If john buys 8 jackets at x dollars a piece and 2 movie tickets at $11 a piece, whats the most he can spend on each jackets if his total budget is $200

The center of mass is given by:
(xbar, ybar, zbar) = (Mx/m, My/m, Mz/m)
                  = (0, 16/(3π), 16/(3π))

To find the mass of the wire, we need to integrate the density function over the length of the wire. The length of the wire can be found using the arc length formula:

ds = sqrt(dx^2 + dy^2 + dz^2)
  = sqrt(1 + 4sin^2(t) + 4cos^2(t)) dt
  = sqrt(5) dt

Integrating this from 0 to 2π gives us the length of the wire:

L = ∫_0^(2π) sqrt(5) dt
 = 2πsqrt(5)

Now we can find the mass of the wire:

m = ∫_0^(2π) ρ ds
 = ∫_0^(2π) (x^2 + y^2 + z^2) ds
 = ∫_0^(2π) (t^2 + 4cos^2(t) + 4sin^2(t)) sqrt(5) dt
 = 4πsqrt(5)

To find the center of mass, we need to find the moments about each coordinate axis:

Mx = ∫_0^(2π) ρ x ds
  = ∫_0^(2π) t(t^2 + 4cos^2(t) + 4sin^2(t)) sqrt(5) dt
  = 0 (due to symmetry)

My = ∫_0^(2π) ρ y ds
  = ∫_0^(2π) 2cos^2(t) (t^2 + 4cos^2(t) + 4sin^2(t)) sqrt(5) dt
  = 32π/(3sqrt(5))

Mz = ∫_0^(2π) ρ z ds
  = ∫_0^(2π) 2sin^2(t) (t^2 + 4cos^2(t) + 4sin^2(t)) sqrt(5) dt
  = 32π/(3sqrt(5))

Finally, the center of mass is given by:

(xbar, ybar, zbar) = (Mx/m, My/m, Mz/m)
                  = (0, 16/(3π), 16/(3π))

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a. Sin A = opposite/hypotenuse = √15/4

b.  (Sin A + Cos B) ÷ 2 = (Sin A + Cos B)/2

c.  Tan A  = 1/5

The both angle could be of same size

Since Cos A = adjacent/hypotenuse,

Applying  the Pythagorean theorem,

we can find the opposite side:

opposite^2 + 1^2 = 4^2

opposite^2 = 16 - 1

opposite = √15

Now we can find the value of Sin A:

Sin A = opposite/hypotenuse = √15/4

b.

Sin A + Cos B = (Sin A) + (Cos B)

(Sin A + Cos B) ÷ 2 = (Sin A + Cos B)/2

c. Since Tan B = opposite/adjacent,  

we use  Pythagorean theorem to  find the hypotenuse:

hypotenuse^2 = 5^2 + 1^2

hypotenuse = √26

Tan A = opposite/adjacent = 1/5

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Solving a system of equations we can see that he has 9 quarters and 16 dimes.

Let's define the variables:

x =  number of dimes

y = number of quarters.

There are 25 coins, so:

x + y = 25

The value is $3.85, so:

x*0.10 + y*0.25 = 3.85

So the system of equations is:

x + y = 25

x*0.10 + y*0.25 = 3.85

We can isolate x on the first equation to get:

x = 25 - y

Replacing that in the other one we get:

(25  -y)*0.10 + y*0.25 = 3.85

2.5 + y*0.15 = 3.85

y = (3.85 - 2.5)/0.15

y = 9

Then the other 16 coins are dimes.

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The area of the regular pentagon is about 9 square units.

To find the area of a regular polygon, we need to know the length of the apothem and the perimeter of the polygon. The apothem is the distance from the center of the polygon to the midpoint of one of its sides, and the perimeter is the sum of the lengths of all the sides.

Since the polygon is regular, all of its sides have the same length. Let's call that length "s". We also know that the polygon has 5 sides, so it is a pentagon. To find the perimeter, we can simply multiply the length of one side by the number of sides:

Perimeter = 5s

Now, to find the apothem, we can use the formula:

Apothem = (s/2) x tan(180/n)

Where "n" is the number of sides. For our pentagon, n = 5, so we have:

Apothem = (s/2) x tan(36)

We can simplify this a bit by noting that tan(36) is equal to approximately 0.7265. So we have:

Apothem = (s/2) x 0.7265

Now we have everything we need to find the area. The formula for the area of a regular polygon is:

Area = (1/2) x Perimeter x Apothem

Substituting in the values we found earlier, we have:

Area = (1/2) x 5s x (s/2) x 0.7265

Simplifying this expression, we get:

Area = (s^2 x 1.8176)

Rounding to the nearest whole number of square units, we have:

Area = 9

So the area of the regular pentagon is about 9 square units.

