Which ordered pair is in the solution set of 5x - 2y > 12?
A: (2, -1)
B: (1, 5)
C: (-1, -9)
D: (0.2, 0.5)

The value of the varaible 'x' will be 4. And the value of the varaible 'y' will be 7.

Dilation is the process of increasing the size of an item without affecting its form. Depending on the scale factor, the object's size can be raised or lowered. There is no effect of dilation on the angle.

a) The equation is given as,

4 / 8 = 3 / (y - 1)

1/2 = 3 / (y - 1)

y - 1 = 6

y = 7

b) The equation is given as,

5 / (7 + 2x) = 2 / (x + 2)

5(x + 2) = 2(7 + 2x)

5x + 10 = 14 + 4x

5x - 4x = 14 - 10

x = 4

The value of the varaible 'x' will be 4. And the value of the varaible 'y' will be 7.

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The amount of interest nearest to cent will be $22,184.62.

A loan or deposit's interest is computed using the starting principle and the interest payments from the ago decade as compound interest.

We know that the compound interest is given as

A = P(1 + r)ⁿ

Where A is the amount, P is the initial amount, r is the rate of interest, and n is the number of years.

The borrowing amount $83,500 at a rate of 4.005% over 6 years. Then the interest is given as,

I = A - P

I = $83,500 (1.04005)⁶ - $83,500

I = $105,684.62 - $83,500

I = $22,184.62

The amount of interest nearest to cent will be $22,184.62.

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Answer:

The light beam will hit the ground at a distance of _756_ ft ahead of the car

Step-by-step explanation:

Let x be the distance in feet ahead of the car at which the light beam hits the ground.

Since the light beam drops 2 inches for each 21 feet measured horizontally, we can write the relationship between the height of the light beam and the distance x as:

24 - (2/21)x = 0

Solving for x, we get:

x = (21/2) * 24

x = 756

So the light beam will hit the ground 756 feet ahead of the car.

The linear equation that represents the relationship between P and C will be C = 0.39P + 6.

A connection between a number of variables results in a linear model when a graph is displayed. The variable will have a degree of one.

The linear equation is given as,

y = mx + c

Where m is the slope of the line and c is the y-intercept of the line.

You take a bundle to the nearby delivery organization. They charge a proper base expense of $6 per bundle in addition to an extra $0.39 per pound.

Let 'P' be the number of pounds and 'C' be the total cost. Then the equation is given as,

C = 0.39P + 6

The linear equation that represents the relationship between P and C will be C = 0.39P + 6.

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Answer:

Each person will get 12 ounces of soda

Step-by-step explanation:

84 ounces divided by 7 people is 12 ounces per person

Answer:

each person will get 12oz

Step-by-step explanation:

84oz divided by the 7 people will get 12oz per person

Answer:

1.             The pattern that I observe in the table above is that the fixed perimeter of these rectangles are 24 meters, and that the graph to represent this function is in the shape of a parabola with a vertex point at (6, 36). As for comparing the patterns to the graph in question A, assuming you're referring to the question I just answered, the graphs both are parabola shaped, with a vertex point and two zeros, one of them being the same at the origin of the coordinate plane (0, 0).

2.            The fixed perimeter for the rectangles represented by this table is 24 meters because if you want to find the fixed perimeter of these rectangles, you can pick any point that is not a zero point of the graph. For example, if the length of a rectangle is 1 meter, and the area is 11 [tex]m^2[/tex], we know the width would be 11 meters. Using this information, we know that the fixed perimeter would be (1 + 11) × 2 = 12 × 2 = 24 meters.

3.            The greatest area possible for a rectangle with a perimeter of 24 meters would be 36 [tex]m^2[/tex] because we can graph these points to form a parabola that represents this situation, and the vertex point of this graph would be the greatest area possible out of all the possible combinations of length and width that would still fit the criteria of having a perimeter of 24 meters.

              Based on the table, the vertex point of the graph would be (6, 36), therefore the greatest area possible for a rectangle with this perimeter would be 36 [tex]m^2[/tex]. As for the dimensions of this rectangle, we know the length is 6 meters, and the area is 36 [tex]m^2[/tex], so the width would be 36 ÷ 6 = 6 meters. Therefore the dimensions of this rectangle would be 6 meters in length and 6 meters in width.

Have a great day! Feel free to let me know if you have any more questions :)

The amount of money you get paid if  the coin comes up heads 3 times is $12.

You flip a coin 3 times,

If you get o heads then $0

If you get 1 heads then $2

If you get 2 heads then $ 4

So if you toss the coin 3 times and 3 heads come up then

1 heads = $2

2 heads = $ 4

3 heads = $ 6

So , amount of money you get paid if  the coin comes up heads 3 times is $12.

