The seats available to a baseball game come in four types: bleacher, box, club, and grandstand. There are 12,600 box seats and 5,400 club seats available. According to the graph, what is the total number of seats available?

The sum of (8a + 2b - 4) and (3b - 5) is (8a + 5b - 9). We can find it in the following manner.

To find the sum of (8a + 2b - 4) and (3b - 5), we can simply add the corresponding coefficients of the variables a and b, as well as any constant terms.

So we have:

(8a + 2b - 4) + (3b - 5)

= 8a + 2b + 3b - 4 - 5 (grouping like terms)

= 8a + 5b - 9

Therefore, the sum of (8a + 2b - 4) and (3b - 5) is (8a + 5b - 9).

We can also explain this process by using the distributive property of addition over subtraction. This property states that the sum of two numbers with the same sign (positive or negative) can be found by adding their absolute values and keeping the common sign.

In this case, we can think of the expression (8a + 2b - 4) as the sum of three terms: 8a, 2b, and -4. Similarly, we can think of the expression (3b - 5) as the sum of two terms: 3b and -5.

Using the distributive property, we can add the terms with the same variable together:

(8a + 2b - 4) + (3b - 5)

= 8a + (2b + 3b) - (4 + 5)

= 8a + 5b - 9

Thus, we obtain the same result.

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Answer:

Step-by-step explanation:

the answer is 785.51

The equation to determine the original price per pound is 3(x + 0.75) = 5.88, where x is original price per pound. so, the original price is  $1.21.

Let x be the original price per pound of apples.

When the price increased, the new price became x + 0.75.

Sam bought 3 pounds of apples at the new price for a total of $5.88. This can be expressed as:

3(x + 0.75) = 5.88

Expanding the left side of the equation, we get:

3x + 2.25 = 5.88

Subtracting 2.25 from both sides, we get:

3x = 3.63

Dividing by 3, we get:

x = 1.21

Therefore, the original price per pound of apples was $1.21.

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Three pοints οn the line are: (0,0), (1,30), and (2,60)

When yοu knοw the slοpe οf the line tο be investigated and the given pοint is alsο the y intercept, yοu can utilise the slοpe intercept fοrmula, y = mx + b. (0, b). The y value οf the y intercept pοint is denοted by the symbοl b in the fοrmula.

Tο sοlve the prοblem, we can start by using the fοrmula fοr the equatiοn οf a line in slοpe-intercept fοrm:

y = mx + b

We can use the given infοrmatiοn tο find the slοpe:

m = tοtal distance / number οf days = 150 miles / 5 days = 30 miles/day

b = 0 miles

Therefοre, the equatiοn οf the line representing the tοtal distance Ms. Ibrahim travels fοr wοrk in x days is:

y = 30x

When x = 0 (i.e., when Ms. Ibrahim dοes nοt wοrk), y = 0.

When x = 1 (i.e., οn the first day), y = 30 miles.

When x = 2 (i.e., οn the secοnd day), y = 60 miles.

Sο, three pοints οn the line are: (0,0), (1,30), and (2,60)

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Therefore, the equation in slope-intercept form that has a y-intercept at (0, -3) and also contains the point (4, 5) is y = 2x - 3.

In mathematics, an equation is a statement that asserts the equality of two expressions. It consists of variables, constants, and mathematical operators such as addition, subtraction, multiplication, and division. An equation is usually written with an equal sign (=) between the two expressions. Equations are used to represent mathematical relationships between quantities, to solve problems, and to model real-world situations. They can be used to find unknown values, to predict outcomes, and to test hypotheses. There are many types of equations, including linear equations, quadratic equations, polynomial equations, trigonometric equations, and differential equations. Each type of equation has its own rules and methods for solving it.

Here,

The slope-intercept form of a linear equation is y = mx + b, where m is the slope and b is the y-intercept. We are given that the y-intercept is (0, -3), so b = -3. To find the slope, we can use the two given points (0, -3) and (4, 5).

slope = (y2 - y1)/(x2 - x1)

= (5 - (-3))/(4 - 0)

= 8/4

= 2

Now that we know the slope and the y-intercept, we can write the equation in slope-intercept form:

y = 2x - 3

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Therefore, the minimum acceptable settlement on the case is $103,000.

Percentage is a way of expressing a number as a fraction of 100. It is often denoted by the symbol "%". For example, 50% means 50 out of 100 or 50/100, which is equivalent to the fraction 1/2 or the decimal 0.5.

