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When the equation y=x³/3-x²/2-2x+5 turns, using the formula x=2 and x=-1 will occur.

A assertion that two expressions, which may include variables and/or numbers, are equal is known as an equation. In essence, equations are questions, and the motivation for the development of mathematics has been the systematic search for answers to these questions.

Considering that,

y=x³/3-x²/2-2x+5

It is necessary to find zero in the gradient function's (derivative's) equation. finding dy/dx = 0 The y-coordinate is obtained by substituting the x-coordinate into the graph's equation. Change "y =" to "x =," for example.

y=x³/3-x²/2-2x+5

dy/dx=3x²/3-2x/2-2

dy/dx=x²-x-2

dy/dx=0

x²-x-2=0

Upon solving the given equation,

x=2 and x=-1

As a result, y=x/3-x²/2-2x+5 will turn at x=2 and x=-1.

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weight of Train A = 102 tons

weight of Train B = 98 tons.

This can be solved using the concept of equation.

The connection between the two expressions on each side of the sign is represented by a mathematical equation. One variable and an equal sign are often present.

Let, weight of of Train A = x

Weight of Train B = y

So, Train A and train B, weigh a total of 200 tons:

x + y = 200 ...... (1)

The difference of their weights is 4 tons:

x - y = 4 ........ (2)

Solving the both equation, we get-

2x = 204

or, x = 102

thus, y = 200 - x

or, y = 200 - 102

y = 98

Thus, weight of Train A = 102 tons

weight of Train B = 98 tons

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Answer:

1) A and B = {1, 3, 5, 7, 9, 0, 2, 4, 6, 8}

2) Yes, A and B are disjoint.

Step-by-step explanation:

The set union of A and B is the set containing all the elements of Set A and Set B. So it would be:

Set A U B = {1, 3, 5, 7, 9, 0, 2, 4, 6, 8}

The set intersection of A and B is the set containing all the elements that are common to both Set A and Set B. So it would be:

Set A ∩ B = {} (empty set)

Yes, A and B are disjoint because they have no elements in common.

According  to the question found the sum,

First number: 44,

Second number: 220,

Third number: 245 .

A number is an arithmetic value used for representing the quantity and used in making calculations. A written symbol like “3” which represents a number is known as numerals. A number system is a writing system for denoting numbers using digits or symbols in a logical manner.

First number: 44

Second number: 220

Third number: 245

The first number, x, is 44 since 5x = 220 and x + 220 + 245 = 289. The second number is 5 times the first number, which is 220. The third number is 100 more than the first number, which is 245.

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The cost allocation to each inventory is:

We can use the ratio of warehouse space usage to calculate the cost allocation to each inventory. Let's first calculate the warehouse space usage for each inventory.

Raw materials: 1/3 * 9.6 million square metres = 3.2 million square metres

Work-in-process: 1/6 * 9.6 million square metres = 1.6 million square metres

Finished goods: 3/8 * 9.6 million square metres = 4.8 million square metres

Next, we can calculate the cost allocation for each inventory by dividing the total cost by the corresponding warehouse space usage.

Raw materials: $11.55 million / 3.2 million square metres = $3.6 million/million square metres

Work-in-process: $11.55 million / 1.6 million square metres = $7.2 million/million square metres

Finished goods: $11.55 million / 4.8 million square metres = $2.4 million/million square metres

Finally, we can multiply the cost per million square metres by the warehouse space usage for each inventory to find the total cost allocation.

Raw materials: $3.6 million/million square metres * 3.2 million square metres = $11.52 million

Work-in-process: $7.2 million/million square metres * 1.6 million square metres = $11.52 million

Finished goods: $2.4 million/million square metres * 4.8 million square metres = $11.52 million

So, the cost allocation to each inventory is:

Raw materials: $11.52 million

Work-in-process: $11.52 million

Finished goods: $11.52 million

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The worth of Cobie's investment after 5 years is 3866 dollars.

