The difference of two numbers is 2. The sum of the same two numbers is 6. Find the numbers. Write the numbers from least to greatest.

Answer:

\(1 \times \frac{1}{4} - \frac{3}{20} (4 \times \frac{1}{3} - 2 \times \frac{1}{2} ) \times 5 \\ \frac{1}{4} - \frac{3}{4}( \frac{4}{3} - 1) \\ \frac{1}{4}- \frac{3}{4} ( \frac{1}{3} ) \\ \frac{1}{4} - \frac{1}{4} \\ \boxed{0}\)

The length of the required chord is approximately equal to 11.8 units.

In Mathematics and Geometry, the chord of a circle refers to a line segment that typically join any two (2) points on a circle.

Based on the equation of the circle, the radius can be determined as follows;

x² + y² = 36

Radius, r = √36

Radius, r = 6 units.

By applying Pythagorean's theorem, side OA can be calculated as follows;

6² - 1² = OA²

OA² = 36 - 1

OA = √35

OA = 5.9

Length of chord = 2 × OA

Length of chord = 2 × 5.9

Length of chord = 11.8 units.

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Answer:

Step-by-step explanation:

sin(63°) = x/22

x = 22sin(63°) ≅ 19.6 units

Weighing the available information and assigning a probability.

A sort of probability called subjective probability is one that is based on a person's subjective assessment or personal knowledge of the likelihood of a particular result. It solely represents the subject's thoughts and prior experience and does not include any formal computations. A "gut instinct" used when making a deal is an illustration of subjective probability.

So, as per the definition of subjective probability

Dividing the number of favourable events by the number of possible events and Studying the fraction of times in the past a particular event has happened, both can be determined through calculations mathematically accurate but for Weighing the available information and assigning a probability we might use a "gut instinct". Thus

Weighing the available information and assigning a probability.

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Answer:

99

Step-by-step explanation:

4x³-2x²+3x​

4×3³-2×3²+3×3

4(27)-2(9)+9

108-18+9

99

99

=(4)(27)−2(32)+(3)(3)

=108−2(32)+(3)(3)

=108−(2)(9)+(3)(3)

=108−18+(3)(3)

=90+(3)(3)

=90+9

=99

Answer:

y >13

Step-by-step explanation:

y - 2 > 11

solve like how you would solve an equation, with inverse operations

y -2 > 11

  +2   +2

y > 13

Answer:

it shoud just be y>13

Step-by-step explanation:

bc you add 2 to each side which cancels the -2 on the left and makes the 11 on the right 13

The value of the line integral is 17/15. None of the given choices (A, B, C, D, E) match the computed value of the line integral.

To find the value of the line integral, we need to parametrize the curve C that bounds the region. Let's parameterize the curve as follows:

x = t

y = t^2

where t ranges from 0 to 1.

Now, we can compute the line integral using the given differential form:

f(x, y) = f(2xy - x^2) dx + (x + y^2) dy

Substituting the parameterization into the differential form, we have:

f(t, t^2) = f(2t(t^2) - t^2) dt + (t + (t^2)^2) 2t dt

Simplifying this expression, we get:

f(t, t^2) = f(t^3) dt + (t + t^4) 2t dt

          = f(t^3) dt + 2t^2 dt + 2t^5 dt

          = t^4 dt + 2t^2 dt + 2t^5 dt

          = (t^4 + 2t^2 + 2t^5) dt

Now, we integrate this expression with respect to t, from 0 to 1:

∫[0,1] (t^4 + 2t^2 + 2t^5) dt

Evaluating this integral, we get:

[(1/5)t^5 + (2/3)t^3 + (2/6)t^6] evaluated from 0 to 1

= [(1/5)(1)^5 + (2/3)(1)^3 + (2/6)(1)^6] - [(1/5)(0)^5 + (2/3)(0)^3 + (2/6)(0)^6]

= (1/5) + (2/3) + (2/6) - 0

= 1/5 + 2/3 + 1/3

= 7/15 + 2/3

= 7/15 + 10/15

= 17/15

Therefore, the value of the line integral is 17/15.

None of the given choices (A, B, C, D, E) match the computed value of the line integral.

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To express the equation x^2(y - 9)^2 = 81 in polar coordinates, we need to substitute the polar coordinate representations for x and y.

