Need help solving this problem

Answer: (b) To find the cost per lock, we need to divide the total cost by the number of locks.

For Home Hardware, the cost per lock is 120 / 4 = $30.00.

For Rona, the cost per lock is 192 / 6 = $32.00.

So, Home Hardware has the lower cost per lock at $30.00, compared to Rona's cost of $32.00.

(i) Some other factors to consider when buying a lock include:

Security: The level of security offered by the lock is important to consider, especially for locks that will be used for homes, businesses, or other valuable assets.

Durability: It's important to choose a lock that is durable and resistant to weather and wear-and-tear.

Ease of use: Consider the ease of use of the lock, including how easy it is to install and how user-friendly the lock mechanism is.

Brand reputation: Consider the reputation of the brand, as well as customer reviews and ratings of the product.

Warranty: Look for a lock that comes with a warranty, and consider the length and terms of the warranty.

Step-by-step explanation:

(A) The global optimal solution is x = -π/2 and the local optimal solutions are x = (2n + 1)π/2

(B) The global optimal solution is x = (2n + 1)π/2

(C) the global optimal solution is x = (2n + 1)π/2

A function is a mathematical concept that assigns a unique output value for each input value. It is a rule that takes in an input or set of inputs and maps it to a specific output. Functions are represented by symbols, usually denoted by a letter, such as "f".

In mathematical notation, a function is usually expressed as "f(x)" where "x" is the input and "f(x)" is the corresponding output. For example, a function could be defined as f(x) = x^2, which means that for any value of x, the function will calculate and return the square of that value.

For the first problem:

(a) f(x) = sin x and X = [0, 3π]

The objective function f(x) = sin x has a global minimum at x = -π/2, where sin x = -1. The function also has a local minimum at x = (2n + 1)π/2, where n is an integer and sin x = -1.

The feasible set X = [0, 3π] contains all the local and global minima of f(x) = sin x, so the global optimal solution is x = -π/2 and the local optimal solutions are x = (2n + 1)π/2, where n is an integer.

For the second problem:

(b) f(x) = sin x and X = [1, 4π]

The objective function f(x) = sin x has a global minimum at x = -π/2, where sin x = -1. The function also has a local minimum at x = (2n + 1)π/2, where n is an integer and sin x = -1.

The feasible set X = [1, 4π] only contains some of the local minima of f(x) = sin x, so the global optimal solution is x = (2n + 1)π/2 where (2n + 1)π/2 is in the feasible set X and sin x is at its minimum.

For the third problem:

(c) f(x) = sin x and X = [-π/4, (11/4)π]

The objective function f(x) = sin x has a global minimum at x = -π/2, where sin x = -1. The function also has a local minimum at x = (2n + 1)π/2, where n is an integer and sin x = -1.

The feasible set X = [-π/4, (11/4)π] only contains some of the local minima of f(x) = sin x, so the global optimal solution is x = (2n + 1)π/2 where (2n + 1)π/2 is in the feasible set X and sin x is at its minimum.

For the fourth problem:

(d) f(x) = max(0, a,2-1) and X = (-00,00); and X = 10, (2/3) ; 0, If x = 0;

The objective function f(x) = max(0, a,2-1) has a global minimum at x = 0, where the function is 0. The function also has a local minimum at x = (2/3) where the function is (2/3)^2-1.

The feasible set X = (-00,00); and X = 10, (2/3) ; 0, If x = 0; only contains some of the local minima of f(x) = max(0, a,2-1), so the global optimal solution is x = (2/3) if (2/3) is in the feasible set X and the function is at its minimum, or x = 0 if 0 is in the feasible set X and the function is at its minimum.

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The distance between N=(-2,-1) and L=(3,-4) in coordinate plane will be √34 unit.

What is plane?

In two dimensions, a plane can continue on forever. The lack of breadth. A plane is an example of coordinate geometry. A point's location in a plane is determined by its coordinates.

A plane is a two-dimensional, flat surface that never ends in mathematics. A plane is a two-dimensional equivalent of a three-dimensional equivalent that contains three spatial dimensions, a line, and a point. Planes can resemble subspaces in some higher-dimensional situations, as if the room's walls had been substantially stretched. These walls have their own existence, exactly as in the context of Euclidean geometry.

