-6 = 3/8x - 2 + 1/8x
Answers:
x = -16
x = 8
x = -8
x = -4

The original price of the coat is 100 dollar.

The unitary method is a method for solving a problem by the first value of a single unit and then finding the value by multiplying the single value. Unitary method is a method by which we find the value of a single unit from the value of multiple devices and the value of more than one unit from the value of a single unit. It is a method that we use for most of the calculations in math.

WE are given that price of a coat was reduced by 20%. two weeks later, it was reduced again by 25%.

Then the final price after the discounts was $60.

So if it reduced by 20% first time, then reduced 25% then we add them we get 45 and them 100-45 we get 55% .

55% of original price is 60 45% left and then

60+40=100

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The expression (2⁷ · 3⁻⁵ · 9)⁴ is equivalent to the power expression 2²⁸ / 3¹² = 505.109.

In this problem we find an expression involving several numbers in power form and we must simplify into a single real number by using algebra properties:

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Answer:

The area of the triangle AOB is 10

Step-by-step explanation:

The line 4x+5y-20=0 forms a triangle AOB as shown in the figure below. The points A and B are the y-intercept and x-intercept respectively, and the point O is the origin.

To find the intercepts, we set the other variable to zero and solve the resulting equation.

Set x=0, the y-intercept is found as follows:

4(0)+5y-20=0

5y=20

y=20/5=4

The y-intercept is y=4

Set y=0, the x-intercept is now found:

4x+5(0)-20=0

4x=20

Solve:

x=20/4=5

The x-intercept is x=5

Now, knowing the base b and the height of the triangle h are 5 and 4 respectively, the area of the triangle is:

\(\displaystyle A=\frac{bh}{2}\)

\(\displaystyle A=\frac{5\cdot 4}{2}=10\)

The area of the triangle AOB is 10

Answer:

The correct option is

\(A. \ \dfrac{1}{c} \times \left | x - 5 \right | = 0.3\)

Step-by-step explanation:

The parameters given are;

The length of the string = 10 inches

The speed or rate of travel of the wave = c inches per millisecond

The position on the string from the left-most end = x

The time duration of motion of the vibration to reach x= 0.3 milliseconds

The distance covered = Speed × Time = c×0.3

Given that the string is plucked at the middle, with the vibration travelling in both directions, the point after 0.3 millisecond is x where we have;

The location on the string where it is plucked = center of the string = 10/2 = 5 inches

Distance from point of the string being plucked (the center of the string) to the left-most end = 5 inches

Therefore, on the left side of the center of the string we have;

The distance from the location of the vibration x (measured from the left most end) to the center of the string = 5 - x = -(x -5)

On the right side of the center, the distance from x is -(5 - x) = x - 5

Therefore, the the equation that can be used to find the location of the vibration after 0.3 milliseconds is \(\dfrac{1}{c} \times \left | x - 5 \right | = 0.3\) or \(\left | x - 5 \right | = 0.3 \times c\) which gives the correct option as A

Answer: 129.9

Step-by-step explanation:

tan 30 = 75/x

x = 75/tan 30

x = 129.9

The correct answer is c. 0.40.

We can use the formula for conditional probability to solve for P(A | B):

P(A | B) = P(A ∩ B) / P(B)

We can also use the formula for the complement of a set to solve for P(A ∩ B):

P((A ∪ B)c) = 1 - P(A ∪ B)

0.2 = 1 - P(A ∪ B)

P(A ∪ B) = 0.8

We can then use the formula for the union of two sets to solve for P(A ∩ B):

P(A ∪ B) = P(A) + P(B) - P(A ∩ B)

0.8 = 0.6 + 0.5 - P(A ∩ B)

P(A ∩ B) = 0.3

Now we can plug in the values for P(A ∩ B) and P(B) into the formula for conditional probability:

P(A | B) = 0.3 / 0.5

P(A | B) = 0.6

Therefore, the correct answer is c. 0.40.

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The probability that a student has a dog, given that they do not have a cat is 5/6.

