Listen In 2010 Glacial HVAC, Inc. sold 3,295 air conditioning units in Fulton County. Glacial's largest competitor, Estes Heating and Air, sold 2,759 units during 2010. Calculate Glacial's relative market share. Round your answer to two decimal places

Answer: B. y = 20x +20

The score for a student that spent 3.8 hours studying is expected to be 96.

Step by step solution:

The point-slope form of a linear equation is y = mx + b, where m is the slope and b the intercept with the y-axis.

To find the line that fits the data and model the relationship, we need to find the slope. Let

y = Test score

x = Study time (hours)

Two pair of coordinates from the line are (2, 60) and (3, 80):

We have m = 20, and b = 20 (intercept with the y-axis)

The equation that model the relationship is:

Second Part. Basing ourselves on the above equation, estimate the score for a student that spent 3.8 hours studying x = 3.8.

The score for a student that spent 3.8 hours studying is expected to be 96.

Answer:

18

Step-by-step explanation:

The arrows on lines AB and CD indicate that these 2 shapes are similar and these 2 lines are corresponding so :

Linear scale factor :

12 ÷ 10 = 1.2 or 6/5

Let's use the fraction form

Using the linear scale factor we can make an equation to solve for x :

2x+4 = 6/5(x+8)

Expand the brackets :

2x+4 = 6/5x + 9.6

Subtract 4 from both sides :

2x = 6/5x + 5.6

Subtract 6/5x from both sides :

4/5x = 5.6

Divide both sides by 4/5 :

x = 7

Now substitute this value into the expression for the length of AE :

AE = 2(7) + 4

AE = 14 + 4

AE = 18

Hope this helped and have a good day

Answer:

116 units

Step-by-step explanation:

AE + ED = 180 because they make a straight angle and a straight angle is 180 degrees or half of a circle 360/2.

AE = 2x + 4 and ED = x +8 added together they equal 180

2x + 4 + x + 8 = 180  Combine the like terms

3x + 12 = 180  Subtract 12 from both sides of the equation

3x = 168  Divide both sides by 3

x = 56

Now that we know that x is 56 we can plug that in for AE to find its length

2x + 4

2(56) + 4

112 + 4

116

[If (r, ) are polar coordinates of the point (x, y) with r > 0, note that not a. ... + y2) In(x2 + y2) (x,y) → (0,0) DNE X Find h(x, y) = g(f(x, y)). g(t) = t + In(t), f(x, y) = 3 - xy 4 ...

The daily rate charged to the client for each associate is $800 and the daily rate for each partner is $1800.  The equations that could be used to determine the number of associates assigned to the case and the number of partners assigned to the case is: 800 x + 1800 y = 17600.

Let variable x = number of associates, assigned to the case

Let variable y = number of partners assigned to the case.

The system of equations to describe this are:

800 x + 1800 y = 17600

y = x + 2

Plugging equation 2 in equation 1, we get,

800 x + 1800(x+ 2) = 17600

2600 x + 3600 = 17,600

Collect like terms

2400 x = 14,000

Divide both side by 2400x

x = 14,000 / 2400

x = 5.8

x = 6 (Approximately)

So,

y = x + 2

y = 5.8 +3

y = 7.8

y = 8 (Approximately)

Therefore the number of associates assigned to the case were 6, and the number of partners associated to the case were 8.

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The resultant of these two forces is 780.31N

If the car has a mass of 3200 kg, the acceleration of the car is 0.244m/s²

The formula for the resultant force is expressed as:

\(R =\sqrt{(\sum F_x)^2+(\sum F_y)^2}\)

Take the sum of force along the horizontal

\(\sum F_x = 450cos10^0+380cos30^0\\\sum F_x =443.16 + 329.09\\\sum F_x = 772.25N\)

Take the sum of force along the vertical

\(\sum F_y = 450sin10^0-380sin30^0\\\sum F_y=78.14 - 190\\\sum F_y= -111.86N\)

Get the resultant force:

\(R =\sqrt{(772.25)^2+(-111.86)^2}\\R = \sqrt{596,370.0625 +12,512.6596}\\R = \sqrt{608,882.7221}\\R = 780.31N\)

Hence the resultant of these two forces is 780.31N

b) According to Newton's second law of motion;

\(R =ma\\a=\frac{R}{m} \\a=\frac{780.31}{3200}\\a = 0.244m/s^2\)

Hence If the car has a mass of 3200 kg, the acceleration of the car is 0.244m/s²

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Answer:

C.120

Step-by-step explanation:

5×4×3×2×1=120 hope its right

Answer:

C. 6.9

Step-by-step explanation:

Pretend this is a 2-d diagram and use the Pythagorean theorem.