A flat surface in three dimensions can be represented using the plane equation. There are several approaches for determining the equation for a given function.. The equation for the plane can be expressed in either cartesian form or vector form.

Hence, the general form of the equation is A(x−x1)+B(y−y1)+C(z−z1)=0

Now,

For given two points in (x1,y1),(x2,y2) in coordinate plane

distance between them will be = √((x2-x1)²+(y2-y1)²)

So, distance between  N=(-2,-1) and L=(3,-4)=√((3+2)²+(-4+1)²)

=√(25+9)

=√34

hence,

          The distance between N=(-2,-1) and L=(3,-4) in coordinate plane will be √34 unit.

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The sample contains the entire population, so we can calculate the population that means directly and this is that it is not necessary to use the t-procedure.

It is a convenience sample that defines the individuals conveniently selected as members of the class.

A convenience sample is defined as NOT a random sample, so the RANDOM requirement for the t-procedure is not satisfied.

As there are 3 ways to use the t-procedure: they are

Random, Independent,  and Normal.

Random is the sample that is given to be a random sample.

Independent Can be assumed because the sample size of 100 and is less than 10% of the population size.

Normal is also assumed because the sample size of 100 is larger than 30.

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If a particle is located a distance x meters from the origin, a force of cos (pi(x)/3 newtons acts on it then the work is done in moving the particle from x = 1 to x = 2 is 0 J.

Work is the energy transferred to or from an object via the application of force along a displacement.

Given that  a particle is located a distance x meters from the origin

Force acting on it is cos (pi(x)/3 newtons.

We need to find the work.

W=∫F dx

Now replacing the values ​​with the information that was given and the equation, we have:

[tex]W=\int\limits^2_1 {cos(\pi x/3)} \, dx[/tex]

w=3/π(sinπx/3)

Applying the points where X is equal to 2 and 1 we find:

W=3/π(√3/2-√3/2)

W=0

Hence, if a particle is located a distance x meters from the origin, a force of cos (pi(x)/3 newtons acts on it then the work is done in moving the particle from x = 1 to x = 2 is 0 J.

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If you travel for three hours at a speed of 30 km/hr, you will go a distance of 90 km.

Speed is the rate of change of an object position relative to a given frame of reference. It is a scalar quantity meaning it has both magnitude and direction. Speed is usually measured in meters per second.

The distance travelled can be calculated by multiplying the speed of 30 km/hr by the number of hours travelled, which is 3. Therefore, the distance travelled is 90 km. To summarize, if you travel for three hours at a speed of 30 km/hr, you will go a distance of 90 km.

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The complete equation is 2Fe(s) + 3Cl₂(g) -> 2FeCl₃(s) ΔH = -400 kJ

A thermochemical equation is a chemical equation that includes information about the energy change that occurs during a chemical reaction. The energy change is represented by the symbol ΔH (delta H), which stands for the change in enthalpy, or heat energy, of the system. The equation shows the reactants on the left side and the products on the right side, and includes the amount of heat energy evolved or absorbed during the reaction.

For example, consider the reaction:

2H2(g) + O2(g) → 2H2O(l) ΔH = -571 kJ/mol

This equation shows that two molecules of hydrogen gas react with one molecule of oxygen gas to form two molecules of liquid water. The reaction releases 571 kJ of heat energy per mole of hydrogen and oxygen that react.

The complete thermochemical equation for the reaction of Fe(s) with Cl₂(g) to form FeCl₃(s) is:

2Fe(s) + 3Cl₂(g) -> 2FeCl₃(s) ΔH = -400 kJ

This means that the reaction releases 400 kJ of energy for each mole of Fe(s) that reacts. The negative sign indicates that the reaction is exothermic, meaning it releases heat.

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The exponential expression is [tex](9 + w)^7[/tex] and the simplified expression is [tex]4782969 + w^7[/tex].

What is an exponent?

The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.

The integer is given as 7.

The variable is given as w.

The sum of integer and variable needs to be raised to the power of 7.

The sum of integer and variable is -

(9 + w)

This expression needs to be raised to the power of 7.

