Melanie knows she needs 5kg of grass seed to make a square lawn 8m by 8m. Grass seed is sold in 3kg boxes. Melanie wants to make a rectangular lawn by 12m by 14m. She has 4 boxes of grass seed. Has Melanie got enough grass seed to make a lawn by 12m by 14. Show your working out

Step-by-step explanation:

The problem bothers on fractions, here we are being presented with mixed fractions.

what we are going to do bascially is to subtract the sum of all the uloaded

peat moss in sites 1 and 2 to get from the peat moss to get the remaining for the third site

therefore

\(10\frac{2}{5}-(2\frac{2}{3}+ 2\frac{1}{4})\)

we then have to convert the mixed fraction to further simplify the problem we have

\(\frac{52}{5}-(\frac{8}{3}+ \frac{9}{4})\)

we then solve the fraction to the right of the negative symbol first

\(=\frac{52}{5}-(\frac{8}{3}+ \frac{9}{4})\\\\=\frac{52}{5}-\frac{32+27}{12} \\\\=\frac{52}{5}-\frac{59}{12} \\\\\=\frac{624-295}{60} \\\\=\frac{329}{60}\)

We can now convert to mixed fraction

\(=\frac{329}{60}\\\\ =5\frac{12}{25}\)

For the third site the remainder is 5 12/25

Answer:

Hello! Your answer would be BELOW

Step-by-step explanation:

A)

D)

C)

Hope I helped! Ask me anything if you have more questions! Brainiest plz! Have a nice mourning! Hope you make an 100%! -Amelia♥

The pattern for the sequence 8, 17, 26, 35, 44, … is 9n - 1

The pattern in the question is given as

8, 17, 26, 35, 44, …

In the above expressions and pattern, we can see that

The current term is added to 9 to get the next term

From the above, we have the following

This means that the pattern is an arithmetic sequence with the following features

a = 8

d = 9

An arithmetic sequence is represented as

f(n) = a + (n - 1)d

When the values of "a" and "d" are substituted in the above equation, we have the pattern to be

f(n) = 8 + (n - 1)9

So, we have

f(n) = 8 + 9n - 9

Evaluate

f(n) = 9n - 1

Hence, the pattern for the sequence is 9n - 1

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The absolute uncertainty in A is approximately 0.022254. Rounding it to the same number of decimal places as A, we express the absolute uncertainty as 0.05995 ± 0.00008.

To calculate the absolute uncertainty in A, we need to determine the maximum and minimum values that A can take based on the uncertainties in b and c. The absolute uncertainty in A can be found by propagating the uncertainties through the equation.

Given:

b = 95.68 ± 0.05

c = 43.28 ± 0.02

To find the absolute uncertainty in A, we can use the formula for the absolute uncertainty in a function of two variables:

ΔA = |∂A/∂b| * Δb + |∂A/∂c| * Δc

First, let's calculate the partial derivatives of A with respect to b and c:

∂A/∂b = 1/π

∂A/∂c = -1/π

Substituting the given values and uncertainties, we have:

ΔA = |1/π| * Δb + |-1/π| * Δc

= (1/π) * 0.05 + (1/π) * 0.02

= 0.07/π

Since the value of π is a constant, we can approximate it to a certain number of decimal places. Let's assume π is known to 5 decimal places, which is commonly used:

π ≈ 3.14159

Substituting this value into the equation, we get:

ΔA ≈ 0.07/3.14159

≈ 0.022254

Therefore, the absolute uncertainty in A is approximately 0.022254.

To express the result in the proper format, we round the uncertainty to the same number of decimal places as the measured value. In this case, A is approximately 0.05995, so the absolute uncertainty in A can be written as:

ΔA = 0.05995 ± 0.00008

Therefore, the correct answer is option b. 0.05995 ± 0.00008.

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First we need to convert the sentence to an algebraic expression

We will break down the parts to do so:

sum of 6 and some number

let the number = n

sum means we will be adding 6 to the number

So, sum of 6 and some number = 6 + n

5 times the sum: this means we will multiply the sum we got above by 5

5 times then sum of 6 and some number = 5(6 + n)

five times the sum of 6 and some number is 20:

This means the multiplication of the sum by 5 equals to 20

So, the final algebraic expression:

5(6 + n) = 20

Next, we will solve for the unknown number which is n in this case:

5(6 + n) = 20

expand the parenthesis:

5(6) + 5(n) = 20

30 + 5n = 20

subtract 30 from both sides:

30 - 30 + 5n = 20 - 30

5n = -10

divide both sides by 5:

5n/5 = -10/5

n = -2

Hence, the unknown number is -2

Answer: He completes 2 4/5 rows per hour

if he completed 140 rows, how many hours did it take?