Pythagorean theorem: a^2 + b^2 = c^2

a = 6 mm

b = 7/2 = 3.5 mm

c = x

6^2 + 3.5^2 = x^2

36 + 12.25 = x^2

48.25 = x^2

\(\sqrt{48.25} = \sqrt{x^2}\)

x = 6.9

Given that the sum of two numbers is 71 and one number is 27 more than the other, we can set up the following system of equations:

What is the straightforward definition of a system of equations solution?

A collection of values for a variable that simultaneously fulfill each equation is the solution to a system of equations. A system of equations must be solved by identifying all possible sets of variable values that make up the system's solutions.

x + y = 71 (equation 1 represents the fact that the sum of the numbers is 71)

y = x + 27 (equation 2 represents the fact that one number is 27 more than the other)

To solve the system of equations, we can use the substitution method. We'll substitute equation 2 into equation 1:

x + (x + 27) = 71

Combining like terms:

2x + 27 = 71

Subtracting 27 from both sides:

2x = 44

Dividing both sides by 2:

x = 22

Now we can substitute x = 22 back into equation 2 to find the value of y:

y = x + 27

y = 22 + 27

y = 49

So the two numbers are x = 22 and y = 49, and they satisfy the given conditions that the sum of the two numbers is 71 and one number is 27 more than the other.

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12.

13.

Answer:

4.38 liter

Step-by-step explanation:

Answer:

78kg

Step-by-step explanation:

76×5= 380kg

380-72-74-75-81= 78kg

4312 liters of water need to be filled to calculate the volume of water occupying 70% volume of the tank.

What is volume ?

Volume is the amount of space occupied by an object or a substance. It is a measure of the amount of three-dimensional space an object or a substance occupies. The volume of an object or substance is typically measured in cubic units, such as cubic meters (m³), cubic centimeters (cm³), or cubic feet (ft³).

A) To calculate the area of glass for the tank without lid, we need to find the total surface area of the rectangular box.

The front and back sides have dimensions 1.1 m x 7 dm = 1.1 m x 0.7 m = 0.77 m² each.

The top and bottom sides have dimensions 1.1 m x 8 m = 8.8 m² each.

The left and right sides have dimensions 7 dm x 8 m = 0.7 m x 8 m = 5.6 m² each.

Therefore, the total surface area of glass for the tank without lid is:

0.77 m² + 0.77 m² + 8.8 m² + 8.8 m² + 5.6 m² + 5.6 m² = 30.6 m²

B) To calculate the volume of water occupying 70% of the tank, we first need to calculate the volume of the tank.

The volume of a rectangular box is found by multiplying its length, width, and height:

Volume = length x width x height

We have:

length = 1.1 m

width = 8 m

height = 7 dm = 0.7 m

Volume = 1.1 m x 8 m x 0.7 m = 6.16 m³

Next, we need to find 70% of the volume of the tank:

70% of 6.16 m³ = 0.7 x 6.16 m³ = 4.312 m³

Finally, we need to convert cubic meters to liters, using the conversion factor given:

1 m³ = 1000 L

Therefore,

4.312 m³ x 1000 L/m³ = 4312 L

Therefore, 4312 liters of water need to be filled to calculate the volume of water occupying 70% volume of the tank.

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The perimeter of the textbook cover should be reported as 123.1 cm, using four significant figures.

When calculating the perimeter of the textbook cover, it is important to consider the number of significant figures in the measurements. The general rule is that the result of a calculation should have the same number of significant figures as the least precise measurement used in the calculation.

In this case, the length of the textbook cover is given as 36.71 cm with four significant figures, while the width is given as 24.83 cm with four significant figures as well. When calculating the perimeter, you add the lengths of all four sides of the rectangle.