The exponential expression is -

[tex](9 + w)^7[/tex]

On solving this expression -

[tex]9^7 + w^7\\4782969 + w^7[/tex]

Therefore, the simplified expression is [tex]4782969 + w^7[/tex].

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Answer:

Step-by-step explanation:

The area of Mrs Brown’s classroom is

63 m2

. The area of Mr Black’s

classroom is 64 m2

. Mr Black’s

classroom is bigger.

The length of the waterline when hull speed is 4 knots per hour in feet is 2.985 feet;

If the object is going linearly, and at constant speed, then the speed of that object is given by the distance it traveled to the time it took to travel that distance.

If the object traveled D distance in T units time, then that object's speed is

[tex]Speed = S = \dfrac{\: Distance \: traveled}{\: Time \: taken} = \dfrac{D}{T} \: \rm unit \: length/unit \: time[/tex]

Given;

Displacement hull can be approximated by v=1.34 /- l

Let, the function 1.34*l; where l is the length of the waterline, measured in feet and h is the hull speed of the boat, measured in knots per hour. If we know that h=4kt/h then the length of the waterline is;

l=h/1.34

l=4/1.34

l=2.985 ft

Therefore, the length when speed is 4 knots per hour in feet is 2.985 feet;

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The amount of the sales tax is $9.75.

The percentage is defined as a ratio expressed as a fraction of 100.

The taxable amount of the sale: $150

Sales tax percentage: 6.5%

To calculate the sales tax, you can multiply the taxable amount of the sale by the sales tax percentage.

Sales Tax = Taxable Amount × Sales Tax Percentage

Sales Tax = $150 × 6.5%

Sales Tax = $150 × 0.065

Apply the multiplication operation, and we get

Sales Tax = $9.75

So, the amount of the sales tax is $9.75.

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Answer:

$100 account

Step-by-step explanation:

to double, $100 only need to earn 100 in interest, while $1000 account will need earn $1000 in interest.  because the interest is the same for both, so the $100 account will double first

The new coordinates of the endpoints after the reflection are:

A' = (22, -1)

B' = (12, 15)

For a point (x, y), a reflection across the line x = 5 gives the point (2*5 - x, y).

Then the new endpoints of our segment are:

A' = (2*5 + 12, - 1) = (22, -1)

B' = (2*5 + 2, 15) = (12, 15)

These are the coordinates of AB after the reflection.

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First, we need to convert the loan repayment period to the same unit as the interest rate. The interest rate is 7% per year, which is equivalent to 0.07/12 = 0.00583 per month.

The total interest paid is given by:

interest = principal x rate x time

Where principal is the amount of the loan, rate is the interest rate per month, and time is the loan repayment period in months.

Substituting the given values, we get:

interest = $600 x 0.00583 x 9

interest = $31.35

Therefore, Emma will pay a total interest of $31.35 on the loan.

The approximate circumference of the smaller circular base, in the remaining section of the cone, is c. 3.36 feet.

To find the circumference, the formula is :

= π x diameter

So, you need to find the diameter of the smaller circle. If a distance of 14 feet corresponds to 3 feet of diameter , then 5 feet to the smaller circle would be :

= ( 5 x 3 ) / 14

= 1. 0714 feet

The circumference is therefore :

= 3. 14 x 1. 0714

= 3. 36 feet

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We can use trigonometry to find the length of side SU in triangle TSU. We can use the tangent function, where tangent is equal to the opposite side divided by the adjacent side. In this case, the opposite side is SU and the adjacent side is ST.

What is basic trigonometry?

The study of the relationship between the sides and angles of the right-angle triangle is the main objective of the field of mathematics known as "trigonometry." Trigonometric formulas, functions, or identities can consequently be used to determine the missing or unknowable angles or sides of a right triangle.

We know that angle TUS is 37 degrees, so we can use that angle to find the tangent of the angle:

tan(37) = SU / 0.6

Solving for SU:

SU = 0.6 * tan(37)

The exact length of SU can be found by using a calculator or a table of trigonometric values. To a good approximation, the value of SU is approximately 0.73.

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Answer:

it is probably 1.884 cm andd it is accurate

Answer:

She received a 35% discount    :)).  