In polar coordinates, we have:

x = r*cos(θ)

y = r*sin(θ)

Substituting these values into the given equation:

x^2(y - 9)^2 = 81

(r*cos(θ))^2((r*sin(θ)) - 9)^2 = 81

Simplifying the equation:

r^2*cos^2(θ)((r*sin(θ)) - 9)^2 = 81

r^2*cos^2(θ)(r*sin(θ) - 9)^2 = 81

Now, we can convert the equation to polar coordinates by replacing x with r*cos(θ) and y with r*sin(θ):

(r^2*cos^2(θ)(r*sin(θ) - 9)^2 = 81

This is the equation of the curve in polar coordinates.

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the interest rate for this compound interest account is 1.5%.

Compound interest is the amount of interest calculated on both the principal amount and the interest previously earned by the account. The formula for compound interest accounts can be written as:\(A = P(1 + r/n)^(nt)\) where A is the amount accumulated, P is the principle, r is the interest rate, n is the number of compounding periods per year, and t is the time in years.To find the interest rate, we can use the formula and plug in the given values. We have:A = $90,000, P = $60,000, t = 15 years, and the interest is compounded monthly, so n = 12. Substituting these values into the formula, we get:90,000 = 60,000\(A = P(1 + r/n)^(nt)\))We need to solve for r, the interest rate. First, we can divide both sides of the equation by \(60,000:1.5 = (1 + r/12)^(12*15)\)Next, we can take the natural logarithm of both sides of the equation:ln(1.5) = \(ln[(1 + r/12)^(12*15)]\)Using the property of logarithms that says ln(a^b) = b*ln(a), we can simplify the right side of the equation:ln(1.5) = 12*15*ln(1 + r/12)Now we can divide both sides of the equation by 180 (12*15) to isolate ln(1 + r/12):ln(1.5)/180 = ln(1 + r/12)Finally, we can take the exponent of both sides of the equation to isolate r:(1 + r/12) = \(e^(ln(1.5)/180)r/12 = e^(ln(1.5)/180) - 1r = 12[e^(ln(1.5)/180)\)- 1]Using a calculator, we can evaluate the right side of the equation and round to 3 decimal places to get:r ≈ 0.015 or 1.5%Therefore.

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The value of B and C for barium(Ba) is 146 and 56 respectively .

Given,

239/94 Pu + 1/0 n ⇒ B/C Ba + 91/38 Sr + 3 1/0 n

Sum of mass number in reactant side is 239+1=240

Sum of atomic number in reactant side is 94+0=94

so the product side sum of mass number should also be 240 and that of atomic number should be 94 .

So to calculate the mass number of barium,

B + 91 + 3*1 = 240

B = 146

Next to calculate the atomic number,

C + 38 + 3*0 = 94

C = 56

Thus the value of atomic number (C) and mass  number (B) is 56 and 146 respectively .

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Answer:

The awnser to this equation is 120 cents

The cost of using a 200-watt television for 30 days, turned on for 2 hours per day, would be $1.20.  

To calculate the cost of using a 200-watt television for 30 days with 2 hours of daily usage at 10 cents per kilowatt-hour, we need to find the total energy consumption and then multiply it by the cost per kilowatt-hour.

First, let's find the total energy consumption:

1. Daily energy usage: 200 watts * 2 hours = 400 watt-hours
2. Monthly energy usage: 400 watt-hours * 30 days = 12,000 watt-hours

Now, we need to convert watt-hours to kilowatt-hours:
3. Monthly energy usage in kilowatt-hours: 12,000 watt-hours / 1,000 = 12 kWh

Finally, let's calculate the cost:
4. Cost of using the television for 30 days: 12 kWh * 10 cents per kWh = 120 cents

So, the cost of using a 200-watt television for 30 days with 2 hours of daily usage at 10 cents per kilowatt-hour is 120 cents.

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Area of a triangle = 1/2 (base x height) Here, we are given the height of the triangle as 10 m; hence, we can use the above formula to determine the base of the triangle.

Area of a triangle = 1/2 (b x 10) Given that we want the base of the triangle, we can rearrange the above equation to obtain the following:

b = (2 x Area of a triangle)/10

Since we do not have the value of the area of the triangle, we will use the Pythagorean theorem to find the third side, which will assist us in determining the area of the triangle.

Pythagorean Theorem states that:

Hence, we can use this theorem to calculate the third side of the triangle. The triangle's hypotenuse is equal to 10m, which is the given height of the triangle.

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Answer:

Step-by-step explanation:

-3x+3<6​

-3x=3

x=-1

Answer:

-1 or -x (Same thing...)

Step-by-step explanation:

6-3=3

3/-3=-x

-x=-1

-1

The Answer: The first step is Rearranging the Equation

v=9

v=-5

Step-by-step explanation:

STEP

1

:

Rearrange this Absolute Value Equation

Absolute value equalitiy entered

     4|-v+2|-3 = 25

Another term is moved / added to the right hand side.