The probability that a student has a dog given that they do not have a cat is :

P ( Has a dog | Does not have a cat ) = P ( Has a dog and does not have a cat) / P ( Does not have a cat )

Total number of students = 11 + 10 + 5 + 2 = 28

P ( Has a dog | Does not have a cat ):

= (10 / 28) / (12 / 28)

= 10 / 12

= 5 / 6

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The solution after using long division of polynomial 2x^3 +7x^2 +2x +9/2x+3 is    x^2   + 2x  -  5  

Long division is a method used to divide two numbers, usually polynomials or multi-digit numbers. It involves a series of steps where the dividend (the number being divided) is divided by the divisor (the number that is dividing the dividend). The process continues until either the remainder becomes zero, or the degree of the remainder is less than the degree of the divisor. The long division of the polynomial 2x^3 + 7x^2 + 2x + 9 by 2x + 3 is as follows:  

               x^2   + 2x  -  5  

   _________________________

2x + 3 |   2x^3  + 7x^2  +  2x  + 9

              2x^3  + 3x^2

       _____________

              4x^2 + 2x

              4x^2 + 6x

              _____________

                     -4x + 9

Therefore, the quotient is x^2 + 2x - 5 and the remainder is -4x + 9. Thus, we can write:

2x^3 + 7x^2 + 2x + 9 = (x^2 + 2x - 5)(2x + 3) - 4x + 9.

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Answer:

\(c=-2\)

Step-by-step explanation:

We are given the function:

\(f(x) = -2c + cx - x^2\)

And that:

\(\displaystyle f^{-1} (5) = -1\)

And we want to determine the value of c.

Recall that by definition of inverse functions:

\(\displaystyle \text{If } f(a) = b, \text{ then } f^{-1}(b) = a\)

So, since f⁻¹(5) = -1, then f(-1) = 5.

Substitute:

\(f(-1) = 5 = -2c + c(-1) - (-1)^2\)

Simplify:

\(5 = -2c - c - (1)\)

Combine like terms:

\(6 = -3c\)

And divide. Hence:

\(c = -2\)

In conclusion, the value of c is -2.

The correct answer is B. created in an iterative and incremental manner.

Unlike traditional Work Breakdown Structures (WBS), evolutionary WBSs are developed in an iterative and incremental manner. This means that they are built and refined over time as the project progresses, allowing for adjustments and additions to be made as new information becomes available. The evolutionary WBS is not organized in a standard manner across all projects (A) and it is not specifically designed for comparison to past projects (C). Therefore, the answer is B. created in an iterative and incremental manner.

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Answer: $112

Step-by-step explanation:

o get the solution, we are looking for, we need to point out what we know.

1. We assume, that the number 560 is 100% - because it's the output value of the task.

2. We assume, that x is the value we are looking for.

3. If 560 is 100%, so we can write it down as 560=100%.

4. We know, that x is 20% of the output value, so we can write it down as x=20%.

5. Now we have two simple equations:

1) 560=100%

2) x=20%

where left sides of both of them have the same units, and both right sides have the same units, so we can do something like that:

560/x=100%/20%

6. Now we just have to solve the simple equation, and we will get the solution we are looking for.

7. Solution for what is 20% of 560

560/x=100/20

(560/x)*x=(100/20)*x       - we multiply both sides of the equation by x

560=5*x       - we divide both sides of the equation by (5) to get x

560/5=x

112=x

x=112

now we have:

20% of 560=112

Mark has 20 marbles to sell, and Don has 82 marbles to sell.

To determine the number of marbles each boy has to sell, we can set up a system of equations based on the given information. Let's represent the number of marbles Mark has as "m" and the number of marbles Don has as "d". We know that the total number of marbles is 102, and Don has 2 more than 4 times the number of marbles Mark has. By solving this system of equations, we can find the values for "m" and "d".
Let's set up the equations based on the given information:
1. m + d = 102 (equation representing the total number of marbles)
2. d = 4m + 2 (equation representing Don's number of marbles in terms of Mark's number of marbles)
We can solve this system of equations by substitution or elimination. Let's use substitution:
Substitute equation 2 into equation 1:
m + (4m + 2) = 102
5m + 2 = 102
5m = 100
m = 20
Substitute the value of m back into equation 2 to find d:
d = 4(20) + 2
d = 82
Therefore, Mark has 20 marbles to sell, and Don has 82 marbles to sell.

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Answer:

3n+9

Step-by-step explanation:

Answer:

66

Step-by-step explanation:

multiply both sides by 6 and get x=11x6=66

Answer:

112 square units.

Step-by-step explanation:

Use the formula for the area of a triangle.

\(A=bh\)

\(b \times h\)

\(14 \times 8\)

\(=112\)

Answer:

B is correct.

The base is 20 feet, and the height is 8 feet, so the area is 20 × 8 = 160 square feet.

Answer:

b. $70.25

Explanation:

• Given:, The fabric cost per yard = $6.69.

• To find:, The total cost for 10½ yards.

Liz needed 10½ yards of the fabric and a yard of the fabric costs $6.69.

To find the total cost, multiply the cost per yard by the total yards needed.

Therefore:

Her total cost was $70.25 (Option B is correct).

