write two equivalent rational numbers of 7/-8​

1) The sale price on the painting is $1,235.

2) The regular price of the mechanic's tool set is $340.

3) The regular price of the battery is $111.84.

1) To find the sale price on a painting that has a regular price of $1,900 and is on sale for 35% off the regular price, we can use the formula: sale price = regular price - (regular price * discount rate).
In this case, the sale price would be $1,900 - ($1,900 * 0.35) = $1,900 - $665 = $1,235.
So the sale price of the painting is $1,235.

2) To find the regular price of a mechanic's tool set that is on sale for $204 after a markdown of 40% off the regular price, we can use the formula: regular price = sale price / (1 - discount rate).
In this case, the regular price would be $204 / (1 - 0.40) = $204 / 0.60 = $340.
So the regular price of the mechanic's tool set is $340.

3) To find the regular price of a battery that has a discount price of $85 and is on sale for 24% off the regular price, we can use the formula: regular price = sale price / (1 - discount rate).
In this case, the regular price would be $85 / (1 - 0.24) = $85 / 0.76 = $111.84.
So the regular price of the battery is $111.84.

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Answer:

-24x^8y^6+32x^2y^5

Step-by-step explanation:

Answer is: AC= 9[tex]\sqrt{3}[/tex] Units, AB = 18 units.

Triangles have three interior angles that add up to 180 degrees, and they can be classified based on the lengths of their sides and the measures of their angles.

In ΔABC, angle C is right angle,

so the triangle is right angle triangle;

tan30° = BC/AC

[tex]\frac{1}{\sqrt{3} }[/tex] = 9/AC

AC= 9[tex]\sqrt{3}[/tex] Units

and

Sin 30° = BC/AB

1/2 = 9/AB

AB = 18 units

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If Lindsay he mows the lawn in 10 hours and with his brother Grant he does it in 2 hours, Grant would mow the lawn alone in 2.5 hours.

To find out how long it would take Grant to mow the lawn alone, we can use the formula for combined work:

1/t₁ + 1/t₂ = 1/ttotal

Where t₁ is the time it takes Lindsay to mow the lawn alone, t₂ is the time it takes Grant to mow the lawn alone, and ttotal is the time it takes both of them to mow the lawn together.

Plugging in the given values:

1/10 + 1/t₂ = 1/2

Multiplying both sides by 20t₂ to clear the fractions:

2t₂ + 20 = 10t₂

Rearranging and simplifying:
8t₂ = 20
t₂ = 20/8
t₂ = 2.5

So it would take Grant 2.5 hours to mow the lawn alone.

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The final expression after multiplying each term by the LCD is (A+B+C)x^3 - (4A+3B+4C)x^2 + (12A+3BC)x - 12AC.

To multiply each term by the LCD, we need to first find the LCD of the given expression. The LCD of the expression is the product of the denominators, which is x(x-4)(x-3).

Now, we can multiply each term by the LCD to get rid of the denominators:

A[x(x-4)(x-3)]/(x) * x(x-4)(x-3) = A(x-4)(x-3)

B[x(x-4)(x-3)]/((x-4)) * x(x-4)(x-3) = B(x)(x-3)

C[x(x-4)(x-3)]/((x-3)) * x(x-4)(x-3) = C(x)(x-4)

Now, we can combine the terms to get the final expression:

A(x-4)(x-3) + B(x)(x-3) + C(x)(x-4) = (A+B+C)x^3 - (4A+3B+4C)x^2 + (12A+3BC)x - 12AC

So, the final expression after multiplying each term by the LCD is (A+B+C)x^3 - (4A+3B+4C)x^2 + (12A+3BC)x - 12AC.

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Answer: :)

Step-by-step explanation:

To classify the triangle as acute, right, or obtuse, we need to determine the measure of the largest angle in the triangle. We can use the Law of Cosines to find the angles of the triangle:

c^2 = a^2 + b^2 - 2ab cos(C)

where c is the length of the side opposite angle C, and a and b are the lengths of the other two sides.

For this triangle, we have:

c = 12

a = 6

b = 9

Using these values in the Law of Cosines, we get:

12^2 = 6^2 + 9^2 - 2(6)(9)cos(C)

144 = 117 - 108cos(C)

27 = 108cos(C)

cos(C) = 0.25

To find angle C, we can take the inverse cosine (cos^-1) of both sides:

C = cos^-1(0.25)

C ≈ 75.5°

Now we can classify the triangle based on its largest angle:

- If C is less than 90 degrees, then the triangle is acute.