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The linearization of the function f(x, y) = e-¹⁰x-⁸y - 8y at (0, 0) is L(x, y) = -10x - 8y + 1. The correct option is C.

To find the linearization of the given function at the point (0, 0), we need to compute the partial derivatives with respect to x and y and then evaluate them at the given point.

The function is f(x, y) = [tex]e^{(-10x-8y)[/tex] - 8y.

First, find the partial derivative with respect to x:
∂f/∂x = [tex]-10e^{(-10x-8y).[/tex]

Now, evaluate ∂f/∂x at (0, 0):
∂f/∂x(0, 0) = [tex]-10e^{(0)[/tex] = -10.

Next, find the partial derivative with respect to y:
∂f/∂y = [tex]-8e^{(-10x-8y)[/tex] - 8.

Now, evaluate ∂f/∂y at (0, 0):
∂f/∂y(0, 0) = [tex]-8e^{(0)[/tex] - 8 = -8 - 8 = -16.

Now, we can form the linearization:
L(x, y) = f(0, 0) + ∂f/∂x(0, 0)(x - 0) + ∂f/∂y(0, 0)(y - 0).

Evaluate f(0, 0):
f(0, 0) = [tex]e^{(-10(0)-8(0))} - 8(0) = e^{(0)} - 0 = 1.[/tex]

Finally, substitute the values into the linearization formula:
L(x, y) = 1 - 10x - 16y.

Comparing to the given options, the answer is:
C) L(x, y) = -10x - 8y + 1

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To factor the polynomial x^2 - x - 6, we need to find two binomials whose product is equal to this polynomial. We can use the following methods to factor the polynomial:

Method 1: Factoring by inspection

- We know that x^2 is the product of x and x, so we can start with the binomial (x )(x ) as a factorization of x^2.

- We then look for two numbers whose product is -6 and whose sum is -1.

- The two numbers are -3 and 2, since (-3)(2) = -6 and (-3) + 2 = -1.

- Therefore, the polynomial x^2 - x - 6 can be factored as (x - 3)(x + 2).

Method 2: Using the quadratic formula

- We can also use the quadratic formula to find the roots of the polynomial, which are the values of x that make the polynomial equal to zero.

- The quadratic formula is x = (-b ± sqrt(b^2 - 4ac)) / 2a, where a = 1, b = -1, and c = -6.

- Plugging in these values, we get x = (-(-1) ± sqrt((-1)^2 - 4(1)(-6))) / 2(1) = (1 ± sqrt(25)) / 2.

- Simplifying, we get x = 3 or x = -2.

- Therefore, the polynomial x^2 - x - 6 can be factored as (x - 3)(x + 2).

So, the pairs of polynomials that, when multiplied together, result in the polynomial x^2 - x - 6 are (x - 3) and (x + 2), as well as (x + 2) and (x - 3).

The solution set for the equation 1/2 = 1/3 - |(x-3/6)+x| is {1/12, -1/12}.

To solve the equation 1/2 = 1/3 - |(x-3/6)+x|, we need to isolate the absolute value expression and solve for x in two cases.

Case 1: (x-3/6)+x is nonnegative, which means the absolute value can be removed.

1/2 = 1/3 - (x-3/6)-x

1/2 = 1/3 - 2x + 1/2

2x = 1/6

x = 1/12

Case 2: (x-3/6)+x is negative, which means the absolute value must be flipped.

1/2 = 1/3 + (x-3/6)+x

1/2 = 1/3 + 2x - 1/2

2x = -1/6

x = -1/12

Therefore, the solution set is {1/12, -1/12}.

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The missing angle for x by the measures add up to 90° is 53°

Complementary angles are pairs of angles whose measures add up to 90°. In this problem, we are given two angles, one of which measures 37°, and the other of which has an unknown measure that we will call x. We are also told that these angles are complementary, which means that their measures add up to 90°.

So, we can set up an equation to represent this relationship:

37 + x = 90

We can simplify this equation by subtracting 37 from both sides:

x = 90 - 37

x = 53

Now we know that the measure of the second angle is 53°. But we can go further and solve for x to get a more complete solution.