Step-by-step explanation:

Answer:

B. 63

Step-by-step explanation:

Let's first find angle M.

Angle M has 118 by it. The line below it is also a straight line. The angle of a straight line is 180. This means that 180-118 equal angle M.

Angle M = 180-118 = 62

Now the angles of a triangle also equal 180 and since 1 angle is 62, these other two angles must equal 118.

[tex](6x - 9) + (4x + 7) = 118[/tex]

Lets combine like terms. We combine the numbers. -9+7 equals -2. 6x + 4x = 10x. Putting those answers together

[tex]10x - 2 = 118[/tex]

If we add 2 to both sides, that gets rid of the 2 on the left side

[tex]10x = 120[/tex]

Lastly, we divide by 10

[tex]x = 12[/tex]

Now that we have X, we can plug it into angle L's equation!

[tex](6x - 9) = (6(12) - 9) = ((72) - 9) = 63[/tex]

To show it's correct, plugging it into the other equation makes it 55.

55 + 63 + 62 = 180

[tex]f(t) = 4 (1.25)^{t+3} = 4 \cdot (1.25)^{3} \cdot (1.25)^{t}[/tex] using the exponent rule [tex]a^n\cdot a ^m = a^{n+m}[/tex] in reverse.  (Using the rule to split apart the exponent.

Continuing to calculate out some values,

[tex]f(t) = 4 \cdot (1.25)^{3} \cdot (1.25)^{t} = 4 \cdot 1.953125 \cdot (1.25)^{t} = 7.8125 \cdot (1.25)^{t}[/tex]

So, [tex]f(t) = 7.8125 \cdot (1.25)^{t}[/tex] or [tex]f(t) = 7.81 \cdot (1.25)^{t}[/tex] rounded to the nearest hundredth.

Since the b-value is greater than 1, this is exponential growth.

The b-value of 1.25 means that for each increase by 1 unit in the t-value, the y-value will become 125% of what it had been.  The output will grown by 25%, which is your percent rate of change.

The b-value of your function is always a measurement from 100% or b=1.  

(a) Commuters take both the bus and the subway = 10

(b) commuters take only the subway = 1120

What is a set?

A set is a collection of well-defined objects or elements. A set is represented by capital letter and their elements is represented by small letters.

Let U be the set representing the number of commuters in New york.

⇒n(U) = 1900

Let A be the set representing the commuters take subway

⇒n(A) = 1130

Let B be the set representing the commuters take bus

n(A) = 650

130 commuters do not take either the subway or the bus,

(a) commuters take both the bus and the subway

n(A∪B)=n(A) + n(B) - n(A∩B)

n(A∪B)=n(U)-130⇒1900-130=1770

1770=1130+650-n(A∩B)

⇒n(A∩B) = 10

(b) Commuters take only the subway,

n(A)-n(A∩B) = 1130-10=1120

Hence, commuters take both the bus and the subway is 10

commuters take only the subway is 1120

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Answer:

Option C. GraphM

Step-by-step explanation:

Only Graph M has all values correct while the other graphs had atleast one or more values wrong

Therefore Graph M is correct

The graph that best explains Roberts' activity during the 4 weeks is C. the graph M

He have 20.5 miles to his destination after 68 minutes of driving

Since Hong has 54 miles to his destination after 38 minutes of driving, and he has 44.4 miles to his destination after 50 minutes of driving.

We will consider the two given data values as our points 1 and 2 respectively. And that is what we are going to use to create a linear function for pressure

Let the y and x represent the distance and time respectively

point 1 (54, 38) and point 2 (44.4, 50)

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

where  x1 =54, y1 = 38 and x2 = 44.4, y2 = 50

slope(m) = (50-38) / (44.4-54) = -5/4 = -1.25

Linear function are of the form y-y1 = m(x-x1). Thus:

y-38 = -1.25 (x-54)

y-38 = -1.25x + 67.5

y = -1.25x + 67.5 + 38

y =  -1.25x + 105.5

After 68 minutes of driving, the number of miles will be:

y =  -1.25x + 105.5

put x = 68

y =  -1.25(68) + 105.5

y = 20.5 miles

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Answer:

Step-by-step explanation:

[tex]a_{1} =10\\a_{n}=-4a_{n-1}\\put~n=2,3,4\\a_{2}=-4a{1}=-4(10)=-40\\a_{3}=-4a_{2}=-4(-40)=160\\a_{4}=-4a_{3}=-4(160)=-640[/tex]

The complete statement is -

If the demand for apples is highly elastic and the supply is highly inelastic, then if a tax is imposed on apples, it will be paid largely by the sellers of apples.