Cobie invest $3500 into an ETF  which earns 2% per years. The amount Cobie investment will be worth if the interest is compounded semi annually can be calculated as follows:

using compound interest formula,

Then solve the equation for A

[tex]A = P(1 + \frac{r}{n} )^{nt}[/tex]

Therefore,

Hence,

[tex]A = 3500(1 + \frac{0.02}{2} )^{2(5)}[/tex]

A = 3,500.00(1 + 0.01)¹⁰

A = $3,866.18

Therefore,

worth of the investment = $3,866

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Answer:C

Step-by-step explanation:Basically time goes on and it starts off with a less percentage based off the amount of weeks later to add up to the most

Using Compound Interest, The largest balance is $780255, so the option A will give them the largest balance after 5 years.

Even though there are several ways to define an investor, compound interest helps investors. When banks lend money and utilize the income they earn to finance other loans, for instance, they profit from compound interest. When depositors earn interest on their bank accounts, bonds, or other investments, compound interest benefits them.

It's crucial to remember that although while "compound interest" includes the word "interest," the idea extends beyond the contexts in which the expression is typically employed, such as bank accounts and loans.

We will calculate compound interest in every case:

Using formula

[tex]Amount = P(1 + \frac{r}{m})^{t}[/tex]

option A: balance after 5 years:

[tex]5,000 (1+ 2 \frac{1}{4}\%) ^{4\times 5} = $7802.55[/tex]

option B:

balance after 5 years:

[tex]5000 (1+ 3\%)^{3\times 5} = $7789.84[/tex]

option C:

balance after 5 years:

[tex]5,000 (1+ 4\frac{1}{2}\%) ^{3\times 5} = $7764.85[/tex]

The largest balance is $780255, so the option A will give them the largest balance after 5 years.

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Answer:

To find an ordered pair (x, y) that is a solution to the equation -x + 2y = 7, we can substitute any values of x and y that satisfy the equation. For example, let x = 3, then we can solve for y:

-3 + 2y = 7

2y = 10

y = 5

So (3, 5) is an ordered pair that is a solution to the equation.

Answer:

Step-by-step explanation:

I reckon C. That symbol in the middle is a congruent angles symbol. hope this helps!

The circle's A and C are similar because A can be mapped onto C by a translation of 3 units to the left and 5 units down, followed by a dilation about its center by a scale factor of 2.5. Option D is correct.

The circle is the locus of a point whose distance from a fixed point is constant i.e center (h, k). The equation of the circle is given by

(x - h)² + (y - k)² = r²

Here,

To prove that the two circles are similar, circle A can be mapped onto C by a translation of 3 units to the right and 5 units up, followed by a dilation about its center by a scale factor of 2.5.

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If matrix c equals matrix d, then matrix d is [tex]\left[\begin{array}{cccc}3&1&-9&8\\2&2&0&5\\16&1&-1&11\end{array}\right][/tex], hence option B is the correct answer.

A collection of numbers lined up in rows and columns to form a rectangular array is called a matrix. The elements, or entries, of the matrix are the integers. In addition to numerous mathematical disciplines, matrices find extensive use in the sectors of engineering, physics, business, and statistics.

Given the elements of the matrix C.

The matrix c is represented by its rows and columns element, and the arrangements are:

C11 = 3    C12 = 1   C13=-9   C14 = 8

C21 = 2   C22=2   C23 =0   C24 = 5

C31 = 16   C32 = 1  C33=-3   C34=11

Hence, the matrix C is:

[tex]\left[\begin{array}{cccc}3&1&-9&8\\2&2&0&5\\16&1&-1&11\end{array}\right][/tex]

From the given option we observe that the matrix d that is similar to matrix c is option B.

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The correct question is:

The momentum of an object is 50 kg m/s and the kinetic energy of an object is 250 Joules.