In the problem statement, we are also given an expression for the second angle in terms of x:

5x + 3

We know that this angle measures 53°, so we can set up another equation to represent this relationship:

5x + 3 = 53

We can solve for x by first subtracting 3 from both sides:

5x = 50

Then, we can divide both sides by 5 to isolate x:

x = 10

Now we know that x has a value of 10, and we can substitute this value back into the expression for the second angle to find its measure:

= 5x + 3

= 5(10) + 3 = 53

Therefore, the missing angle is 53°, and x has a value of 10.

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The cost of one pine tree is $17.50.

To find the cost of one pine tree, we can use the information provided about the orders from the Greenery Landscaping Company. We have the following two equations:

1) 2P + 5H = $150 (2 pine trees and 5 hydrangea bushes)

2) 3P + 4H = $144.50 (3 pine trees and 4 hydrangea bushes)

Now, let's solve these equations using the substitution or elimination method. Here, we'll use the elimination method.

Step 1: Multiply the first equation by 3 and the second equation by 2 to make the coefficients of H the same:

1) 6P + 15H = $450

2) 6P + 8H = $289

Step 2: Subtract the second equation from the first equation:

(6P + 15H) - (6P + 8H) = $450 - $289

0P + 7H = $161

Step 3: Divide by 7 to find the cost of one hydrangea bush (H):

H = $161 / 7

H = $23

Step 4: Substitute the value of H back into one of the original equations to find the cost of one pine tree (P). We'll use the first equation:

2P + 5($23) = $150

2P + $115 = $150

Step 5: Subtract $115 from both sides of the equation:

2P = $35

Step 6: Divide by 2 to find the cost of one pine tree (P):

P = $35 / 2

P = $17.50

So, the cost of one pine tree is $17.50.

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The value of c in equation y= 0. 884 sin(0. 245x - 1. 093) + 0. 400 is c. 0. 245.

The given equation represents a sine regression model, where y is the dependent variable and x is the independent variable. The equation includes a sine function with a frequency of 0.245 and an amplitude of 0.884. The constant term, 0.400, represents the vertical shift or the y-intercept of the graph. The phase shift, 1.093, determines the horizontal shift of the graph.

To find the value of c, we need to look at the coefficient of x in the sine function. In this case, the coefficient of x is 0.245, which represents the frequency or the number of complete cycles that occur in a given interval. Therefore, the answer is (c) 0.245.

It's important to note that the coefficient of x in a sine regression model represents the frequency and not the phase shift or the horizontal shift. The phase shift is determined by the constant term in the sine function.

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The area of the triangle is 6 cm².

Let's denote the width of the triangle as "w." According to the given information, the length of the triangle is three times its width, so the length can be expressed as "3w."

The perimeter of a rectangle is given by the formula: Perimeter = 2(length + width). In this case, the perimeter of the rectangle is given as 24 cm.

We can set up the following equation based on the given information:

24 = 2(3w + w)

Simplifying the equation:

24 = 2(4w)

12w = 24

w = 24/12

w = 2 cm

Now that we have the width of the triangle, we can find the length:

Length = 3w = 3 * 2 = 6 cm

The area of a triangle is given by the formula: Area = (base * height) / 2. In this case, the base of the triangle is the width (2 cm) and the height is the length (6 cm).

Area = (2 * 6) / 2

Area = 12 / 2

Area = 6 cm²

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Answer: x ≅ -0.9 or -1.8

Step-by-step explanation:

[tex]3(3x+4)^2 - 6 = 0[/tex]

[tex]3(3x+4)^2 = 6[/tex]

[tex]3(9x^2+24x+16) = 6[/tex]

[tex]9x^2+24x+16 = 2[/tex]

[tex]9x^2+24x+14 = 0[/tex]

Use the quadratric formula to get:

x ≅ -0.9 or -1.8

By using Mai’s method, the skirt will cost $21.67, By using Elena’s method, the skirt will cost $21 and I think Mai’s method is correct.

(1) We need to find out how much the skirt cost if we use the Mai method. the Mai method is to multiply $30 by 0.80 and then we need to again multiply it with the result which can be given as,

= 30 × 0. 85 × 0. 85

= 21.67

Therefore, By using Mai’s method, the skirt will cost $21.67.