Percentages are commonly used to express proportions, rates, or changes. They are used in many different fields, such as finance, statistics, science, and everyday life. For instance, we might use percentages to describe the rate of interest on a loan, the percentage of people who have received a vaccine, or the percentage increase or decrease in the stock market.

by the question.

First, we need to calculate the total fee the attorney will earn based on the hourly rate and the percentage of the settlement.

The attorney's fee is the sum of the hourly fee and the percentage of the settlement:

hourly fee = 110 hours x $175 per hour = $19,250

percentage of the settlement = 25% of the settlement

total fee = hourly fee + percentage of the settlement

We know that the total fee must be greater than or equal to $45,000, so we can set up an equation to solve for the minimum acceptable settlement:

$19,250 + 0.25S ≥ $45,000

where S is the settlement amount.

Subtracting $19,250 from both sides, we get:

0.25S ≥ $25,750

Dividing both sides by 0.25, we get:

S ≥ $103,000

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Answer:

a. m(arc) CD = 65°

b. m(arc) AE = 120°

c. m(arc) BC = 55°

d. m(arc) AC = 115°

e. m(arc) ADC = 245°

f. m(arc) AED = 180°

g. m(arc) CE = 125°

h. m(arc) BAD = 240°

Step-by-step explanation:

a.

m<CPD = 180 - 55 - 60 = 65

m(arc) CD = 65°

b.

m<APB = 60°

m<APE = 180° - 60° = 120°

m(arc) AE = 120°

c.

m(arc) BC = 55°

d.

m(arc) AC = 60° + 55° = 115°

e.

m(arc) ADC = 120° + 60° + 65 = 245°

f.

m(arc) AED = 180°

g.

m(arc) CE = 60° + 65° = 125°

h.

m(arc) BAD = 60° + 120° + 60° = 240°

The translation of circle A to circle B is achieved using the translation rule

The scale factor of Circle A to Circle B is 2

In geometry, translation refers to a transformation that moves an object in a straight line without changing its size, shape, or orientation.

This movement is done by sliding the object along a line, which is called the axis of the translation.

The scale factor is solved by comparing the diameter

Circle A has diameter of 2 units

Circle B has diameter of 4 units

let the scale factor be k

diameter of circle A * k = diameter of circle B

2 * k = 4

k = 4 / 2

k = 2

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Answer:

Step-by-step explanation:

Step 1: Find the TV price:

£1200×(100%+20%)= £1440

Step 2: Find the final price Harry have to pay:

since he deposited £300 so the ammout he have to pay is:

£1440 - £300 = £1140

Step 3: Find the monthly payment

in this case he pays equally every month so we take the ammount he has to pay devided by 10 months

£1140÷10=£114

Conclusion: He has to pay £114 every month

Answer: 0.000012

Step-by-step explanation: The exponent is -5, making it 10 to the power of negative 5. When an exponent is negative, the solution is a number less than the origin or base number. To find our answer, we move the decimal to the left 5 times

1.2 -> 0.000012

The cost of the concrete used to make the cylinder was approximately $6,776.89.

The problem is asking us to find the cost of the concrete used to make a cylindrical pillar, given its dimensions and the cost per cubic meter of concrete. We first need to calculate the volume of the cylinder using the formula for the volume of a cylinder:

[tex]V=pir^2h[/tex]

where V is the volume, r is the radius, h is the height, and π is the constant pi (approximately 3.14159).

In the problem, the diameter of the cylinder is given as 4 meters, which means the radius is half of that, or 2 meters. The height of the cylinder is given as 5 meters.

Substituting these values into the formula, we get:

[tex]V = \pi r^2h = \pi (2)^2(5) = 20\pi cubic meters[/tex]

Next, we need to find the cost of the concrete used to make the cylinder, given that the cost per cubic meter of concrete is $107. We can do this by multiplying the volume of the cylinder by the cost per cubic meter of concrete:

20π × $107 = $6,776.89

Rounding to the nearest cent, we get that the cost of the concrete used to make the cylinder was approximately $6,776.89.

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Answer:

The hypotenuse.

Step-by-step explanation:

The area of the equilateral triangle with a side length of 8 cm is 16√(3) cm².

To find the altitude of an equilateral triangle with a side length of 8 cm, we can use the Pythagorean theorem.

The Pythagorean theorem is states that in a right-angled triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the other two sides.

