle of figure-ground, which describes how we tend to perceive objects as being distinct from their surrounding context.

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Answer:

x + y = 500

215x + 615y = 187,500

Step-by-step explanation:

The first equation can show the amount of land.  The farmer has 500 acres to plant corn, x, and cotton, y.

x + y = 500

The second equation can show the cost.  The farmer has $187,500 to invest when corn costs $215 per acre and cotton costs $615 per acre.

215x + 615y = 187,500

The system of equations is

x + y = 500

215x + 615y = 187,500

The correct system of represents this scenario will be,

⇒ x + y = 500

⇒ 215x + 615y = 187,500

Where,' x' is plant acres of corn and 'y' is acres of cotton.

What is an expression?

Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.

Given that;

A farmer has 500 acres to plant acres of corn, x, and acres of cotton, y.

And, Corn costs $215 per acre to produce, and cotton costs $615 per acre to produce. He has $187,500 to invest this season.

Now,

Let us take  'x' is plant acres of corn and 'y' is acres of cotton.

Since, A farmer has 500 acres to plant acres of corn, x, and acres of cotton, y.

So, we can formulate;

⇒ x + y = 500

And, He has $187,500 to invest this season for corn costs $215 per acre to produce, and cotton costs $615 per acre to produce.

So, We can formulate;

⇒ 215x + 615y = 187,500

Thus, The correct system of represents this scenario will be,

⇒ x + y = 500

⇒ 215x + 615y = 187,500

Where,' x' is plant acres of corn and 'y' is acres of cotton.

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(a) The firm is operating in the long run, and its supply function is determined by the profit maximization condition.

(b) The firm's input demand functions can be derived from the profit function, and their degree of homogeneity is 1/2. Changes in input prices will impact the firm's input demand.

(c) The market supply function can be derived by aggregating the supply functions of all 40 firms operating in the market.

(d) Given the market conditions and demand function, the total market supply can be calculated.

(a) The firm is operating in the long run because it has the flexibility to adjust its inputs and make decisions based on market conditions. The firm's supply function is determined by maximizing its profit, which is achieved by setting the marginal cost equal to the market price. In this case, the supply function for each firm can be derived by taking the derivative of the profit function with respect to the price of output (p).

(b) The input demand functions for the firm can be derived by maximizing the profit function with respect to each input price. The degree of homogeneity of the input demand functions can be determined by examining the exponents of the input prices. In this case, the degree of homogeneity is 1/2. Changes in the input prices will affect the firm's input demand as it adjusts its input quantities to maximize profit.

(c) The market supply function can be derived by aggregating the individual supply functions of all firms in the market. Since there are 40 identical firms, the market supply function can be obtained by multiplying the supply function of a single firm by the total number of firms (40).

(d) To determine the total market supply, we substitute the given market conditions and demand function into the market supply function. By solving for the market quantity at a given market price, we can calculate the total market supply.

In conclusion, the firm is operating in the long run, and its supply function is determined by profit maximization. The input demand functions have a degree of homogeneity of 1/2, and changes in input prices impact the firm's input demand. The market supply function is derived by aggregating the individual firm supply functions, and the total market supply can be calculated using the given market conditions and demand function.

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The given function is f(x, y) = x²y². We are to determine if this function has a single global minimum and is relatively easy to minimize or not. To check if a function has a global minimum, we need to take the partial derivative of the function with respect to x and y.

Let's evaluate it.∂f/∂x = 2xy² ∂f/∂y = 2x²y Equating both the partial derivatives to zero, we get;2xy² = 0 => xy² = 0 => x = 0 or y = 0 2x²y = 0 => x²y = 0 => x = 0 or y = 0

Hence, the stationary points are (0,0), (0, y), and (x,0). Let's use the second derivative test to determine if the stationary point (0,0) is a global minimum, maximum, or saddle point.∂²f/∂x² = 2y² ∂²f/∂y² = 2x² ∂²f/∂x∂y = 4xy

The determinant is;∆ = ∂²f/∂x² * ∂²f/∂y² - (∂²f/∂x∂y)² = 4x²y²Since (0,0) is a stationary point, we have ∂f/∂x = 0 and ∂f/∂y = 0 which implies that x = 0 and y = 0, respectively. Thus, ∆ = 0 which means that the second derivative test is inconclusive and we cannot determine if (0,0) is a global minimum, maximum, or saddle point. The given function does not have a single global minimum and is not relatively easy to minimize.

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Answer:

I believe the answer would be m = -28

Step-by-step explanation:

To remove the demoninater, multiple both sides by 7

12*7 = 84 so now you have -3 = 84

Divide 84 by -3, giving you -28

Answer: y = 2(x + 2)² - 5

Step-by-step explanation:

          We are going to use the completing the square method to transform this quadratic equation from standard form to vertex form.