(2) We need to find out how much the skirt cost if we use Elena’s method. Elena’s method is to  multiply $30 by 0. 70 it can be given as,

= 30 × 0. 70

=$21

Therefore, By using Elena’s method, the skirt will cost $21.

(3) I think Mai’s method is correct because she took one 15% discount first and then considered the second discount which is given by the shop. whereas  Elena considered the two discounts at once and calculated it as 30% where the shop offered a 15% discount on the dress and then added a second discount on the purchase cost or bill amount that is why Mai’s method is correct.

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The probability of getting a number less than 5 or greater than 9 is:

P = 0.583

The probability is equal to the quotient between the number of outcomes for the given event and the total number of outcomes.

The numbers that are less than 5 or greater than 9 are:

{1, 2, 3, 4, 10, 11, 12}

So 7 out of the total of 12 outcomes make the event true, then the probability we want to get is the quotient between these numbers:

P = 7/12 = 0.583

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The component form of u + v can be found using the given lengths and angles and it  is (6, √3).

To find the component form of u + v given the lengths of u and v and the angles that u and v make with the positive x-axis we will sum the u and v.

Given Ilull = 5 and Ou = 0°, we can represent vector u as (5, 0) in component form. Given |Iv|I = 2 and Ov = 60°, we can represent vector v as (2cos60°, 2sin60°) = (1, √3) in component form.

To find u + v, we add the corresponding components of u and v. This gives us:

u + v = (5, 0) + (1, √3) = (5+1, 0+√3) = (6, √3)

Therefore, the component form of u + v is (6, √3).

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Answer:

$7973.26

Step-by-step explanation:

PV = $6700

i = 5.8% ÷ 365

n = 3 years · 365

Compound formula

FV = PV (1 + i)^n

FV = 6700 (1 + 5.8% ÷ 365)^(3 · 365)

FV = $7973.26 (rounded to the nearest cent)

Answer:

The value of Eva's investment after 3 years will be approximately $8,108.46. Rounded to the nearest cent, this is $8,108.45.

Step-by-step explanation:

We can use the formula for compound interest:

where:

In this case, we have:

Plugging these values into the formula, we get:

Therefore, the value of Eva's investment after 3 years will be approximately $8,108.46. Rounded to the nearest cent, this is $8,108.45.

In this scenario, the domain would be the set of all possible values for the amount of time it takes Sammy Speedster to drive from Houston to San Antonio. Since he is driving on a daily basis, the domain could be considered a continuous range from zero to some maximum value, perhaps 10 hours.

It's possible that Sammy could complete the trip in less than 3 hours if he were driving at a very high speed, but this would not be a common occurrence. Therefore, a reasonable domain could be considered to be between 3 and 10 hours.

The range, on the other hand, would be the set of all possible distances that Sammy could drive in the allotted time. Since we know that the distance is a constant 200 miles, the range would simply be 200 miles. It's possible that Sammy could drive more than 200 miles in a day if he were assigned additional routes, but this would not be relevant to this scenario.

In summary, a reasonable domain for Sammy's logbook would be between 3 and 10 hours, and the range would be a constant 200 miles.

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If we have 30 total participants in a between-subjects design with three groups, we can assign any number of participants to each group as long as the sum of participants in each group adds up to 30. The number of participants in each group is 10 in the 8-ounce group, 15 in the 24-ounce group, and 5 in the no-caffeine group.

If we have a total of 30 participants in a between-subjects design, we need to divide them into three groups according to the conditions.

Let x be the number of participants who received 8 ounces of a caffeinated beverage, y be the number of participants who received 24 ounces of a caffeinated beverage, and z be the number of participants who received no caffeine. Since we have a total of 30 participants, we can write

x + y + z = 30

We don't know the specific number of participants in each group, but we do know that they must add up to 30.

However, we also know that each participant can only be in one group, which means that we have mutually exclusive groups. Therefore, we can assume that there is no overlap between the groups, which means that the total number of participants in each group is

x + y + z = 30

z = 30 - (x + y)

So, we can assign any value to x and y, as long as the sum of x and y is less than or equal to 30. Then, we can find the value of z using the equation above.

For example, if we assign 10 participants to the 8-ounce group and 15 participants to the 24-ounce group, we would have

x = 10

y = 15

z = 30 - (10 + 15) = 5

So, there would be 10 participants in the 8-ounce group, 15 participants in the 24-ounce group, and 5 participants in the no-caffeine group.