In these triangles, the side opposite the 60-degree angle is half the length of the hypotenuse, which is 8 cm. Using the Pythagorean theorem, we can find that the length of the altitude is:

Altitude = √(8² - (4²)) = √(48) = 4√(3)

Now that we know the altitude, we can plug it into the formula for the area of a triangle:

Area = (base x height) / 2 = (8 x 4√(3)) / 2 = 16√(3) cm²

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The coaster starts at a height of 250, then drops down to 0 at x=500, and then rises back up to a height of 250. The bump is located at x=500 and is the highest point on the coaster.

y = -0.0005(x-500)² + 250

The coaster starts at the highest point (y=250) when x=0 and then drops down to x=500 by following the equation y=ax(x-1000). To create the bump, we need to make the coaster rise before it falls, so we use a quadratic equation that has a vertex at x=500 and y=250 (the initial height).

The equation y = -0.0005(x-500)² + 250 is a downward-facing quadratic equation with a maximum value of y=250 at x=500. This means that as the coaster approaches x=500, it starts to rise, and then falls down again. The coefficient -0.0005 controls the steepness of the coaster's drop and the height of the bump.

Here's a graph of the coaster:

         ^

       260|                               *

          |                          *    

          |                     *  

          |                *    

          |            *  

 height   |        *      

          |     *          

          |  *            

        0 +--------------->

            0      500    1000   x-axis

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Answer:28 and 16 cams

Step-by-step explanation: let the two parts be x cms and 44 -x cms.

So side of squares will be x/4 and (44-x)/4 resp

Area will be (x/4)^2 and ((44-x)/4)^2 resp

Equation is(x/4)^2  + ((44-x)/4)^2 = 65

(X-28)(x-16) = 0

X =28 or x = 16 cms

If the distribution of values is normal with a mean of 93.2 and a standard deviation of 87.4. the score separating the bottom 81% from the top 19% is 168.24.

 The value of p81, which is the score separating the bottom 81% from the top 19%, can be calculated as follows:

 The given, Mean = μ = 93.2

                    Standard deviation = σ = 87.4

      We are supposed to find the score separating the bottom 81% from the top 19% which is nothing but the 81st percentile.

       Let X be a random variable with a normal distribution, then the z-score of the 81st percentile is calculated as follows:

               z = InvNorm(0.81)

               z ≈ 0.8 (by standard normal distribution tables)

    The 81st percentile in terms of X is given by:

              p81 = μ + zσp81

                     = 93.2 + 0.8(87.4)p81

              p81 = 168.24

   Thus, the score separating the bottom 81% from the top 19% is 168.24.

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-1

To use regrouping to solve, we need to add and subtract the numbers in the expression, taking care to keep track of any negative signs.

10 - 1 - 1 - 6 - ² - 2

= 10 - (1 + 1) - 6 - ² - 2 [Group the first two numbers together and add them]

= 10 - 2 - 6 - ² - 2 [Simplify the first three terms]

= (10 - 2) - 6 - ² - 2 [Group the first two terms together and subtract them]

= 8 - 6 - ² - 2 [Simplify the first two terms]

= 2 - ² - 2 [Simplify the first two terms]

= -1 [Simplify the expression by subtracting ² and 2 from -1]

Therefore, the final answer is -1.

The correct option - d. control.  After identifying the variables that are independent and dependent in an experiment, we can decide what to do with the remaining variables. We are diminishing "control" if we keep everything else constant.

Something kept constant or constrained in a research study is referred to as a control variable. Although not being relevant to the study's goals, this variable is controlled since it could have an impact on the results.

Thus, after identifying the variables that are independent and dependent in an experiment, we can decide what to do with the remaining variables. We are diminishing "control" if we keep everything else constant.

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Answer:

5 hours

Step-by-step explanation:

Since Shen drove at the same rate for both distances, we can use a proportion to solve for the time it would take him to drive 335 miles:

[tex]\frac{d_{1} }{t_{1} }=\frac{d_{2} }{t_{2} }[/tex]

where d1 is 603 miles, t1 is 9 hours, d2 is 335, and t2 is the unknown value.

Thus, we can simply plug in everything to the equation and solve for t2:

[tex]\frac{603}{9}=\frac{335}{t_{2} }\\ 67=\frac{335}{t_{2} }\\ 67t_{2}=335\\ t_{2}=5[/tex]

(*Note that 9 divides evenly into 603 and becomes 67, which is why I didn't cross-multiply first with he 603 and t2 and the 335 and 9, although you'd still get the same result for t2)

Thus, it would take Shen 5 hours to drive 335 miles.

You can check by finding the rate for both equations since we know that distance is equal to the product of rate and time (d = rt):

First equation:  603 miles = 9 hours * r mph

67 mph = r

603 = 67 * 9

Second equation: 335 miles = 5 hr * r mph

67 mph = r

335 = 67 * 5

The solution curve represents a spiral that converges towards the origin.