Answer:

140 comied

Step-by-step explanation:

Answer:

a

Step-by-step explanation:

40° + 3y + 2y = 180°

↔ 5y = 140°

↔ y =28°

Answer:

\(x=-\dfrac{1}{6}\)

Step-by-step explanation:

For a quadratic function in standard form  \(y=ax^2 + bx + c\), the axis of symmetry can be expressed as \(x=\dfrac{-b}{2a}\)

For the equation \(y=3x^2+x\)

\(a=3, b=1, c=0\)

Therefore, the axis of symmetry is \(x=-\dfrac{1}{6}\)

Answer:

x=1.3 continuing

Step-by-step explanation:

Answer:

Step-by-step explanation:

To convert square meters to square centimeters, we need to multiply by the conversion factor (100 cm / 1 m)^2.

So,

3.9 m² = 3.9 × (100 cm / 1 m)²

3.9 m² = 3.9 × 10,000 cm²

3.9 m² = 39,000 cm²

Therefore, 3.9 square meters is equal to 39,000 square centimeters.

The ball reached its maximum height at a time of 1 second.

In this problem we have the case of a ball that experiments a free fall, that is, a case of an uniform accelerated motion due to gravity. The position of the ball as a function of time is represented by a quadratic equation:

y' = y + v · t + 0.5 · g · t²

Where:

And to determine the time related to the highest point, we need to rearrange the expression into its standard form:

y' - k = C · (t - h)²

Where:

First, write the quadratic equation:

y' = y + v · t + 0.5 · g · t²

y' = 10 + 16 · t - 8 · t²

Second, complete the square until the standard form is found:

y' - 10 = 16 · t - 8 · t²

y' - 10 = - 8 · (t² - 2 · t)

y' - 18 = - 8 · (t² - 2 · t + 1)

y' - 18 = - 8 · (t - 1)²

The ball takes a time of 1 second to reach its maximum height.

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Answer:

Step-by-step explanation:

0.85=17/20

0.5=1/2

(17/20) / (1/2)

Answer:

3 quarts and 14 ounces of honey remain in the beehive.

Step-by-step explanation:

Pint = 16 ounces

Gallon = 128 ounces

Quart = 32 ounces

So, we start with a total of 640 ounces of honey. The beekeeper removes 530 ounces, leaving 110 behind. 32 ounces in a quart means that there are 3 full quarts in the hive as well as 14 ounces.

The second solution is: y2(x) = -1 / x¹⁸ + 29x sin(5lnx) ∫ e^(29u) / sin(u) du/5 + Cx sin(5lnx) where C is a constant of integration.

To find a second solution y2(x) for the given differential equation x²y'' - xy' + 26y = 0 with the function y1(x) = x sin(5 ln x), we'll use the reduction of order formula:y2(x) = y1(x) * e^(-∫P(x)dx) * ∫(e^(∫P(x)dx) / y1(x)^2 dx)
First, rewrite the given differential equation in the standard form:
y'' - (1/x)y' + (26/x²)y = 0
From this, we can identify P(x) = -1/x.
Now, calculate the integral of P(x):
∫(-1/x) dx = - ln|x|
Now, apply the reduction of order formula:
y2(x) = x sin(5 ln x) * e^(ln|x|) * ∫(e^(-ln|x|) / (x sin(5 ln x))² dx)
Simplify the equation:
y2(x) = x sin(5 ln x) * x * ∫(1 / x² (x sin(5 ln x))² dx)
y2(x) = x² sin(5 ln x) * ∫(1 / (x² sin²(5 ln x)) dx)
Now, you can solve the remaining integral to find the second solution y2(x) for the given differential equation.

To find the second solution y2(x), we will use the reduction of order method. Let's assume that y2(x) = v(x) y1(x), where v(x) is an unknown function. Then, we can find y2'(x) and y2''(x) as follows:
y2'(x) = v(x) y1'(x) + v'(x) y1(x)
y2''(x) = v(x) y1''(x) + 2v'(x) y1'(x) + v''(x) y1(x)
Substituting y1(x) and its derivatives into the differential equation and using the above expressions for y2(x) and its derivatives, we get:
x^2 (v(x) y1''(x) + 2v'(x) y1'(x) + v''(x) y1(x)) - x(v(x) y1'(x) + v'(x) y1(x)) + 26v(x) y1(x) = 0
Dividing both sides by x^2 y1(x), we obtain:
v(x) y1''(x) + 2v'(x) y1'(x) + (v''(x) + (26/x^2) v(x)) y1(x) - (1/x) v'(x) y1(x) = 0
Since y1(x) is a solution of the differential equation, we have:
x^2 y1''(x) - x y1'(x) + 26y1(x) = 0
Substituting y1(x) and its derivatives into the above equation, we get:
x^2 (5v'(x) cos(5lnx) + (25/x) v(x) sin(5lnx)) - x(v(x) cos(5lnx) + v'(x) x sin(5lnx)) + 26v(x) x sin(5lnx) = 0
Dividing both sides by x sin(5lnx), we obtain:
5x v'(x) + (25/x) v(x) - v'(x) - 5v(x)/x + v'(x) + 26v(x)/x = 0
Simplifying the above expression, we get:
v''(x) + (1/x) v'(x) + (1/x² - 31/x) v(x) = 0