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If your rate of pay is $36 per hour and you bill by the quarter hour, you would bill $162 for 4 hours and 30 minutes project.

Based on the given information, your rate of pay is $36 per hour, and you bill by the quarter hour. You spent 4 hours and 30 minutes on a client project.

To calculate the bill, first convert the 30 minutes into quarter hours: 30 minutes = 2 quarter hours. In total, you worked for 4 hours and 2 quarter hours (18 quarter hours).

Now, multiply your rate of pay ($36) by the number of quarter hours (18) and divide by 4 to account for the quarter hour billing: ($36 * 18) / 4 = $162. Therefore, you would bill the client $162 for the project.

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The equation that represents the Ferrells' savings after x months is y = 150x

In this equation, x represents the number of months that the Ferrells have been saving, and y represents the amount of money they have saved after x months.

The coefficient 150 represents the amount of money the Ferrells save each month, and it is multiplied by the number of months x to get the total savings y. For example, after 5 months of saving, the Ferrells would have saved:

y = 150(5) = $750

This equation can be used to calculate their savings at any point in time, as long as they continue to save $150 each month.

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Let's first calculate the total cost of using Green Lawns for 30 weeks. We can use the formula for the sum of a geometric series to do this:

Total cost of Green Lawns =[tex]2(1 - 0.9^30) / (1 - 0.9) + 0.9^30 * 2[/tex]

Total cost of Green Lawns = [tex]2(1.7379) / 0.1 + 0.0359[/tex]

Total cost of Green Lawns = 38.8179

Now let's calculate the total cost of using Green Thumbs for 30 weeks:

Total cost of Green Thumbs = [tex]400 + 40 * 29[/tex]

Total cost of Green Thumbs = 1160

Therefore, the Yert family would save:

$1160 - $38.8179 = $1121.18

So the Yert family would save $1,121.18 by choosing Green Lawns over Green Thumbs for 30 weeks.

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To determine this family's annual medical aid tax credit, we need to consider their medical aid expenses for the year. Medical aid expenses are expenses related to medical services that are not covered by the government or medical insurance.

This family can claim a tax credit of up to R310 per month for the main member and the first dependent, and R209 per month for each additional dependent. This tax credit is only applicable to registered medical schemes and is deducted from the tax payable.

In addition to medical aid expenses, this family will also need to consider the 15% VAT payable on all goods and services, except for sanitary pads, fresh produce, and a few other staple food items. This means that if this family spends R10,000 on goods and services, they will need to pay an additional R1,500 in VAT.

However, the good news is that they won't have to pay VAT on their fresh produce and staple food items. This will help to reduce their overall expenditure on food, which is an essential expense for every family.

In conclusion, while this family will need to pay VAT on most goods and services, they can claim a tax credit for their medical aid expenses. Additionally, they won't have to pay VAT on fresh produce and staple food items, which will help to reduce their overall food expenditure.

By carefully managing their expenses and taking advantage of tax credits and exemptions, this family can ensure that they are able to provide for their essential needs while also managing their financial obligations.

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The length and width of the chocolate bar is 14.5 feet and 7.6 feet.

What is length?

Length is a measure of the size of an object or distance between two points. It refers to the extent of something along its longest dimension, or the distance between two endpoints.

What is width?

Width refers to the measure of the distance from one side of an object to the other side, perpendicular to the length. In geometry, width is usually measured in units such as meters, feet, or inches.

According to the given information:

Let's start by assigning variables to represent the length and width of the chocolate bar. Let x be the width of the chocolate bar in feet. Then, according to the problem:

The length of the chocolate bar is 0.3 feet shorter than twice its width, which means the length is (2x - 0.3) feet.

The base area of the chocolate bar is given as 61.04 square feet. We can use this information to set up an equation:

x(2x - 0.3) = 61.04

Expanding the left side of the equation:

2x^2 - 0.3x = 61.04

Moving all the terms to one side of the equation:

2x^2 - 0.3x - 61.04 = 0

Now we can solve for x using the quadratic formula:

x = (-b ± sqrt(b^2 - 4ac)) / 2a

where a = 2, b = -0.3, and c = -61.04. Substituting these values and simplifying:

x = (0.3 ± sqrt(0.3^2 + 4(2)(61.04))) / (2(2))

x ≈ 7.6 or x ≈ -4.0

Since the width of the chocolate bar cannot be negative, we can discard the negative solution. Therefore, the width of the chocolate bar is approximately 7.6 feet.