(a) To classify the behavior of the system, we can use the (A,T) chart. Here, A is the sum of the elements in each row of the system matrix and T is the sum of the absolute values of the off-diagonal elements.

The system matrix for this scenario is:

[ 0   1 ]

[-1   1 ]

So, A = 1 for both rows, and T = 1 (absolute value of the off-diagonal element).

Using the (A,T) chart, we can see that the system is a focus.

(b) To find the eigenvalues and eigenvectors of the system, we need to solve the characteristic equation:

| 0-lambda  1       |   |u|    |0|

| -1        1-lambda| [tex]\times[/tex] |v| =  |0|

Expanding the determinant, we get:[tex]\lambda^2[/tex] -[tex]\lambda[/tex] + 1 = 0

Solving for lambda using the quadratic formula, we get:[tex]\lambda[/tex] = (1 +/- sqrt(3)i) / 2

So, the eigenvalues are complex conjugates with a real part of 1/2. The eigenvectors can be found by solving the system of linear equations:(0 - lambda)u + v = 0

(-1)u + (1 - lambda)v = 0

For lambda = (1 + sqrt(3)i) / 2, we get:u = [1, -1 + sqrt(3)i]

For lambda = (1 - sqrt(3)i) / 2, we get:u = [1, -1 - sqrt(3)i]

(c) To sketch the solution curve that starts at R(0) = 1, J(0) = 1, we can use the eigenvectors and eigenvalues. The general solution for the system can be written as:[x(t), y(t)] = [tex]c_1 \times u_1 \times e^(l \ambda1 \times t) + c2 \times u2 \times e^(\lambda2 \times t)[/tex]

where c1 and c2 are constants determined by the initial conditions, u1 and u2 are the eigenvectors, and lambda1 and lambda2 are the eigenvalues.

Plugging in the values, we get:

[tex][x(t), y(t)] = c_1 \times [1, -1 +\ sqrt(3)i] \times e^{((1 + \sqrt(3)i)t} / 2) + c_2\times [1, -1 - \sqrt(3)i] \times e^{((1 - \sqrt(3)i)t} / 2)[/tex]

Using the initial condition R(0) = 1, J(0) = 1, we get:

[tex]c_1 + c_2 = 1[/tex]

(-1 + sqrt(3)i)c1 + (-1 - sqrt(3)i)c2 = 1

Solving for [tex]c_1[/tex] and [tex]c_2[/tex], we get:

[tex]c_1[/tex] = (1 + sqrt(3)i) / (2[tex]\times[/tex] sqrt(3)i)

[tex]c_2[/tex]= (1 - sqrt(3)i) / (2 [tex]\times[/tex] sqrt(3)i)

Plugging in these values, we get:

[x(t), y(t)] = [1, 0] [tex]\times[/tex] e^((1 + sqrt(3)i)t / 2) + [0, 1] [tex]\times[/tex]  e^((1 - sqrt(3)i)t / 2)

This solution curve represents a spiral that converges towards the origin.

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Explanation

Add up the frequencies:

7+6+12+19+19 = 63

Out of those 63 total spins, 6 of them landed on blue.

The empirical (aka experimental) probability of landing on blue is therefore 6/63 = 2/21

(a) The discriminant is positive (25)

(b) The quadratic equation has two zeros.

(c) The type of the zeros is real and distinct.

The given quadratic equation is: x² - 7x + 6 = 0

To find the discriminant, we use the formula:

Discriminant = b² - 4ac

Here, a = 1, b = -7, and c = 6.

So, the discriminant is:

b² - 4ac = (-7)² - 4(1)(6) = 49 - 24 = 25

Therefore, the discriminant is 25.

To determine the number of zeros, we use the discriminant as follows:

Here, the discriminant is positive (25), so the quadratic equation has two real and distinct roots.

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200 m/s  is the wave speed of a wave that has a frequency .

What do you name a wave?

There are two different types of waves: longitudinal and transverse. Longitudinal waves are similar to those of sound in that they alternate between compressions and rarefactions in a medium, much like transverse waves in that the surface of the medium rises and falls.

                             The pattern of disruption brought about by the movement of energy through a medium (such as air, water, or any other liquid or solid matter) as it spreads away from the source of the sound is known as a sound wave.

The wave speed (v) of a wave can be calculated by multiplying its frequency (f) by its wavelength (λ). Mathematically, we can express this as

v = f x λ

Substituting the given values of frequency and wavelength into this formula, we get:

v = 500 Hz x 0.40 m

Multiplying these values, we get:

v = 200 m/s

Therefore, the wave speed of a wave that has a frequency of 500 Hz and a wavelength of 0.40 m is 200 m/s.