This is a second-order linear homogeneous differential equation with variable coefficients. We can use formula (5) in Section 4.2 to find the second linearly independent solution:
y2(x) = y1(x) ∫ e^(-∫P(x) dx) / y1^2(x) dx
where P(x) = 1/x - 31/x^2. Substituting y1(x) and P(x) into the above formula, we get:
y2(x) = x sin(5lnx) ∫ e^(-∫(1/x - 31/x²) dx) / (x sin(5lnx))² dx
Simplifying the exponent and the denominator, we get:
y2(x) = x sin(5lnx) ∫ e^(31lnx - ln(x)) / x^2sin²(5lnx) dx
y2(x) = x sin(5lnx) ∫ x^30 / sin²(5lnx) dx
Let u = 5lnx, then du/dx = 5/x, and dx = e^(-u)/5 du. Substituting u and dx into the integral, we get:
y2(x) = x sin(5lnx) ∫ e^(30u) / sin²(u) e^(-u) du/5
y2(x) = x sin(5lnx) ∫ e^(29u) / sin²(u) du/5
Using integration by parts, we can find that:
∫ e^(29u) / sin^2(u) du = -e^(29u) / sin(u) - 29 ∫ e^(29u) / sin(u) du + C
where C is a constant of integration. Substituting this result into the expression for y2(x), we get:
y2(x) = -x sin(5lnx) e^(29lnx - 5lnx) / sin(5lnx) - 29x sin(5lnx) ∫ e^(29u) / sin(u) du/5 + Cx sin(5lnx)
Simplifying the first term and using the substitution u = 5lnx, we get:
y2(x) = -x⁶ e^(24lnx) + 29x sin(5lnx) ∫ e^(29u) / sin(u) du/5 + Cx sin(5lnx)
y2(x) = -x⁶ / x^24 + 29x sin(5lnx) ∫ e^(29u) / sin(u) du/5 + Cx sin(5lnx)
y2(x) = -1 / x¹⁸ + 29x sin(5lnx) ∫ e^(29u) / sin(u) du/5 + Cx sin(5lnx)
Therefore, the second solution is: y2(x) = -1 / x¹⁸ + 29x sin(5lnx) ∫ e^(29u) / sin(u) du/5 + Cx sin(5lnx) where C is a constant of integration.

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A fair coin is tossed 7 times. the results were 4 heads and 3 tails, the probability the last two flips were heads is 1/4 or 0.25 .

The probability of getting a head on a fair coin toss is 1/2, and the probability of getting a tail is also 1/2. When a coin is tossed multiple times, each toss is independent of the others.

Given that the first 5 flips resulted in 4 heads and 1 tail, the probability of the last 2 flips being heads can be calculated as follows:

Probability of getting a head on the 6th toss = 1/2

Probability of getting a head on the 7th toss = 1/2

Therefore, the probability of getting two consecutive heads in the last two tosses is:

= Probability of getting a head on the 6th toss * Probability of getting a head on the 7th toss

= (1/2) * (1/2)

= 1/4

So the probability that the last two flips were heads, given that the first five flips resulted in 4 heads and 1 tail, is 1/4 or 0.25.

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The question is incomplete. The complete question is :

To bill customers for water usage, one city converts the number of gallons used into units. This relationship is represented by the equation g = 748u, where g is the total number of gallons of water used and u is the number of units. Determine which statements about the relationship are true. Check all that apply.

g is the dependent variable.

u is the dependent variable.

g is the independent variable.

u is the independent variable.

The variables cannot be labeled without a table of values.

The variables cannot be labeled since any value can be selected for either

Solution :

Given equation :

g = 748 u

Here, g = total number of gallons of water used

         u = number of units

Customers uses the number of units of water.

The unit of water is independent of the total number of gallons of water used.

So the number of units u is an independent variable.

But the value of gallons of water depends on the number of units that is used.

Therefore, number of gallons of water g is a dependent variable.

Thus, we can say that :