To find the length, we can use the equation we set up earlier:

length = 2x - 0.3

Substituting x = 7.6:

length = 2(7.6) - 0.3

length ≈ 14.5

Therefore, the length of the chocolate bar is approximately 14.5 feet and the width is approximately 7.6 feet.

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Answer:

Modise is right.

This diagram does not represent a function because each input value does not correspond to exactly one output value. The input value 5 corresponds to two outputs, 2 and 9.

In order to evaluate h'(9), we need to use the product rule, which states that the derivative of a product of two functions is equal to the first function times the derivative of the second function, plus the second function times the derivative of the first function. Mathematically, this can be expressed as:

(h(x))' = f(x)g'(x) + g(x)f'(x)

Using the given values, we can substitute them into the formula and solve for h'(9):

h'(x) = f(x)g'(x) + g(x)f'(x)
h'(9) = f(9)g'(9) + g(9)f'(9)
h'(9) = 9(2) + 3(-1.5)
h'(9) = 18 - 4.5
h'(9) = 13.5

Therefore, the value of h'(9) is 13.5.

In simpler terms, the product rule tells us that when we have a function that is the product of two other functions, we can find the derivative of that function by multiplying one function by the derivative of the other and adding it to the other function multiplied by the derivative of the first. In this case, we have two functions f(x) and g(x), and we use their respective values and derivatives to find the derivative of their product h(x).

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There are 24 three-digit numbers without repeating digits, and 64 three-digit numbers with repeating digits.

1) Pentru a alcătui numere de trei cifre în care cifrele să nu se repete, putem utiliza principiul combinatoric al permutărilor. Având la dispoziție cifrele 1, 2, 3 și 4, vom avea 4 posibilități pentru a alege prima cifră, 3 posibilități pentru a alege a doua cifră și 2 posibilități pentru a alege a treia cifră. Prin înmulțirea acestor numere, obținem:

4 * 3 * 2 = 24

Există deci 24 de numere de trei cifre în care cifrele nu se repetă, utilizând cifrele 1, 2, 3 și 4.

2) Pentru a alcătui numere de trei cifre în care cifrele se repetă, vom avea 4 posibilități pentru a alege oricare dintre cele trei cifre și anume 1, 2, 3 și 4. Prin urmare, avem:

4 * 4 * 4 = 64

Există 64 de numere de trei cifre în care cifrele se pot repeta, utilizând cifrele 1, 2, 3 și 4.

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This system represents the purchase made by Muriel (2 boxes of pencils and 4 erasers for $11) and Ramon (1 box of pencils and 3 erasers for $7).

The correct system of equations to find the price of one box of pencils (p) and one eraser (e) is:

2p + 4e = 11

p + 3e = 7

This system represents the purchase made by Muriel (2 boxes of pencils and 4 erasers for $11) and Ramon (1 box of pencils and 3 erasers for $7).

By solving this system of equations, you can determine the individual prices for a box of pencils and an eraser.

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Alissa's new fish tank should hold 35 gallons of water.

"Gallons" is a unit of measurement for volume, typically used to measure liquids or gases. It is commonly abbreviated as "gal" and is equivalent to 3.785 liters in the metric system.

Alissa's old fish tank holds 20 gallons of water. To find out how many gallons of water her new fish tank should hold, we need to multiply the old tank's capacity by 175% or 1.75 (since 175% = 1.75 as a decimal).

So, the new tank's capacity should be:

20 gallons x 1.75 = 35 gallons

Therefore, Alissa's new fish tank should hold 35 gallons of water.

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x = -5, dx/dt is equal to -2/25.

To find dx/dt, we need to use the chain rule of differentiation.

We know that dy/dt = -4 and we have the equation y = -5x^2 + 2.

Taking the derivative of both sides with respect to t, we get:

dy/dt = d/dt (-5x^2 + 2)

Using the chain rule, we can write this as:

dy/dt = (-10x) (dx/dt)

Now, we can plug in x = -5 and dy/dt = -4:

-4 = (-10(-5)) (dx/dt)

Simplifying, we get:

-4 = 50 (dx/dt)

Dividing both sides by 50, we get:

dx/dt = -4/50

Simplifying further, we get:

dx/dt = -2/25

Therefore, at x = -5, dx/dt is equal to -2/25.

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The main types of markets are:

So, the correct answer is "consumer" and "industrial".

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