- If C is exactly 90 degrees, then the triangle is right.

- If C is greater than 90 degrees, then the triangle is obtuse.

In this case, since C ≈ 75.5°, which is less than 90 degrees, we know that this triangle is an acute triangle.

Answer:

28 are red

Step-by-step explanation:

(1/5) are blue.  The rest are red, which would be 4/5 of the total.  (1/5)+(4/5) = 1 or 100%

(1/5)*(35) = 7 are blue

(4/5)*(35 = 28 are red

--------------------

Total = 35 cars

The simplified expression is 45°, which is closest to option a. 38°.

Lines are one-dimensional geometrical objects that extend infinitely in both directions. Angles are formed when two lines intersect, and they measure the amount of rotation between the lines.

We can use the formula:

arctan(x) + arctan(y) = arctan[(x + y) / (1 - xy)]

to simplify the expression.

Setting x = 1/3 and y = 2/3, we have:

arctan(1/3) + arctan(2/3) = arctan[(1/3) + (2/3) / (1 - (1/3)(2/3))]

= arctan(1)

= 45°

Therefore, the simplified expression is 45°, which is closest to option

a. 38°.

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The velocity of the bird is approximately 40.04 km/hour.

What is velocity ?

Velocity is a measure of the rate at which an object changes its position in a particular direction. It is a vector quantity, which means that it has both a magnitude (speed) and a direction.

To find the velocity of the bird, we can use the formula:

velocity = distance/time

Given that the bird flies 961 km in 24 hours, we can substitute these values into the formula:\

velocity = 961 km / 24 hours

Simplifying this expression, we get:

velocity = 40.04 km/hour (rounded to two decimal places)

Therefore, the velocity of the bird is approximately 40.04 km/hour.

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The distribution of Sn + Tm is a binomial distribution with parameters (n+m, p).

This can be proved using the fact that the sum of independent binomial random variables follows a binomial distribution with the sum of the number of trials and the same probability of success.



Let X ~ Binomial(n, p) and Y ~ Binomial(m, p) be independent random variables representing the number of heads in the first n coin tosses and the last m coin tosses, respectively.

Then, the sum of X and Y, Z = X + Y, follows a binomial distribution with parameters (n+m, p).

The probability mass function of Z can be written as:

P(Z = k) = P(X + Y = k) = ∑ P(X = i) * P(Y = k-i) for i = 0 to k

Since X and Y are independent, we can write:

P(Z = k) = ∑ P(X = i) * P(Y = k-i) = ∑ (n choose i) * p^i * (1-p)^(n-i) * (m choose k-i) * p^(k-i) * (1-p)^(m-k+i)

Simplifying the above equation, we get:

P(Z = k) = (n+m choose k) * p^k * (1-p)^(n+m-k)

Therefore, Z ~ Binomial(n+m, p).

As a result, the distribution of Sn + Tm has the parameters (n+m, p) of a binomial distribution.

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Cristiano is said to have racked up around 300 assists in his third year in power.

This estimate is based on the fact that Cristiano has been a prolific passer in his whole career and has frequently improved every season. Assuming he's maintained similar level of assists in his third season and Cristiano has improved season after season, his tally assists in his third year is likely higher than his average of 251 per season.

That's why it is safe to assume that Cristiano completed around 300 passes in his third year, a significant improvement over the previous 2 years. It increase in assists is likely due to Cristiano's increased confidence and comfort in the team, as well as learning more about the club and their plan. All of this together would allow Cristiano to make more passes and become a more efficient player overall.

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Answer:

We know that cot A = adjacent side / opposite side = 21/20.

Let x be the length of the adjacent side and y be the length of the opposite side.

Using the Pythagorean theorem, we have:

x^2 + y^2 = (20k)^2, where k is some positive constant.

Since angle A is in Quadrant I, x is positive and y is positive. Thus, we can take the square root of both sides to get:

x + y = 20k.

Now, we can use the fact that cot A = adjacent side / opposite side = 21/20 to get:

x/y = 21/20.

Multiplying both sides by y, we get:

x = (21/20)y.