     4|-v+2| = 28

STEP

2

:

Clear the Absolute Value Bars

Clear the absolute-value bars by splitting the equation into its two cases, one for the Positive case and the other for the Negative case.

The Absolute Value term is 4|-v+2|

For the Negative case we'll use -4(-v+2)

For the Positive case we'll use 4(-v+2)

STEP

3

:

Solve the Negative Case

     -4(-v+2) = 28

    Multiply

     4v-8 = 28

    Rearrange and Add up

     4v = 36

    Divide both sides by 4

     v = 9

STEP

4

:

Solve the Positive Case

     4(-v+2) = 28

    Multiply

     -4v+8 = 28

    Rearrange and Add up

     -4v = 20

    Divide both sides by 4

     -v = 5

    Multiply both sides by (-1)

     v = -5

    Which is the solution for the Positive Case

STEP

5

:

Wrap up the solution

v=9

v=-5

The system of equations has two solutions: (0,2) and (-4/5, -6/5).

The substitution method is a way to solve a system of two linear equations with two variables. The method involves solving one of the equations for one of the variables, and then substituting that expression into the other equation in place of the same variable. This process reduces the system of two equations and two variables to a single equation and a single variable, which can then be solved.

We have the system of equations:

4x² + y² = 4 ........(1)

y = x + 2 ........(2)

We can solve this system of equations by substitution.

Substitute (2) into (1) to eliminate y:

4x² + (x + 2)² = 4

Simplify and solve for x:

4x² + x² + 4x + 4 = 4

5x²+ 4x = 0

x(5x + 4) = 0

x = 0 or x = -4/5

If x = 0, then from equation (2), y = 2. So one solution is (x,y) = (0,2).

If x = -4/5, then from equation (2), y = -6/5. So the other solution is (x,y) = (-4/5, -6/5).

Therefore, the system of equations has two solutions: (0,2) and (-4/5, -6/5).

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The rate at which Macros is pumping gas into his car is 1/6 gallons per second, which simplifies to 1 gallons per second. The correct answer is a. 1 gallons per second.

The slope of the line is equal to the change in y-values (gallons of gas in car) divided by the change in x-values (seconds spent pumping gas).

To calculate the rate at which Macro is pumping gas into his car, we need to determine the slope of the line represented by the table values.

We can calculate the slope by subtracting the y-values for the first two points

(3 - 5 = -2)

and the x-values for the first two points

(0 - 12 = -12).

The slope is then equal to -2/-12 = 1/6.

Since the slope represents the rate of change, the rate at which Macro is pumping gas into his car is 1/6 gallon per second. This means that for every second he pumps gas into his car, he will add 1/6 gallon of gas.

This means that for every 6 seconds Macros pumps, he increases the amount of gas in his car by 1 gallon. Thus, the rate at which Macros is pumping gas into his car is 1/6 gallons per second, which simplifies to 1 gallons per second.

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Amir’s gas tank had 1L of gas in it. Then he drove to his cousin’s house and back and had 1/3 L left.  Amir used a total of 1/3L gas in each direction

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

Initial amount = 1L

Remaining amount = 1/3L

The amount of gas he used in each direction is calculated as

Amount used in each direction =(Initial amount - Remaining amount)/2

Substitute the known values in the above equation, so, we have the following representation

Amount used in each direction =(1L - 1/3L)/2

Evaluate

Amount used in each direction =1/3L

Hence, the amount is 1/3L

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Here is the complete question:

Amir’s gas tank had 1L of gas in it. Then he drove to his cousin’s house and back and had 1/3 L left. How much gas did he use in each direction?

Answer:

answer 67.98

explanation= ; built different

Based on the  average daily profit of an electronics store which is $28,465, the maximum the company expected for returned items is $3,774.46

What portion of the average daily profit is lost ?

The portion of the average daily profit which is lost each to returns is 13%, hence, the 13% of the average daily profit which is the base loss to return is computed thus:

loss to return=13%*$28,465

loss to return=$3,700.45

On the basis that margin of error is ±2%, that +2% or -2%, the maximum the company can expect for returned items is as shown below:

maximum expected for returned items=$3,700.45*(1+2%)

maximum expected for returned items=$3,774.46

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Answer: $4269.75

Step-by-step explanation:

So the Question asks for the ""The average daily profit of an electronics store is $28,465. The company estimates that 13%"" is lost each day to returns, with a margin of error of ±2%.