In contrast to momentum, which is an object's size in motion, kinetic energy is the energy that any material has as it speeds. The relationship between kinetic energy and momentum exists because of how they relate to mass and velocity.

By using the following formula:

Momentum = mass x velocity, we will find the momentum of an object.

Substituting the values of mass and velocity,

Momentum = 5 km x 10 m/s

Momentum = 50,000 kg m/s

Kinetic energy = ½ x mass x (velocity)2

Kinetic Energy = ½ x 5 km x (10 m/s)2

Kinetic Energy = 250 J

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The individual entrepreneur's income tax amount is 30,000 manat.

To calculate the income tax amount for an individual entrepreneur in Azerbaijan, we need to first calculate their total taxable income for the year.

Based on the information provided, their total taxable income for the year is calculated below.

40,000 + 30,000 + 25,000 + 55,000 = 150,000 manat.

Next, we need to determine the applicable tax rate based on their taxable income. According to the tax laws in Azerbaijan, the tax rate for individuals with a taxable income of up to 120,000 manat is 20%. For income between 120,000 manat and 200,000 manat, the tax rate is 25%, and for income exceeding 200,000 manat, the tax rate is 30%.

Since the individual's taxable income is 150,000 manat, the applicable tax rate is 20%. Therefore, their income tax amount is 150,000 × 20% = 30,000 manat.

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Answer: 8.24%

Step-by-step explanation:

To calculate the annual percentage rate (APR) and the effective annual rate of interest on Aruna's investment, we need to know the following information:

The initial investment amount (Rs 150,000)

The final investment amount (Rs 168,925)

The time period of the investment (18 months)

The frequency of interest payments (every 3 months)

The interest earned on the investment is the difference between the final investment amount and the initial investment amount. In this case, the interest earned is:

Rs 168,925 - Rs 150,000 = Rs 18,925.

Calculate the interest rate per period: To find the interest rate per period, divide the interest earned by the initial investment amount and multiply by the number of periods per year. In this case, the interest rate per period is:

(Rs 18,925 / Rs 150,000) * (4 periods per year) = 0.08%.

Calculate the APR: The APR is the interest rate per period multiplied by the number of periods in the investment. In this case, the APR is:

0.08% * 18 months = 8%.

The effective annual rate of interest takes into account the compounding of interest over time. To calculate the effective annual rate of interest, we use the formula:

(1 + r/n)^n - 1, where r is the interest rate per period and n is the number of compounding periods per year.

In this case, the effective annual rate of interest is:

(1 + 0.08%/4)^4 - 1 = 8.24%.

So the annual percentage rate (APR) is 8% and the effective annual rate of interest is 8.24%

The energy expended in traveling by car is 3.6 mj/passenger-kilometer. the value for traveling by train is 1.1 mj/passenger-kilometer. Increase the number of passengers would be the best means to increase the efficiency of traveling by car. So the option 1 is correct.

Some ways to increase the efficiency of traveling by car:

1. Drive carefully and slowly

Driving on the open road is never the time for aggression. It impairs judgement and can cause rash actions. When operating your automobile, you must maintain a similar sense of composure and careful handling.

2. Turn off the engine while the car is idling.

If your car will be sitting still for more than 30 seconds, experts suggest shutting off the engine. Keeping your car's engine running when it is idling will only result in increased fuel consumption.

3. Travel at a steady pace.

Driving at a modest speed is the solution to the question of how to increase the mileage of your car. When this easy habit is followed, it will actually change things.

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The complete question is:

The energy expended in traveling by car is 3.6 mj/passenger-kilometer. the value for traveling by train is 1.1 mj/passenger-kilometer. What would be the best means to increase the efficiency of traveling by car? Please choose the correct answer from the following choices, and then select the submit answer button.

1. Increase the number of passengers

2. Decrease the number of passengers

3. Drive at High speed

4. Use aggressive driving

Yes, the new teaching method is quite successful.