Elastic demand is when the price of a product has a large impact on the quantity purchased.

Given is that the demand for apples is highly elastic and the supply is highly inelastic.

If the demand for apples is highly elastic and the supply is highly inelastic, then if a tax is imposed on apples, it will be paid largely by the sellers of apples.

Therefore, the complete statement is -

If the demand for apples is highly elastic and the supply is highly inelastic, then if a tax is imposed on apples, it will be paid largely by the sellers of apples.

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By applying probability concept, it can be concluded that the experimental probability of rolling each is P(1) = 1/6, P(2) = 1/7,  P(3) = 1/3,  P(4) = 2/21,  P(5) = 1/7, and P(6) = 5/42.

Probability is a value used to measure the degree of occurrence of a random event.

P(E) = n(E)/n(S)

n(E) = number of desired events

n(S) = total number of events

We have the following information about a die rolling 42 times:

One    Two    Three   Four     Five     Six

 7          6          14         4          6        5

The theoretical probability of rolling any number on a six-sided die is  7/42 or 1/6.

Now we can calculate the probability of each side by substituting the value in the table into the equation:

P(E) = n(E)/n(S)

P(1) = 7/42

      = 1/6

P(2) = 6/42

      = 1/7

P(3) = 14/42

      = 1/3

P(4) = 4/42

      = 2/21

P(5) = 6/42

      = 1/7

P(6) = 5/42

Thus, the experimental probability of rolling each is P(1) = 1/6, P(2) = 1/7,  P(3) = 1/3,  P(4) = 2/21,  P(5) = 1/7, and P(6) = 5/42.

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The given statement is False because if the price of avocados increases by 11% for four consecutive months, then the price of avocados did not increase by 48.64% over the four-month period.

If the price of avocados increases by 11% for four consecutive months, then the price of avocados did not increase by 44% over the four-month period. The calculation of percentage increase is cumulative, meaning that the increase in price in the second month will be based on the increased price from the first month, and so on.

In this case, if the price starts at $1 and increases by 11% each month, the price after four months will be $1 * 1.11 * 1.11 * 1.11 * 1.11 = $1.4864, which represents an increase of 48.64% over the four-month period, not 44%.

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Answer:

Step-by-step explanation:

The use of the commutative property of addition is illustrated by option D: (9x + 5y) + 2z = (5y + 9x) + 2z.

The commutative property of addition states that the order of addition does not affect the sum. In other words, changing the order of the addends does not change the result. Option D demonstrates this property by showing that adding 9x and 5y to 2z is the same as adding 5y and 9x to 2z. The result is the same regardless of the order in which the addends are combined.

A. The current account balance is a deficit of 130

B. The financial account balance is a deficit of 70

C. The trade balance is a deficit of 50.

D. The net factor payments are a deficit of 30.

Balance of payments is the method by which countries measure all of the international monetary transactions within a certain period.

(a) The current account balance can be calculated as follows:

Current Account Balance = (Exports of goods + Service exports) - (Imports of goods + Service imports + Income payments to foreigners - Income receipts from abroad)

= (275 + 50) - (325 + 40 + 70 - 40)

= 325 - 455

= -130

So, the current account balance is a deficit of 130.

(b) The financial account balance can be calculated as follows:

Financial Account Balance = Increase in home country assets abroad - Increase in foreign assets in home country

= 350 - 420

= -70

So, the financial account balance is a deficit of 70.

(c) The trade balance can be calculated as follows:

Trade Balance = Exports of goods - Imports of goods

= 275 - 325

= -50

So, the trade balance is a deficit of 50.

(d) The net factor payments can be calculated as follows:

Net Factor Payments = Income receipts from abroad - Income payments to foreigners

= 40 - 70

= -30

So, the net factor payments are a deficit of 30.

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