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The point (11,10) lies on the circle with center (5,2).

The equation of the circle with center (5,2) and point (11,10) is given by [tex](x-5)^2 + (y-2)^2 = (x-11)^2 + (y-10)^2.[/tex]

Substitute the coordinates of the center and point in the equation and simplify, we get

[tex](x-5)^2 + (y-2)^2 = (x-11)^2 + (y-10)^2= (x-5)^2 + (y-2)^2 = (x-11)^2 + (y-10)^2= x^2 - 10x + 25 + y^2 - 4y + 4 = x^2 - 22x + 121 + y^2 - 20y + 100= -10x + 25 - 4y + 4 = -22x + 121 - 20y + 100= -10x - 22x = 121 - 25 - 20y + 4y=-32x = 96= x = 3[/tex]

Substitute this value of x in [tex](x-5)^2 + (y-2)^2 = (x-11)^2 + (y-10)^2[/tex] and simplify, we get

[tex](3-5)^2 + (y-2)^2 = (3-11)^2 + (y-10)^2= (-2)^2 + (y-2)^2 = (-8)^2 + (y-10)^2= 4 + y^2 - 4y + 4 = 64 + y^2 - 20y + 100= -4y + 8 = -20y + 96= 16 = 16[/tex]

Hence, the point (11,10) lies on the circle with center (5,2).

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complete question

Explain with formula and calculation how a circle with center (5,2) contains the point (11,10).

It will take 32 hours for the water level to drop 2 feet.The rate of leaking is 0.40 cubic feet per minute.

To calculate how many hours it will take for the water level to drop 2 feet, we can use the following formula:Time (in hours) = Volume of water (in cubic feet) ÷ Rate of leaking (in cubic feet per minute)In this case, the volume of water is equal to the volume of the pool, which can be calculated using the formula V = l × w × h, where l is the length of the pool, w is the width of the pool, and h is the height of the pool. In this case, l = 24, w = 8, and h = 4, so the volume of the pool is V = (24)(8)(4) = 768 cubic feet.The rate of leaking is 0.40 cubic feet per minute.Therefore, the time (in hours) it will take for the water level to drop 2 feet is equal toTime (in hours) = 768 cubic feet ÷ 0.40 cubic feet per minute Time (in hours) = 1920 minutes Time (in hours) = 32 hoursTherefore, it will take 32 hours for the water level to drop 2 feet.

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Answer:

6436

Step-by-step explanation:

78 x 82

= (80-2) * (80+2)

= (80^2 - 2^2)  

= 6436

The hypotenuse's length could therefore be between 9.03 and 10.70 units based on these estimates.

The term "right triangle" refers to a triangle with an internal angle of 90 degrees. The hypotenuse, the side that faces the right angle and is also the side with the longest side in a right triangle, and the height and base are the two limbs of the right angle.

Based on the information provided, it is reasonable to infer that we have a right-angled triangle with two sides that are y and 7, and we need to determine the length of the hypotenuse.

The hypotenuse's square length is equal to the total of the squares of the lengths of the other two sides, according to the Pythagorean theorem.

The result is:

y² + 7² = hypotenuse²

hypotenuse² = y² + 49

we can determine the length of the hypotenuse by assuming that y is somewhere between 5.7 and 8.1.

If y is 5.7, then:

hypotenuse² = 5.7² + 49

hypotenuse² = 81.49

hypotenuse ≈ 9.03

If  y is 8.1, then:

hypotenuse² = 8.1² + 49

hypotenuse² = 114.61

hypotenuse ≈ 10.70

So, based on these estimations, the length of the hypotenuse could be around 9.03 or 10.70 units.

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Complete question

Estimate the length of the hypotenuse, If the length of the two sides is y and 7 respectively

1) If y= 5.7

2) If y= 8.1

[tex]\begin{array}{|c|ll} \cline{1-1} \textit{\textit{\LARGE a}\% of \textit{\LARGE b}}\\ \cline{1-1} \\ \left( \cfrac{\textit{\LARGE a}}{100} \right)\cdot \textit{\LARGE b} \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{47.5\% of 1600}}{\left( \cfrac{47.5}{100} \right)1600}\implies 760~\hfill \underset{ females }{\stackrel{1600~~ - ~~760 }{\text{\LARGE 840}}}[/tex]

Answer:

7 seconds

Step-by-step explanation:

d is 1225, and we need to find t.

plug in 1225 for d:

1225/25 = t^2

49 = t^2

t = 7