What is the equation of the line that passes through (-1, -7) and has a slope of 2?

Answer: C

Step-by-step explanation: Absolute value means all the values in the | | are positive so make them positive and you will see it’s 3.5, 4.2, and 9 in order from least to greatest.

Answer:

A is the answer

Step-by-step explanation:

because it is equal to the first triangle

The hotel should overbook enough rooms to maximize revenue without incurring expensive costs due to last-minute cancellations. To determine the optimal number of rooms to overbook, consider the following:

1. The average number of cancellations is 5 with a standard deviation of 3.
2. The average room rate is $80.
3. The cost of accommodating overbooked customers in a nearby hotel is $200.

Using these figures, the hotel can calculate the expected revenue for each room overbooked, while considering the risk of cancellations. The best approach is to use a probabilistic model, such as the normal distribution, to estimate the optimal number of rooms to overbook based on these statistics.

A detailed analysis would require further calculations and simulations, which are beyond the scope of this answer. However, a basic guideline for the hotel would be to overbook only a few rooms (e.g., 1-3) to minimize the risk of incurring the high cost of accommodating customers in nearby hotels while still maximizing the revenue from potential cancellations.

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Answer: See explanation

Step-by-step explanation:

You didn't say what you want to get but I'm guessing that you want to know who had the cheapest deal or the best deal.

Robby went on Monday and bought three movies for $15.36. The cost per movie will be:

= $15.36/3

= $5.12

Paula went on Wednesday and bought five movies for $27.40. The cost per movie will be:

= $27.40/5

= $5.48

Trey went on Thursday and bought four movies for $20.08. The cost per movie will be:

= $20.08/4

= $5.02

Madison went on Friday and bought six movies for $31.44. The cost per movie will be:

= $31.44/6

= $5.24

We can see that Trey had the best deal.

Answer:

\(x=3c\sqrt{a} -b^2\)

Step-by-step explanation:

\(\sqrt{a} =\dfrac{x+b^2}{3c}\)

Multiply both sides by 3c:

\(\implies \sqrt{a} \cdot 3c=\dfrac{(x+b^2) \cdot 3c}{3c}\)

\(\implies 3c\sqrt{a} =x+b^2\)

Subtract \(b^2\) from both sides:

\(\implies 3c\sqrt{a} -b^2=x+b^2-b^2\)

\(\implies 3c\sqrt{a}-b^2=x\)

Switch sides:

\(\implies x=3c\sqrt{a} -b^2\)

There is no exact measure of θ that satisfies the condition cos(θ) = 3√2 in the first quadrant.

Given that the terminal side of angle θ is in the first quadrant and cos(θ) = 3√2, we can determine the exact measure of θ by using the inverse cosine function, also known as arccosine.

Since cos(θ) = adjacent/hypotenuse, we can set up a right triangle in the first quadrant with the adjacent side as 3√2 and the hypotenuse as 1. The opposite side of the triangle can be found using the Pythagorean theorem.

Let's calculate the length of the opposite side:

opposite^2 + adjacent^2 = hypotenuse^2

opposite^2 + (3√2)^2 = 1^2

opposite^2 + 18 = 1

opposite^2 = 1 - 18

opposite^2 = -17

Since the length of a side cannot be negative, we see that there is no real solution for the length of the opposite side. Therefore, the given cosine value of 3√2 does not correspond to an angle in the first quadrant.

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Notice that AD also creates two supplementary angles, BDA and ADE. Let y be the measure of the smaller angle, ADE; then the measure of the larger angle, BDA, is 180° - y.

Since AD bisects angle A, we have by the law of sines

sin(A/2)/x = sin(y)/8

and

sin(A/2)/6 = sin(180° - y)/12

Now,

sin(180° - y) = sin(180°) cos(y) - cos(180°) sin(y) = sin(y)

so that

sin(A/2) = x/8 sin(y)

and

sin(A/2) = 6/12 sin(y) = 1/2 sin(y)

Solve for x :

x/8 sin(y) = 1/2 sin(y)

x/8 = 1/2

x = 8/2

x = 4

Part A: The total number of items purchased is 200, so the sum of the quantities of mats, towels, and carrying cases should be equal to 200. We can write this as x + y + 125 = 200.

Part B: If both equations hold true, then the records are accurate.

In this case, the equations are satisfied, so the records are accurate. The instructor indeed purchased 25 mats, 50 towels, and 125 carrying cases, totaling 200 items.

Part A: To define variables and write a system of equations, let's assign variables to the quantities of each item the yoga instructor purchased.

Let's say:
- x represents the number of yoga mats purchased
- y represents the number of yoga towels purchased

Since the instructor purchased twice as many towels as mats, we can write the equation y = 2x.

The total number of items purchased is 200, so the sum of the quantities of mats, towels, and carrying cases should be equal to 200. We can write this as x + y + 125 = 200.

Part B: To determine if the records are accurate, let's substitute the values provided in the problem into the equations. According to the records, the instructor purchased 25 mats, 50 towels, and 125 carrying cases.