Here, we have been told that the average score of the class mentioned in the question is 73 out of 100. This means that most of the class has been able to score at least 73% on the test.

This means that the new teaching method is quite successful as most of the students, that is 97% of the class, are able to understand what is being taught. Since the percentage of passing students is more than the percentage of children failing, we can conclude that the new teaching method is indeed successfully.

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Answer:

Charlotte can skate for 3 hours.

Step-by-step explanation:

To solve this equation, we can set up an equation that looks like this: 13.50h = 40.50

We can then divide both sides of the equation by 13.50 to get: h = 40.50/13.50

Simplifying this, we get: h = 3

Therefore, Charlotte can skate for 3 hours.

Answer: READ BELOW

Step-by-step explanation:

To divide decimals, you can follow these steps:

1.  Move the decimal point in the divisor (the number you're dividing by) to the right, counting the number of places you move it.

2. Move the decimal point in the dividend (the number you're dividing into) the same number of places to the right.

3. Divide the numbers as if they were whole numbers.

4. Place the decimal point in the quotient (the result) the same number of places from the right as the number you counted when moving the decimal points in step 1 and 2.

For example:

To divide 12.5 by 2.5, you would move the decimal point in 2.5 two places to the right to get 25, and move the decimal point in 12.5 two places to the right to get 1250. Then divide 1250 by 25 to get 50. Finally, place the decimal point two places from the right in the quotient 50 to get the final answer of 0.50.

Answer: To solve the problem, we need to find the total number of juice boxes.

We know that there are 3 packages of 10 juice boxes, which is 3*10 = 30 juice boxes.

And there are 7 extra juice boxes.

So the total number of juice boxes is 30 + 7 = 37 juice boxes.

We can write the number of tens and ones as:

Tens: 3

Ones: 7

And the total number of juice boxes is 37.

Step-by-step explanation:

The polygons are classified as;

33. 3 sides

34. 23 sides

A polygon can be defined as a plane figure that is described by a finite number of straight line segments which are all connected to form a closed polygonal chain.

The different types of polygons are;

From the information given,

The polygon has a measure of 180 degrees

The formula for calculating the sum of the angles of a polygon is;

(n-2) 180

(3-2)180

180. It is a triangle

(23--2) 180

21(60)

3960. It has 23 sides

Hence, the values are 3 and 23

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The probability that all six dice show a one is 1/46656

From the question, we have the following parameters that can be used in our computation:

Number of dices = 6

Outcome = all 1

The probability of rolling a one on one die is 1/6.

So the probability of rolling a one on all six dice is:

(1/6) * (1/6) * (1/6) * (1/6) * (1/6) * (1/6) = (1/6)^6

So the probability of all six dice showing a one is 1/46656

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Answer:

b. The money cannot be fully insured and earn annual interest of $39,740.

Step-by-step explanation:

Simple interest is calculated by multiplying the principal deposited by the interest rate (in decimal form) and the time (in years).

Let x be the amount invested in the savings account that pays 12% simple interest and where deposits are insured to only $250,000.

Therefore:

As the total amount the student is investing is $390,000, the amount invested in the second account that pays 6.6% simple interest is (390000 - x).  Therefore:

To determine if the money can be deposited so that it earns annual interest of $39,740, equate the sum of the two expressions for interest to $39.740 and solve for x:

[tex]\begin{aligned}0.12x+0.066(390000 - x)&=39740\\0.12x+25740-0.066x&=39740\\0.054+25740&=39740\\0.054&=14000\\x&=259259.26\;\sf(2\;d.p.)\end{aligned}[/tex]

As x is not less than or equal to $250,000, it is not possible to deposit the money so that it is fully insured and earns the desired interest.