We should divide the work completed by the amount of work done per hour.

So, 140/(2 4/5) =  

2 4/5 is equivalent to 2.8  

so 140/2.8 = 50 hours

Step-by-step explanation:

The required length of the right rectangular prism is 18 in whose volume is 540 cu. in

Having six faces, a rectangular prism is a three-dimensional shape (two at the top and bottom and four are lateral faces). The prism's faces are all rectangular in form. There are three sets of identical faces as a result. A rectangular prism is often referred to as a cuboid because of its form. A rectangular prism may be found in everyday objects like a geometry box, notebooks, diaries, and rooms.

Rectangular prism characteristics

There are two categories into which rectangular prisms can be divided. These are:

A rectangular prism is a prism with rectangular bases. A right rectangular prism is a prism with six rectangle-shaped faces with angles that are all right angles.

Vertices of a rectangular prism = 8

Edges of a rectangular prism = 12

Faces of a rectangular prism= 6 (including bases)

total volume of the prism = 540 cubic inches.

Width = 6 in

Height = 5 in

We know volume is length * breadth* height

⇒ 540 = 5*6* length

⇒length = 18 in

The required length of the right rectangular prism is 18 in.

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Answer:

the second option 2a-6b+c

Answer:

2a - 6b + c

Step-by-step explanation:

(a+a)(-5b-b)(2c-c)

2a-6b+c

Answer: 83r^2 - 59 + 60

Step-by-step explanation:

R^2 - 59R - 82r^2 + 60

= 83r^2 - 59 + 60

The probability that a randomly chosen fitness club member signs up for a free running session is 0.4.

Let total s members sign up for the weightlifting session.

So, the total members for the running session is 2x.

And the total members for the swimming session be 2x.

Also here it is given that, thirty of the fitness center members sign up for a free session.

⇒ x + 2x + 2x = 30

⇒ 5x = 30

⇒ x = 30/5

⇒ x = 6

Thereofre, the probability that a randomly chosen fitness club member signs up for a free running session

= total number of members in running session/ number of members sign up for a free session

= 12/30

= 0.4

Hence, the probability that a randomly chosen fitness club member signs up for a free running session is 0.4.

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Answer:

See below

Step-by-step explanation:

All other parabolas are transformations of \(y=x^2\)

Transformations include:

There are a total of 7 ways to seat eight people around a table if Alice and Bob won't sit next to each other. This is because the seating arrangement must be a permutation of the seven people not including Alice and Bob.

We can calculate this by taking the factorial of the number of people not including Alice and Bob, which is seven. Since a factorial is the product of an integer and all the integers below it, we can calculate the factorial of seven by multiplying all the integers from one to seven.

This gives us 7=5040, which is the total number of ways to seat eight people around a table if Alice and Bob won't sit next to each other.

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Answer: I am terrible at these kinds of "sit-uating" problems (haha). My idea is that the three people can be situated in (3−1)!

ways and that the rest can be situated in (5−1)!

ways. Then, the ordering of the five people depends on the partitions of 5 into 3 groups:

Step-by-step explanation:

The equation 3x+2y=14 can be written as in the slope-intercept form is y = (-3/2)x + 7.

It is defined as the relation between two variables, if we plot the graph of the linear equation we will get a straight line.

If in the linear equation, one variable is present, then the equation is known as the linear equation in one variable.

It is given that:

The equation of the line is:

3x + 2y = 14

The slope-intercept form is:

y = mx + c

Here m is the slope of the line and c is the y-intercept.

After arranging:

2y = -3x + 14

y = (-3/2)x + 7

Thus, the equation 3x+2y=14 can be written as in the slope-intercept form is y = (-3/2)x + 7.

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65 1/3

Try long division. You may have to add some blank 0 places to it so it goes evenly. Convert the remainder into the numerator of your number after simplifying.

The quotient of 147 divided by 2.25 is is 65.33

To find the answer to the equation 147 divided by 2.25, we can simply perform the division calculation:

147 / 2.25 = 65.333...

Or 147/ 2.25

= 147 x 100 /225

= 14700/ 225

                      225 | 14700 | 65.333

                                 1350

                              _______

                                   1200

                                    1125

                                  ______

                                      750  

                                      675

                                   ______

                                       750

                                       675

                                      ______

                                           75

Therefore, the quotient of 147 divided by 2.25 is is 65.33 (rounded to two decimal places).