Substituting this into x + y = 20k, we get:

(21/20)y + y = 20k

Simplifying, we get:

(41/20)y = 20k

y = (20k)/(41/20) = (400k)/41

Now, we can use the Pythagorean theorem to find x:

x^2 + y^2 = (20k)^2

(21/20)y^2 + y^2 = (20k)^2

(441/400)y^2 = (20k)^2

y^2 = (400/441)(20k)^2

y = (20k/441)sqrt(441 x 20)

y = (20k/21)sqrt(20)

Therefore, angle A in simplest radical form using a rational denominator is given by:

tan A = y/x = [(20k/21)sqrt(20)] / [(21/20)y] = sqrt(20)/21

A = arctan(sqrt(20)/21)

The rule that could be used to prove that the two triangles are congruent is given as follows:

A. Side - Side - Side.

The Side-Side-Side congruence theorem states that if all three sides of a triangle are congruent (identical) to the corresponding sides of another triangle, then the triangles themselves are also congruent.

For this problem, we have that the two congruent sides are given as follows:

If the third sides are congruent, then the Side-Side-Side congruence theorem can be used.

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The measure of angle KYC, considering the concept of vertical angles, is given as follows:

m < KYC = 69º.

Vertical angles are angles that are opposite by the same vertex on crossing segments, hence they share a common vertex, thus being congruent, meaning that they end up having the same angle measure.

The vertical angles for this problem are given as follows:

<KYC and 69º.

As they are opposite by the vertex at the crossing of the two diagonal segments for this problem.

Hence the measure of angle KYC is given as follows:

m < KYC = 69º.

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The solution to the system of linear equations -1.2x+0.3y=-8.4 -1.4x+0.2y=10.6, is x = -27 and y = -136.

The given system of linear equations is:

-1.2x+0.3y=-8.4
-1.4x+0.2y=10.6

To determine whether the system has a solution, we can use the method of elimination. First, we need to multiply each equation by a constant to make the coefficients of one of the variables the same in both equations. In this case, we can multiply the first equation by 2 and the second equation by 3 to make the coefficients of y the same:

-2.4x+0.6y=-16.8
-4.2x+0.6y=31.8

Next, we can subtract the second equation from the first equation to eliminate the y variable:

1.8x=-48.6

Finally, we can solve for x:

x=-27

Now we can plug this value of x back into one of the original equations to solve for y:

-1.2(-27)+0.3y=-8.4
32.4+0.3y=-8.4
0.3y=-40.8
y=-136

So the solution to the system of linear equations is x=-27 and y=-136. Therefore, the given system of linear equations does have a solution.

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By answering the above question, we may state that Without having both  expressions the original concept and Megan and Mindy's drawings, it is impossible to tell which drawing is mistaken.

In mathematics, you can multiply, divide, add, or take away. The following is how an expression is put together: Numeric value, expression, and math operator The elements of a mathematical expression include numbers, parameters, and functions. It is feasible to use contrasting words and expressions. Any mathematical statement containing variables, numbers, and a mathematical action between them is known as an expression, often known as an algebraic expression. As an example, the expression 4m + 5 is composed of the expressions 4m and 5, as well as the variable m from the above equation, which are all separated by the mathematical symbol +.  

If Megan and Mindy both depicted the entire playground, then their pictures ought to match. Their designs ought to depict the remaining 4/6 of the playground if the plan they viewed only showed 2/6 of it.

You may assess a drawing's accuracy by contrasting it with the first design that Megan and Mindy viewed. They are correct if their designs depict the remaining 4/6 of the playground and the original plan matches. Their drawings are incorrect if they do not reflect the original design or do not depict the remaining 4/6 of the playground.

Without having both the original concept and Megan and Mindy's drawings, it is impossible to tell which drawing is mistaken.

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The number 240 is a composite number and can be written as the product of prime factors 2 x 2 x 2 x 2 x 3 x 5.

The number 240 is a composite number. This is because it can be divided by numbers other than 1 and itself.

To write 240 as the product of prime factors, we can use the factor tree method:

240
/  \
2   120
  /  \
 2    60
     /  \
    2    30
        /  \
       2    15
           /  \
          3    5

So, the prime factors of 240 are 2, 2, 2, 2, 3, and 5.

We can write this as:

240 = 2 x 2 x 2 x 2 x 3 x 5

Therefore, the number 240 is a composite number and can be written as the product of prime factors 2 x 2 x 2 x 2 x 3 x 5.