The probability function that X will have a value less than or equal to x is known as the Cumulative Distribution Function (CDF) of a real-valued random variable X, assessed at x. It is employed to describe a table's random variables' probability distribution. And with this data, we can quickly make a CDF graphic on an Excel spreadsheet.

So, CDF determines the cumulative probability for the specified value.

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1) Based on the slope equation, between 2003 and 2008, the school population grew by 265 students.

2) It took 5 years for the school population to grow from 1,389 to 1,654.

3) The average population growth per year was 53 students per year.

4) In the year 2000, the school population was 1,230.

5) The equation for the population, P, of the school in t years after 2000 is given as P = 1,230 + 53t.

6) Based on the equation above, the population of the school can be predicted to be 2,025 in 2015.

The slope describes the quotient or ratio of the rise and run.

The slope is found from the linear equation, y = mx + b, where m is the slope and b is the y-intercept.

The school population in 2003 = 1,389

The school population in 2008 = 1,654

Rise (increase) in population = 265 (1,654 - 1,389)

Run (Increase) in years = 5 years (2008 - 2003)

The slope = Rise/Run = 265/5 = 53

Annual increase in the school population = 53 students

Population in 2000:

Difference in years between 2003 and 2000 = 3

Population in 2000 = 1,389 + 53(-3)

= 1,230

Population after 2000:

= 1,230 + 53t

In 2015, the Population should be:

1,230 + 53t

1,230 + 53(15)

= 1,230 + 795

= 2,025

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Answer:504

Step-by-step explanation:

The correlation between Rate and Year is positive. The slope of the regression line is 0.0275 and the intercept is -9.8086. The model predicts that the interest rate in 2020 will be 2.38%.

The correlation between Rate and Year is positive, which means that as the years go by, the interest rate on 3-month Treasury bills is increasing. The slope of the regression line (0.0275) tells us that the average increase in the interest rate per year is 0.0275%. The intercept of the regression line (-9.8086) represents the interest rate in 1950.

This model predicts that the interest rate in 2020 will be 2.38%, which is obtained by plugging in 1970 for the Year variable and solving for the Rate. It's important to keep in mind that this model is based on historical data, and future interest rates may not follow the same pattern as in the past.

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Answer:

Equal to

Step-by-step explanation:

Answer:

2x² - 3x + 1

Step-by-step explanation:

x - 2 | 2x³ - 7x² + 7x - 2

    --   2x³ - 4x²                  <== 2x²

                - 3x² + 7x - 2

          --    - 3x² + 6x          <== -3x

                              x - 2

                     --       x - 2      <==  1    

                                   0 |  2x² - 3x + 1

Thus, the quotient is 2x² - 3x + 1

Answer:

Hello! :)

Answer:

Solved using long polynomial division: [tex]2x^{2} -3x + 1[/tex]

Solved using polynomial division: (2x-1)(x-1)

Sorry I was in a hurry and didn't type out the whole step-by-step.

Dan spent 1.25 at each table.

The formula used to solve this problem is m = 16 - 6/8. The calculation is as follows: 16 is the total amount of money Dan spent, 6 is the admission fee, and 8 is the number of tables. The equation is set up to find the amount of money Dan spent at each table. Taking the total amount of money spent, 16, and subtracting the admission fee, 6, leaves us with 10. We then divide this amount, 10, by the number of tables, 8, to find the amount of money spent at each table, which is 1.25. Therefore, Dan spent 1.25 at each table.

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a) The probability of having at least 1 rotten strawberry among the 5 is 0.262.

b) 1 strawberry must be picked so that the probability of having exactly 2 rotten strawberries among them equals 2/35.

What is probability?

Probability is a way to gauge how likely something is to happen. Many things are difficult to forecast with absolute confidence. Using it, we can only make predictions about the likelihood of an event happening, or how likely it is. Probability can range from 0 to 1, with 0 denoting an impossibility and 1 denoting a certainty.

The probability that Kyle selects exactly k rotten strawberries among the five she randomly picks is -

P( exactly k rotten strawberries) = [tex]\frac{(^2c_k)(^{34}c_{5-k}) }{^{36}c_5}[/tex]

since if she picks k of the 2 rotten strawberries, Kyle must also select 5 - k of the 36 -2 = 34 good strawberries.