Answer:

Step-by-step explanation: The equation that models the final balance A given principal P and time t is:A = P(1 + 0.077)^tTo find the equivalent monthly interest rate, we need to find the rate that when compounded monthly gives the same final balance as the annual rate of 7.7% compounded annually.First, we know that 1 year has 12 months, so we can find the number of months in t years by multiplying t by 12.Let's call this number of months n.n = t*12Next, we can use the property of exponents that (a^b)^c = a^(bc) and rewrite the equation as:A = P(1 + 0.077)^(n/12)Now we can find the monthly rate (r) by dividing the annual rate by 12r = 0.077/12 = 0.006416666666666666In percentage form, the equivalent monthly interest rate is approximately 0.64 %

The total population of the wolves after 2 years will be 500 + 125 = 625 wolves

a) After 1 year, the number of wolves in the forest will increase by 25% of the current population, which is 400 wolves.

The increase in population is equal to 0.25 * 400 = 100 wolves

The total population after 1 year will be 400 + 100 = 500 wolves

b) After 2 years, the number of wolves in the forest will increase by 25% of the population from the previous year, which is 500 wolves.

The increase in population is equal to 0.25 * 500 = 125 wolves

The total population after 2 years will be 500 + 125 = 625 wolves

Percentage is a way of expressing a number as a fraction of 100. It is denoted using the symbol %. For example, 50% means 50 per hundred, or 50/100.

Percentage is a convenient way of representing a ratio of a number to a whole, and it is often used to describe proportions and changes in quantities. For example, if a person's salary increases by 10%, their salary will be 10% higher than it was before. In mathematical terms, a percentage can be converted to a decimal or a fraction by dividing it by 100. For example, 50% can be written as 0.5 (as a decimal) or 1/2 (as a fraction).

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The true statements from the given statements are : 'If 7 is an odd number, then February does not have 30 days.' and 'If 7 is an even number, then January has exactly 28 days.'

Therefore the answer is (c) and (d).

(a) False. February does not have 30 days, it has 28 or 29 days (in a leap year). The statement is false, because 7 being an odd number has no connection to the number of days in February.

(b) False. January has 31 days, but 7 is an odd number.

(c) True. 7 is an odd number, and February has 28 or 29 days, but never 30 days.

(d) True. 7 being an odd number and the number of days in January, which cannot be 28 days, it is 31 days.

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Let the lengths of the pieces, in inches, be [tex]x, x+6, x+8[/tex].

The lengths of these pieces add to [tex]56[/tex] inches.

[tex]x+x+6+x+8=56 \\ \\ 3x+14=56 \\ \\ 3x=42 \\ \\ x=14[/tex]

So, the lengths of the pieces are 14 in, 20 in, and 22 in.

The standard matrix A is [ (1/2, √3/2) (√3/2, -1/2) ]

To find the standard matrix of a linear transformation, we need to find the images of the standard basis vectors under the transformation.

The standard basis vectors in R2 are (1,0) and (0,1). Let's find their images under T.

The image of (1,0) under a 30∘ clockwise rotation is (√3/2, 1/2). The image of this under reflection through the line y=x is (1/2, √3/2).

The image of (0,1) under a 30∘ clockwise rotation is (-1/2, √3/2). The image of this under reflection through the line y=x is (√3/2, -1/2).

The standard matrix of T is then the matrix whose columns are the images of the standard basis vectors:

A = [ (1/2, √3/2) (√3/2, -1/2) ]

= [tex]\left[\begin{array}{cc}1/2&\sqrt{3} /2\\\sqrt{3} /2&-1/2\end{array}\right][/tex]

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Answer:

Neither.

Step-by-step explanation:

Parallel equations have the same y-intercept. Perpendicular equations have negative reciprocal slopes.

First, turn x-y=9 into y-intercept form.

x-y-x=9-x

-y = 9 - x

(-y = 9 - x)-1

The equations are now

y = x-9 and

y= -5x+1 

They don't share the same y-intercept nor do they have negative reciprocal slopes, so it's neither.

Answer:85 percent of the teachers in the meeting were first-year teachers.

Step-by-step explanation:85/100=0.85