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Answer:

x=36

y=6

system of equations

Answer:

A) 59°

Step-by-step explanation:

m<ADC is a right angle, therefore it is 90°

so that means you can now subtract the angle that you already know [31°] from it to get the angle that is left over, m<ADB

90°-31°= 59° (subtracting m<ADC [90°] from m<BDC [31°] leaves your remaining angle m<ADB [59°]

The answer of this question is -4,298,008. We solve this question by taking the LCM of denominators.

The smallest multiple that two or more numbers share is known as the least common multiple. Least Common Multiple short form is LCM.

We can find LCM of these number by taking least common multiple.

LCM of 3, 3, 17, 13 is 663 .

(a) [tex]-\frac{22}{3} *663 = -22*221[/tex]

[tex]= -4862[/tex]

(b) [tex]\frac{4}{3} * 663 = 4 * 221[/tex]

[tex]= 884[/tex]

(c) [tex]\frac{6}{17} *663 = 6 * 17[/tex]

[tex]= 102[/tex]

(d) [tex]\frac{2}{13}*663 = 2*51[/tex]

[tex]=102[/tex]

So, the answer is -4,298,008 .

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The probability that a person is randomly assigned a seat in rows A,B,C, E is 4/15.

The probability that a person is randomly assigned a seat in rows A,B,C, E can be calculated by dividing the number of desired outcomes by the total number of possible outcomes.

In this case, the desired outcomes are the rows A,B,C, and E, which is a total of 4 rows. The total number of possible outcomes are the 15 rows of bleachers in the school gym, labeled A through O.

So, the probability is calculated as follows:

P(A,B,C, or E) = 4/15

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Answer: 12.124355653

Step-by-step explanation: I did the math on a calculator

The final answer is:

4C+2D = [28 28]
       [14 26]

To find 4C+2D, we first need to multiply the matrices C and D by their respective scalars, 4 and 2. Then, we add the resulting matrices together.

First, let's multiply matrix C by 4:

4C = 4[5 3] = [20 12]
   [1 2]   [ 4  8]

Next, let's multiply matrix D by 2:

2D = 2[4 8] = [ 8 16]
   [5 9]   [10 18]

Now, we can add the resulting matrices together:

4C+2D = [20 12] + [ 8 16] = [28 28]
       [ 4  8]   [10 18]   [14 26]

So, the final answer is:

4C+2D = [28 28]
       [14 26]

I hope this helps! Let me know if you have any further questions.

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According to the Census Bureau, of the people 21 to 64 years old, 12.3% are not high school graduates, 27.8% have graduated high school, 30.6% have some college, 16.9% have a bachelor's degree, and 8.8% have an advanced degree. The words that look like different answers to one question are "not high school graduates," "graduated high school," "some college," "bachelor's degree," and "advanced degree."

These words all describe different levels of education and could be potential answers to a question about a person's education level. The paragraph describes the educational attainment of people between the ages of 21 and 64. The different percentages represent the proportion of individuals in each education category.

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The perimeter of the base is 32 cm.

The area of the base is 48 cm².

The total surface area of the triangular prism is 1184 cm².

The diagram above is a triangular prism. Therefore, let's find the perimeter of the base, area of the base and surface area of the triangular prism.

Hence,

perimeter of the base = 10 + 10 + 12

perimeter of the base = 20 + 12

perimeter of the base = 32 cm

Area of the base = 1 / 2 bh

where

Therefore,

Area of the base = 1 / 2 × 12 × 8

Area of the base = 48 cm²

Hence,

total surface area of the triangular prism = bh + l(s₁ + s₂ + s₃)

total surface area of the triangular prism = 12(8) + 34(10 + 10 + 12)

total surface area of the triangular prism = 96 + 34(32)

total surface area of the triangular prism =96 + 1088

total surface area of the triangular prism = 1184 cm²

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The area of the circle is 63.62 square meters

To work out the area of a circle, we need to use the formula A = πr^2, where A is the area of the circle, π is a mathematical constant approximately equal to 3.142, and r is the radius of the circle.

In this problem, we are given the diameter of the circle, which is the distance across the circle passing through its center. The radius is half of the diameter, so we can find it by dividing the diameter by 2.

In this case, the diameter is 9 meters, so the radius is 9/2 = 4.5 meters. We then substitute this value into the formula:

A = πr^2

A = 3.142 x (4.5)^2

A = 3.142 x 20.25

A = 63.6175

A ≈ 63.62 square meters

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The given question is incomplete, the complete question is:

Work out the area of the circle where diameter is 9 meter

Take π it to be 3.142 and give your answer to 2 decimal places.