Therefore, the probability that Kyle picks at least one rotten strawberry is -

P(at least 1 rotten strawberry) = P(exactly 1 rotten strawberry) + P(exactly 2 rotten strawberries)

P(at least 1 rotten strawberry) =[tex]\frac{(^2c_1)(^{34}c_{4}) }{^{36}c_5} + \frac{(^2c_2)(^{34}c_{3}) }{^{36}c_5}[/tex]

P(at least 1 rotten strawberry) = [(2 × 46376) / 376992] + [(1 × 5984) / 376992]

P(at least 1 rotten strawberry) = (92752 / 376992) + (5984 / 376992)

P(at least 1 rotten strawberry) = 0.246 + 0.016

P(at least 1 rotten strawberry) = 0.262

The probability of selecting exactly 2 rotten strawberries among n is

P(exactly 2 rotten strawberries) = [tex]\frac{(^2c_2)(^{34}c_{n-2}) }{^{36}c_n} = \frac{(^{34}c_{n-2}) }{^{36}c_n}[/tex]

The value for n is 2/35.

P(exactly 2 rotten strawberries) =[tex]\frac{(^{34}c_{\frac{-33}{35}}) }{^{36}c_{\frac{2}{35} }}[/tex]

P(exactly 2 rotten strawberries) = 1 / 1

P(exactly 2 rotten strawberries) = 1

Therefore, the probability is 0.262 and 1 strawberry must be picked.

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Where the OADB is a sector of a circle, and Angle AOB  = 80°, and the Radius of OB = 12cm,:

A circular sector (symbol: ) is the piece of a disk (a closed region circumscribed by a circle) contained by two radii and an arc, where the smaller area is known as the minor sector and the bigger as the major sector.

Given m∠AOB = 98°, OB = OA = 25cm (The radii are congruent) Thus,

m∠OAB = m∠OBA,

m∠OAB = (180 - 98) /2

m∠OAB = 41°

In the Right Triangle OBC, OB = 25cm, m∠OBC = 41°

Hence,

OC /OB = Sin ∠OBC ,
OC = OB (Sin ∠OBC )

= 25 * Sin41°

= 16.4cm; thus,

OC = 16.4cm

Where BC/OB = Cos ∠OBC,

BC = OB ( Cos ∠OBC)

= 25 * Cos 41° Thus,

BC = 16.4cm


The area of the ΔOAB = 1/2 * OA * OB * Sin98°
= 1/2 * 25 * 25 * Sin 98°

= 309.5cm²


The area of the Sector OADB = (98°/360°) * π * 25²

= 0.2722222222 * 3.14 * 25²

= 0.2722222222 * 3.14 * 252

= 534.5cm²

The percentage of the diagram that is shaded is given as:

309.5/534.5 * 100

= 0.5790458372 *100

= 57.9%

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We have the DE, [tex]y'+y=0[/tex], verify that [tex]y=e^{\frac{-x}{8}}[/tex] is a solution.

We have, [tex]y=e^{\frac{-x}{8}}[/tex], find [tex]y'[/tex].

=> [tex]y'=\frac{-1}{8} e^{\frac{-x}{8}}[/tex]

Plug [tex]y[/tex] and [tex]y'[/tex] into the DE.

=> [tex]y'+y=0[/tex]

=>[tex](\frac{-1}{8} e^{\frac{-x}{8}})+(e^{\frac{-x}{8}})=0[/tex]

=> [tex]e^{\frac{-x}{8}}=\frac{1}{8} e^{\frac{-x}{8}}[/tex]

=> [tex]e^{\frac{-x}{8}}\neq \frac{1}{8} e^{\frac{-x}{8}}[/tex]

Thus, [tex]y=e^{\frac{-x}{8}}[/tex], is not a solution to the given DE.

Answer:

Happy New Years sir it is 12:00 in the morning.

Step-by-step explanation:

yes

The value of x rounded to one decimal place is 176. 0 units

Using the trigonometric identity, sine, let's find the value of the hypotenuse for the smaller triangle, we have;

sin 60 = 88/x

find the value of sin 60

0. 8660x = 88

Divide both sides by 0. 8660

x = 101. 62

Then to determine the value of x, we have;;

tan 30 = 101.62/x

Find the value of the trigonometric identity, we have;

0. 5774x = 101. 62

divide both sides by the coefficient of x

x = 101. 62/0. 5774

divide the values

x = 175. 99 units

Hence, the value is 176. 0 units

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By solving the equation 3x = x² - 4, we know that the positive solution of the given problem is x = 4.

Using the equal symbol, they are linked.

For instance, a formula might be 3x - 5 = 16. After solving this equation, we learn that the value of the variable x is 7.

So, using the given  information, form the following equation:

3x = x² - 4

Now, solve this equation as follows:

3x = x² - 4

0 = x² - 3x - 4

0 = (x-4)(x+1)

Then, x = 4 and x = -1

Therefore, by solving the equation 3x = x² - 4, we know that the positive solution to the given problem is x = 4.

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Therefore , the solution of the given problem of equation comes out to be another point on the line would be (3, 110).