Given:

     y = 2x² + 8x + 3

Factor the 2 out of the first two terms:

     y = 2(x² + 4x) + 3

Add and subtract \(\frac{b}{2} ^2\):

     y = 2(x² + 4x + 4 - 4) + 3

Distribute the 2 into -4 and combine with the 3:

     y = 2(x² + 4x + 4) - 5

Factor (x² + 4x + 4):

     y = 2(x + 2)² - 5

Answer:

86

Step-by-step explanation:

Answer: the answer is 86

Step-by-step explanation:

Answer:

The measure of angle A is 64 degrees

Step-by-step explanation:

To solve this problem let us first find the measure of angle C so it can be easier to solve later. To find angle C you have to use the inscribed angles theorem, which states that an inscribed angle is half the degrees of its corresponding arc. So because angle C's corresponding arc is the measure of AB or 52 you would divide it by two to get  26. After finding angle C we can now find angle a by doing 180-26-90 (You use 180 because a triangle has 180 degrees) to get your answer of 64

Another way to solve this can be found in the attachment.

Answer:

Step-by-step explanation:

\(\frac{4}{5}+\frac{3}{20}\\ \\ \frac{4}{5}\left(\frac{4}{4}\right)+\frac{3}{20}\\ \\ \frac{16+3}{20}\\ \\ \frac{19}{20}\)

Answer:

26

Step-by-step explanation:

2 + 6 = 8

62 - 8 = 54

guess and check

Answer:

0.86 ppg

Step-by-step explanation:

25% of 1.15 = 0.25 × 1.15 = 0.2875

1.15 - 0.2875 = 0.8625

The identified parameters are:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/6 minutes^(-1)

rθ = 1/11 minutes^(-1)

ta: Mean time between calls to the center

tθ: Effective response time

∂a: Standard deviation of the time between calls to the center

∂θ: Standard deviation of the effective response time

ra: Rate of calls to the center (inverse of ta, i.e., ra = 1/ta)

rθ: Rate of effective response (inverse of tθ, i.e., rθ = 1/tθ)

Given information:

Mean time between calls to the center (ta) = 6 minutes

Standard deviation of time between calls (∂a) = 4 minutes

Effective response time (tθ) = 11 minutes

Standard deviation of effective response time (∂θ) = 20 minutes

Using this information, we can determine the values of the parameters:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/ta = 1/6 minutes^(-1)

rθ = 1/tθ = 1/11 minutes^(-1)

So, the identified parameters are:

ta = 6 minutes

tθ = 11 minutes

∂a = 4 minutes

∂θ = 20 minutes

ra = 1/6 minutes^(-1)

rθ = 1/11 minutes^(-1)

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From the figure, angle ACB anf angle BCD are complementary, that is,

∠ACB + ∠BCD = 90°

Replacing with data

61° + ∠BCD = 90°

∠BCD = 90° - 61°

∠BCD = 29°

From the picture, angle BCD and angle FCE are vertical angles, then they are congruent, which means that:

∠FCE = ∠BCD = 29°

Angle FCA is a right angle, that is, ∠FCA = 90°. Therefore:

∠FCE + ∠FCA = ∠ACE

29° + 90° = ∠ACE

119° = ∠ACE

The given value which is 0.3282828... can be expressed as 1457/2500 in p/q form.

To express 0.3282828... as a fraction in p/q form, we need to find a pattern in the decimal representation. Notice that the repeating portion of the decimal is 0.2828..., which we can represent as x. Therefore, we have:

0.3282828... = 0.3 + x

x = 0.282828...

Now, we can multiply both sides of the equation by 100 to get rid of the decimal points:

100(0.3 + x) = 30 + 100x

28.2828... = 100x

Solving for x, we get:

x = 28.2828.../100 = 2828/10000

Therefore, we can express 0.3282828... as a fraction in p/q form:

0.3282828... = 0.3 + x = 3/10 + 2828/10000 = (3000 + 2828)/10000 = 5828/10000

To simplify the fraction, we can divide both the numerator and denominator by their greatest common factor, which is 4. This gives us:

0.3282828... = 5828/10000 = 1457/2500

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Complete question is:

Express 0.3282828……. in p/q form, where p and q are integers and q ≠ 0.​

Answer:

7.6

Step-by-step explanation:

We want to find the distance between (0,6) and (-3,-1)

We can find the distance between any two points using the distance formula

Distance between two points =

\( \sqrt{(x2 - x1)^{2} +(y2 - y1) {}^{2} } \)

Where the values of x and y are derived from the the two points. (x1,y1) and (x2,y2)

Here the two points are (0,6) and (-3,-1)

So we have (x1,y1) = (0,6) so x1 = 0 and y1 = 6

And we have (x2,y2) = (-3,1) so x2 = -3 and y2 = -1

Now we plug in the values of x and y into the formula and evaluate to get the distance.

Again recall distance = √(x2-x1)²+(y2-y1)²

==> plug in x2 = -3 , x1 = 0, y2 = -1 and y1 = 6

Distance = √(-3-0)²+(-1-6)

==> evaluate operations inside of parenthesis

Distance = √(-3)²+(-7)²

==> evaluate all exponents

Distance = √9+49

==> and 9 and 49

Distance = √58 = 7.6 (rounded)