Perimeter = 2(length + width) = 2(36.71 cm + 24.83 cm)

To maintain the same level of precision as the least precise measurement, we need to consider the width, which has four significant figures. Thus, the result should be reported with four significant figures.

Perimeter = 2(36.71 cm + 24.83 cm) = 2(61.54 cm) = 123.08 cm

Therefore, the perimeter of the textbook cover should be reported as 123.1 cm, using four significant figures.

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The amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

As per the given problem:

Amount deposited = $60.00

Interest rate per year = 9%

The formula for calculating the interest is given by:

Interest = (Principal × Rate × Time)/100

Where Principal is the initial amount invested or deposited

Rate is the percentage of interest that you earn per annum

Time is the duration for which you want to calculate the interest

Putting the values in the above formula, we get:

Interest = (60 × 9 × 2)/100= (108 × 1)/1= $108

So, the amount of interest earned on a deposit of $60.00 at a rate of 9% per annum for 2 years is $108.

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Distribute the parentheses:

2(x + 1)

2 · x = 2x

2 · 1 = 2

2(x + 1) = 2x + 2

The answer is 25.

2^4 + 3^5 = 25.

Answer:

The person above me is correct :))

Step-by-step explanation:

The innovation that was made possible in part because of the Carterfone decision in 1968 is the public Internet. The correct answer is option C

The Carterfone decision was a landmark ruling by the Federal Communications Commission (FCC) that allowed for the interconnection of third-party devices to the telephone network. Prior to this decision, telephone companies had a monopoly on the equipment that could be used on their networks, and customers were not allowed to attach their own devices.

This decision paved the way for the development of the public Internet by allowing for the interconnection of third-party devices to the telephone network, which enabled the creation of new technologies, such as modems. Without the Carterfone decision, the public Internet as we know it today may not have been possible.

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Her new chance of being pregnent given posite result is roughly 99%

What's probability?

Probability is a fine conception that measures the liability of an event being. It's expressed as a number between 0 and 1, where 0 indicates that the event is insolvable, and 1 indicates that the event is certain to do.

his problem can be answered using Bayes' Theorem. Let P( P) be the probability that your friend is pregnant, and let P(| P) be the probability that the test is positive given that your friend is pregnant. also, let P(-| ¬ P) be the probability that the test is negative given that your friend isn't pregnant.

From the problem statement, we have

P( P) = 0.5(50/50 chance of being pregnant before the test)

P(| P) = 0.91( the probability of a positive test given a pregnant woman)

P(-| ¬ P) = 0.99( the probability of a negative test given anon-pregnant woman)

We want to calculate P( P|), the probability that your friend is pregnant given a positive test. We can apply Bayes' Theorem to find this

P( P|) = P(| P) * P( P)/ P()

where P() is the probability of a positive test, which can be calculated using the law of total probability

P() = P(| P) * P( P) P(| ¬ P) * P( ¬ P)

where P( ¬ P) is the complement of P( P), i.e., the probability that your friend isn't pregnant

P( ¬ P) = 1- P( P) = 0.5

Substituting these values, we get

P() = 0.91 *0.50.01 *0.5 = 0.46

Now we can calculate P( P|)

P( P|) = P(| P) * P( P)/ P() = 0.91 *0.5/0.46 ≈0.99

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The number of shares of each girl will be R200, R300, and R700.

Given that:

Ratio, 2:3:7

When two objects are equal, a statement is said to be proportional.

The equation for the share of 3 girls is given as,

2x + 3x + 7x = 1200

Simplify the equation, then we have

2x + 3x + 7x = 1200

12x = 1200

x = 1200 / 12

x = 100

The shares of each girl are calculated as,

2x = 2 × 100 = 200

3x = 3 × 100 = 300

7x = 7 × 100 = 700

Thus, the number of shares of each girl will be R200, R300, and R700.

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Heidi is able to walk 10/3 miles in 1 hour (60 min).

It is a method for determining the value of a single unit by subtracting the value of multiple units and subtracting the value of multiple units from of the value of a single unit.

Now, for the given question;

It takes Heidi 12 minutes to walk 2/3 miles.

Applying the unitary method.

Then, for in 1 minutes Heidi will walk = 2/(3×12).

For walking in 1 hour or 60 min =  (2×60)/(3×12).