In arithmetic equations, the identical sign (=) is used to denote the equivalence of two assertions. It is demonstrated that using mathematical methods, which have acted as manifestations of reality, it is feasible to compare different numerical factors. For fact, the equal sign splits the number 12 into two separate parts, even if the answer is y + 6 = 12. It is possible to determine how many letters are also present on either end of this character.

Here,

The equation for the total cost of a party at this venue for p people is:

C = 20p + 70

To graph this equation, you can plot two points and draw a line passing through them.

One point can be the y-intercept (0, 70), which represents the fixed event fee charged by the venue.

The second point can be any other point on the line. For example, when there are 3 people at the party, the total cost would be:

C = 20(3) + 70 = 110

So another point on the line would be (3, 110). Plotting these two points and drawing a line passing through them will give you the graph of the total cost as a function of the number of people at the party.

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Answer:1200

Step-by-step explanation:1200

Answer: 678.58

Step-by-step explanation:

The work done by the force 4i−3j+2k is the scalar product of the force vector and the displacement vector between the two points. In this case, the displacement vector is (3−2, 2−(−1), −1−4) or (1,3,−5). The scalar product of these two vectors is (1)(4)+(3)(−3)+(−5)(2) = 15 units.

Work is the scalar product of the force and displacement vectors. The force vector in this problem is given as 4i−3j+2k, while the displacement vector (the vector from the starting point to the end point) is (3−2, 2−(−1), −1−4) or (1,3,−5). The scalar product of these two vectors is (1)(4)+(3)(−3)+(−5)(2) = 15 units. This means that the work done by the force is 15 units.

The work done by a force is the energy transferred to an object by the force. It is calculated by taking the scalar product of the force and displacement vectors. This scalar product gives the magnitude of the work done by the force, which in this case is 15 units. This means that the force transferred 15 units of energy to the object by moving it from the starting point to the end point.

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The solution to the given inequality 2x/2 - 5x -3 ≥ 0 is x ≤ - 3/8.

Inequality is defined as mathematical statements that have a minimum of two terms containing variables or numbers that are not equal.

We have to solve 2x/2 - 5x -3 is greater than or equal to zero algebraically.

As per the question, we have inequality as follows:

2x/2 - 5x -3 ≥ 0

2x/2 - 5x ≥ 3

Multiply by 2 on both sides of the inequality,

4x - 20x ≥ 6

-16x ≥ 6

Divided by -16 and flip the sign of the above inequality,

x ≤ - 6/16

x ≤ - 3/8

This is the solution to the given inequality.

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Answer:

84.8 squared centimeters

Step-by-step explanation:

You know the height is 8 cm

You know one of the bases has a length of 15.5 cm

You know one of the bases has a length of 5.7 cm

Formula to find a trapezoid:

[tex]\frac{b_{1}+b_{2}}{2}[/tex]×h

so...

substitute!!!!!

The length of the rectangular patio is 57 ft.

In Euclidean geometry, a parallelogram is a simple quadrilateral with two pairs of parallel sides. The opposite or facing sides of a parallelogram are of equal length and the opposite angles of a parallelogram are of equal measure.

Given is that the perimeter of a rectangular patio is 204 feet and the width of the patio is 45 feet.

We can write -

2(L + B) = 204

L + B = 102

L = 102 - 45

L = 57

Therefore, the length of the rectangular patio is 57 ft.

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{Question in english -

The perimeter of a rectangular patio is 204 feet if the width of the patio is 45 feet what is the length of the patio}

The data are discrete because the data can only take on specific values, So correct option is B.

Discrete data refers to data that can only take on specific, separate values. It is a type of data that can be counted or enumerated, but not measured. In other words, the values can't be expressed as fractions or decimals between two whole numbers. Some examples of discrete data include the number of siblings in a family, the number of pets owned by an individual, and the number of correct answers on a test. Discrete data is distinct from continuous data, which can take on any value within a certain range.

The data are discrete because the data can only take on specific values (e.g. a time of 20 minutes, 21 minutes, 22 minutes, etc.). They cannot take on any value in an interval, such as 20.5 minutes. Discrete data represent a countable number of values, while continuous data can take on any value within a given range.

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Answer:

(3, -11)

Step-by-step explanation:

Rearranging the equation becomes a slope-intercept form:

[tex]y = 2 - 3x[/tex]

where   m = slope of equation = [tex]-3[/tex]

      and c = intercept = [tex]2[/tex]

Substitute any value of x into the above slope-intercept equation to determine it's corresponding y value. Together these x and y values will form an ordered pair.

For example:

Take x = 3 and substitute in the above mentioned equation:

[tex]y = 2 - 3(3)[/tex]

  [tex]= 2 - 9[/tex]

y = [tex]-11[/tex]

∴ An ordered pair that is a solution to the equation: (3, -11)

Answer:

b

Step-by-step explanation:

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