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The value of x in the solution to the system of equations is: 5/3

There are three main ways of solving simultaneous equations are:

Substitution methos

Elimination Method

Graphical Method

We are given the simultaneous equations as:

6x + 3y = 13   -----(1)

3x - y = 4   -----(2)

Making y the subject in equation 2 gives:

y = 3x - 4

Plugging 3x - 4 for y in eq 1 is:

6x + 3(3x - 4) = 13

6x + 9x - 12 = 13

15x = 25

x = 25/15

x = 5/3

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Complete question is:

What is the value of x in the solution to the system of equations below?

6x + 3y = 13

3x - y = 4

1

(5/3)

(8/3)

(7/3)

Answer:

12.

Step-by-step explanation:

6x10 = 60.

60 divided by 12 =5.

Answer:

12

Step-by-step explanation:

5x = 60

x  = 12

The standard deviation of the calls received per day is 12.25.

The standard deviation of the calls received per day is 12.25. We know that the number of calls received follows a Poisson distribution and the average number of calls received per day is 150. The formula for the Poisson distribution is:P(x) = (e^(-λ) * λ^x) / x!Where:P(x) is the probability of x number of calls being received per day.λ is the average number of calls received per day.x is the number of calls received per day.We are given that the average number of calls received per day (λ) is 150.The formula for the standard deviation (σ) of a Poisson distribution is:σ = sqrt(λ)Therefore, substituting λ = 150, we get:σ = sqrt(150)σ = 12.25Therefore, the standard deviation of the calls received per day is 12.25.

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Answer:

7

Step-by-step explanation:

Answer:

Step-by-step explanation:

Since there are four aces and 52 total cards.

P(A)=4/52=1/13

Answer:

The probability that you would draw an ace in a deck of cards would be 8%

A parallelogram possesses rotational symmetry of order 2, but no line symmetry.

The rotational symmetry of a parallelogram:

Therefore, a parallelogram possesses rotational symmetry of order 2, but no line symmetry.

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Answer:

in picture ....

Step-by-step explanation:

Answer:

y=2/5x-7

Step-by-step explanation:

i hope this is what you were asking for

To find the critical points of the function f(x,y) = x' + y - 6y - 3x + 9, we need to take the partial derivatives with respect to x and y and set them equal to zero.

∂f/∂x = -3 = 0

∂f/∂y = 1 - 6 = -5 = 0

So the system of equations is:

-3 = 0

-5 = 0

These equations have no solutions, which means there are no critical points for this function.

Therefore, the list of critical points is empty.
Hello! I'd be happy to help you find the critical points of the given function. The function is:

f(x,y) = x' + y - 6y? - 3x + 9

To find the critical points, we need to find the partial derivatives of the function with respect to x and y, and then set them equal to zero:

∂f/∂x = ∂(x' + y - 6y? - 3x + 9)/∂x
∂f/∂y = ∂(x' + y - 6y? - 3x + 9)/∂y

Now, let's calculate the partial derivatives:

∂f/∂x = 1 - 3
∂f/∂y = 1 - 12y

The system of equations is:

1. ∂f/∂x = 1 - 3 = 0
2. ∂f/∂y = 1 - 12y = 0

Now let's solve the system of equations:

1. 1 - 3 = 0 → -2 = 0 (this equation cannot be satisfied)

Since the first equation cannot be satisfied, there are no critical points for the given function.

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(a) The z-score corresponding to x = 25 is -1. (b)The z-score corresponding to x = 42 is 2.4.(c) The raw score corresponding to z = -3 is 15. (d)  The raw score corresponding to z = 1.5 is 37.5.

For a normal distribution with mean μ = 30 and standard deviation σ = 5:

(a) To find the z-score corresponding to x = 25, we use the formula:

z = (x - μ) / σ

Substituting the values, we get:

z = (25 - 30) / 5 = -1

Therefore, the z-score corresponding to x = 25 is -1.

(b) To find the z-score corresponding to x = 42, we again use the formula:

z = (x - μ) / σ

Substituting the values, we get:

z = (42 - 30) / 5 = 2.4

Therefore, the z-score corresponding to x = 42 is 2.4.

(c) To find the raw score (x) corresponding to z = -3, we use the formula:

z = (x - μ) / σ

Rearranging the formula, we get:

x = μ + zσ

Substituting the values, we get:

x = 30 + (-3) x 5 = 15

Therefore, the raw score corresponding to z = -3 is 15.