Further simplifying;

In 1 hour = 10/3 miles.

Therefore, Heidi would be be able to walk 10/3 miles in 1 hour.

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Answer:

Step-by-step explanation:

The graph covers the interval

Inequality to reflect this

Answer:

-3 < x ≤ 2

Step-by-step explanation:

Answer:

$2,898.00

Step-by-step explanation:

FV=2500(1.03)^5

FV=2500(1.159274)

FV=$2,898.00

Answer:

9:12

Step-by-step explanation:

a simple explanation would be that since the ratio is 3:4, put it into fractions and multiply each number by the same number. since 3 x 3 and 4 x 3 = 9:12 the answer could be 9:12.  

Answer:

Lets start with the top row.

First, add the two values.

5+14=19

Now, divide each value by the total.

5/19=0.26315789473

Round the decimal to the nearest hundredth.

5/19=0.26

14/19=0.73684210526

Round it to the nearest hundredth.

14/19=0.74

Now, The second row.

Add the two values.

16+7=23

Divide the first value by the total.

16/23=0.69565217391

Round it to the nearest hundredth.

16/23=0.70

Divide the second value by the total.

7/23=0.30434782608

Round to the nearest hundredth.

7/23=0.30

Done!

Answer:

Row 1: 0.26 0.74

Row 2: 0.70 0.30

Step-by-step explanation:

Khan

Answer:

1/38

Step-by-step explanation:

Given :

Probability = required outcome / Total possible outcomes

Total possible outcomes = total Numbe rod sections = 38

Required outcome = number of 1's on the entire section = 1

Hence, the probability of spinning a one equals :

P(spinning a 1) = 1 / 38

Answer:

I think it is five but I cannot see all the lines too well so I don't know

Answer:

the slope is 5

Step-by-step explanation:

50/10 = 5

y= 5x

By using sum or difference formulas, cos(-a) can be written as - cos(a). Explanation: We know that cosine is an even function of x, therefore,\(cos(-x) = cos(x)\) .Then, by using the identity \(cos(a - b) = cos(a) cos(b) + sin(a) sin(b)\), we can say that:\(cos(a - a) = cos²(a) + sin²(a).\)

This simplifies to:\(cos(0) = cos²(a) + sin²(a)cos(0) = 1So, cos(a)² + sin(a)² = 1Or, cos²(a) = 1 - sin²\)(a)Similarly,\(cos(-a)² = 1 - sin²(-a)\) Since cosine is an even function, \(cos(-a) = cos(a)\) Therefore, \(cos(-a)² = cos²(a) = 1 - sin²(a)cos(-a) = ±sqrt(1 - sin²(a))'.\)

This is the general formula for cos(-a), which can be written as a combination of sine and cosine. Since cosine is an even function, the negative sign can be written inside the square root: \(cos(-a) = ±sqrt(1 - sin²(a)) = ±sqrt(sin²(a) - 1) = -cos\).

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For a 44° elevation angle, the grade will be 96%.

Given that,

if the angle of elevation of the road is 44 degrees,

The difference in the road's altitude over a horizontal distance of 100 feet is what is referred to as the percentage grade. For instance, a road with a 5% slope will rise 5 feet for every horizontal 100-foot distance.)

A tangent ?

One of the six basic trigonometric functions is tangent, denoted as tan().

The ratio of the opposite side length to the adjacent side length is the definition of the tangent value of the one sharp angle,, in a right triangle.

\(tan \alpha = sin\alpha /cos \alpha\)

The tangent of the angle is the ratio of rise to run.

tan(angle) = grade

tan(44°) ≈ 0.96 = 96%

Therefore, The grade will be 96% for an angle of elevation of 44°.

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Answer:

\(g(f(x)) = gof(x) =( x - 7)^{2} \\ = {x}^{2} - 14x + 49 \\ g(f(4) )\times g(f(4)) = (4^{2} - 14 \times 4 + 49 )\times( 4 ^{2} - 14 \times 4 + 49) \\ = 9 \times 9 \\ = 81\)

Answer:

PROBABLY ABOUT 27 OR 26.6666666667

Answer:

Ben's Score = 60

Sam's Score = 20

Step-by-step explanation:

60 + 20 = 80

I really don't know how to explain this.