The average daily profit can be calculated by finding 13% of 28,456.

What is the maximum the company can expect for returned items? So Adding the maximum (2%) we find 15% of 28,456 which is -

|$4269.75|

The probability of selecting at least one defective item at random is 0.3017.

The probability of an event occurring at least once will be calculated as the complement of the probability of the event never occurring. You can use exponents to multiply the number of events that occurred when calculating this amount.

Defect rate = P(defect) = 0.05

Probability is defined as the required outcome divided by the total number of possible outcomes.

P( at least 1 is defective) = 1 - P(none is defective)

P(not defective) = 1 - P(defective) = 1 - 0.05 = 0.95

P(none is defective) = P(non defective)^7

P(none defective) = 0.95× 0.95 × 0.95 × 0.95 × 0.95× 0.95× 0.95=0.6983

P(at least one is defective) = 1 - 0.6983 = 0.3017

Therefore, probability of at least one defective item is 0.3017.

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In total, there are 660 ways to arrange the 10 identical math books and 2 different English books on the shelf such that the English books are not placed next to each other.

To calculate the total number of arrangements, we can consider the English books as distinct entities and treat them separately from the math books.

We have 12 books in total, including 10 identical math books and 2 different English books. Let's denote the English books as E1 and E2.

If the English books are placed together, we can treat them as a single entity. This reduces the problem to arranging 11 entities: the combined English books (E1E2) and the 10 math books. There are 11! (factorial) ways to arrange these entities.

However, within the combined English books (E1E2), there are 2! ways to arrange the individual English books. Therefore, we need to multiply the total number of arrangements by 2!.

Since the total number of arrangements with the English books together is 11! × 2!, we need to subtract the number of arrangements where the English books are placed next to each other from this total.

If the English books are next to each other, we can treat them as a single entity. This reduces the problem to arranging 11 entities: the combined English books (E1E2) and the 10 math books. There are 11! ways to arrange these entities.

Hence, the number of arrangements where the English books are next to each other is 11!.

Finally, we subtract the number of arrangements where the English books are next to each other from the total number of arrangements:

Total arrangements = 11! × 2! - 11!

Simplifying this expression, we get:

Total arrangements = 11! × (2 - 1) = 11! = 39,916,800

Therefore, there are 39,916,800 ways to arrange the books on the shelf such that the English books are not placed next to each other.

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The equation which models the number of calculators packed by the machine in certain minutes is x = 2.5y

No. of calculators packed after 10 minutes = 25 calculators

No. of calculators packed after 30 minutes = 75 calculators

Using the unitary method for finding calculators packed in a minute,

10 minutes = 25 calculators

1 min = 25/10 = 2.5 calculators

Let x be the number of minutes the machine is running

Let y be the number of calculators packed

Formulation of the equation we get:

x = 2.5y

Hence, the equation which gives the number of calculators packed after certain minutes is given by: x = 2.5y

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Answer:

Z = 63º

Step-by-step explanation:

X = 180 - 61 - 31 = 88º Angles in a triangle add to 180º

Y = 180 - X = 180 - 88 = 92º Angles in a straight line add to 180º

Z = 180 - 25 - Y = 180 - 25 - 92 = 63º Angles in a triangle add to 180º

So Z = 63º

In linear equation ,Jerry's expression is correct.

What in mathematics is a linear equation?

As you can see, starting with border 1, we have 6 daises (white squares) surrounded by 10 tulips (colored squares). Through Jerry's expression we expected:

= 8(b − 1) + 10

= 8(1 − 1) + 10

= 0 + 10

= 10 tulips.

When considering border 2, we expect:

= 8(b − 1) + 10

= 8(2 − 1) + 10

= 8 + 10

= 18 tulips.

Indeed, we have the 10 tulips from border 1 and 8 additional tulips, for a total of 18 tulips.

Then, consider border 3, we expect:

= 8(b − 1) + 10

= 8(3 − 1) + 10

= 16 + 10

= 26 tulips.

Again, this is correct: we have the 10 tulips used in border 1 plus other 16 tulips, for a total of 26.

Therefore, Jerry's expression is correct.

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[Mathematical Problem]

\((2x)^2y; x=4,y=8\)

Solution:

Substitute the value of the variable into the expression, then simplify.

\((2(4))^2\) × \(8\)

↓

\((8)^2\)

↓

\((8)^2\) × \(8\)

↓

\(64\)

↓

\(64\) × \(8\) = 512

Hence, our solution is 512.

Hope this helps! It's been a while since I've done this, but this should be correct. Lmk if it helps! Thanks and good luck!