(d) To find the raw score (x) corresponding to z = 1.5, we use the same formula:

x = μ + zσ

Substituting the values, we get:

x = 30 + 1.5 x 5 = 37.5

Therefore, the raw score corresponding to z = 1.5 is 37.5.

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The simplified expression of (5.1)(5.1^2)^4 is (5.1)^9

The expression is given as:

(5.1)(5.12)4

Rewrite the expression properly as follows:

(5.1)(5.1^2)^4

Rewrite the expression properly as follows:

(5.1)(5.1^2)^4 = (5.1) * (5.1^2)^4

Apply the power law of indices

(5.1)(5.1^2)^4 = (5.1) * (5.1^8)

Apply the power law of indices

(5.1)(5.1^2)^4 = (5.1)^(1 + 8)

Evaluate the sum

(5.1)(5.1^2)^4 = (5.1)^9

Hence, the simplified expression of (5.1)(5.1^2)^4 is (5.1)^9

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A process in which a number is changed, such as by adding, subtracting, dividing, or multiplying is called Mathematical Expression.

When we combine numbers and variables in a valid way, using operations such as addition, subtraction, multiplication, division, exponentiation, and other operations and functions as yet unlearned, the resulting combination of mathematical symbols is called a Mathematical Expression.

Addition is adding two or more numbers to find their sum.

Subtracting is finding the difference between two or more numbers.

Division is finding the quotient of two number by dividing the both numbers.

Multiplying is finding the product of two or more numbers.

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Answer:

1234588765

Step-by-step explanation:

As per the linear equation the system has one solution, which is x = 1 and y = 1.

A linear equation is a mathematical expression that represents a straight line. A linear equation has a set of variables, and the coefficients (numbers in front of the variables) are constant.

The reason why most overdetermined linear systems are inconsistent is that there are more restrictions placed on the variables than what is required to find a solution.

It is possible for an overdetermined linear system to have one solution, but this is a rare occurrence.

When an overdetermined system has infinitely many solutions, this means that there are an infinite number of combinations of values that satisfy all of the equations simultaneously.

For example, consider the following system of linear equations:

2x + 3y = 6

4x + 6y = 12

This system is overdetermined because there are two equations and only one variable (x and y). In this case, the system has one solution, which is x = 1 and y = 1.

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Personal car would be the best option to manage both tasks efficiently. While the train is a reliable mode of transportation, it may have fixed schedules that might not align perfectly with Patrick's needs.

On the other hand, using his personal car provides more flexibility and allows him to tailor the departure time according to his daughter's coding class schedule.

If Patrick decides to take the train, he would need to check the train schedule to see if there are convenient departure and arrival times for both the soccer game and the coding class. This option would require planning and coordination to ensure he arrives at the game on time and can pick up his daughter afterward.

Using his personal car gives Patrick the freedom to leave at a time that accommodates both the soccer game and the coding class. He can drop off his daughter at her coding class, attend the soccer game, and then pick her up afterward without being restricted by train schedules.

Considering the circumstances, Patrick might find it more convenient to use his personal car to manage both tasks effectively and ensure he can attend his son's soccer game while also ensuring his daughter arrives at her coding class on time.

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To solve the given linear programming (LP) problem using the graphical LP approach, we will plot the feasible region, identify the corner points, and determine the optimal solution.

Here are the steps:

Step 1: Plot the constraints:

- Plot the line 5x + y = 32, which represents the constraint 5x + y ≤ 32. To do this, find two points that lie on this line by assigning values to x and solving for y. For example, when x = 0, y = 32, and when x = 6, y = 2. Connect these points to draw the line.

- Plot the line x + 3y = 12, representing the constraint x + 3y ≥ 12. Again, find two points on this line and connect them. For instance, when x = 0, y = 4, and when x = 12, y = 0.

- Draw the lines representing x = 20 and y = 20 as vertical and horizontal lines passing through x = 20 and y = 20, respectively.

Step 2: Identify the feasible region:

- Shade the area that satisfies all the constraints. The feasible region is the intersection of the shaded regions.

Step 3: Identify the corner points:

- Find the coordinates of the corner points of the feasible region. These points are the intersections of the lines representing the constraints.

Step 4: Evaluate the objective function:

- Calculate the objective function Z = 3x + 12y for each corner point.

Step 5: Determine the optimal solution:

- Identify the corner point that gives the minimum value of the objective function Z. This point corresponds to the optimal solution of the LP problem.

Once you have completed these steps, you will have the complete solution to the LP problem using the graphical LP approach.

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