Substituting these values into the equations, we have:
- x + y + 125 = 200
- 25 + 50 + 125 = 200

If both equations hold true, then the records are accurate.

In this case, the equations are satisfied, so the records are accurate. The instructor indeed purchased 25 mats, 50 towels, and 125 carrying cases, totaling 200 items.

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Answer:

8$/lb

Step-by-step explanation:

because 8 x 5 is 40 there for each pound would be 8$ if there are 5 pounds

\(\frac{AB}{A"B"} = \frac{1}{4}\)  equation clearly illustrates how AABO and AA"B"C relate to one another.

An equation is, for instance, 3x - 5 = 16. We can solve this equation and determine that the value of the variable x is 7.

The three main types of linear equations are the slope-intercept form, standard form, and point-slope form.

Considering the data:

Dilation by a scale factor of 4 from the origin in the form of an A'B'C' reflection over x = 1

<=> The two triangles are comparable to one another since triangles can have the same shape but differ in size, so A′′B′′C′′ is 4 times larger than ABC.

=> the connection between "ABC" and "A"B"C" .

\(\frac{AB}{A"B"} = \frac{1}{4}\)

We settle on C.

\(\frac{AB}{A"B"} = \frac{1}{4}\)  equation clearly illustrates how AABO and AA"B"C relate to one another.

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i believe its √49.

the square root of 49 is 7, and 7 is a rational number

Step-by-step explanation: To find the circumference, remember that the formula for the circumference of a circle is C = 2πr.

Since we're given that the radius of our circle is 9,

we have 2π(9) or 18π.

So the circumference of the circle is 18π.

To find the area of the circle, remember that the formula

for the area of a circle is A = πr².

Since we're given that the radius of our circle is 9,

we have π(9)² or π(81) which is written as 81π.

So the area of the circle is 81π.

Circumference ≈ 56.52 units

C = π x d (you can remember this by saying “chocolate pies are delicious”)

C = π x 18 (diameter is radius x 2 or radius + radius)

(you can round π to 3.14)

C ≈ 56.52 units

Area ≈ 254.34 units squared

A = π x r^2 (you can remember this by saying “apple pies are too” [building off of ‘chocolate pies are delicious‘])

A = π x 9^2

A = π x 81

(you can round π to 3.14)

A ≈ 254.34 units squared

The set that best represents the domain of this function would be:

{0, 1, 2, 3, 4, 5, 6, 7, 8}

What is domain?

In mathematics, a domain typically refers to a set of values for which a mathematical function or expression is defined and produces a valid output.

The domain of a function represents the set of all possible input values that the function can take. In this case, the function represents the number of bouquets used by the florist for the wedding, and the constraint is that no more than 8 bouquets can be used.

Therefore, the set that best represents the domain of this function would be:

{0, 1, 2, 3, 4, 5, 6, 7, 8}

This set includes all possible values of bouquets that the florist can use, and it satisfies the given constraint of not using more than 8 bouquets.

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The scale of drawing of Bonnie's drawing is 5 inches : 6 yards.

She measured a city and made a scale drawing.

The neighbourhood park is 115 inches long in the drawing. The actual park is 138 yards long.

Therefore, the scale of the drawing can be calculated as follows:

Hence,

115 inches = 138 yards

5 inches = ?

cross multiply

scale of the drawing = 5 × 138 / 115

scale of the drawing = 690 / 115

Therefore,

scale of the drawing is 5 inches : 6 yards

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The value of the given integral is approximately 3104.4.

The given region of integration is the first quadrant of the circle centered at the origin with radius 4, which can be expressed in polar coordinates as 0 ≤ r ≤ 4, 0 ≤ θ ≤ π/2.

To convert the given double integral to polar coordinates, we use the transformation:

x = r cosθ

y = r sinθ

and the area element in polar coordinates is given by: da = r dr dθ.

Substituting these into the given integral, we get:

∫∫r1√(625 - \(x^2\) - \(y^2\)) da = ∫∫r1√(625 - \(r^2\)) r dr dθ

Integrating with respect to r from 0 to 4 and with respect to θ from 0 to π/2, we get:

∫\(0^{(\pi/2)\)∫\(0^4\) r√(625 - \(r^2\)) dr dθ

We can evaluate this integral by making the substitution u = 625 - \(r^2\), which gives du = -2r dr. Substituting this, we get:

-1/2 ∫\(625^9\)∫\(u^{(1/2)\)0 du dθ

Using the power rule of integration, we get:

-1/2 ∫\(625^9 (2/3)u^{(3/2)}\)  | from 0 to \(u^{(1/2)}\) dθ

= -1/2 ∫\(625^9 (2/3)u^{(3/2)}\) dθ

= -1/2 (2/5)\(u^{(5/2)}\)| from 625 to 9

= (-1/5)\((9^{(5/2)} - 625^{(5/2)})\)

= (-1/5)(243 - 15625)

= 3104.4

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To evaluate the given double integral ∬r1√(625-x²-y²) da, we can convert the integral into polar coordinates.

First, we need to find the limits of integration for r and θ.And then find the integral in polar coordinates. Using these we find the value of the given integral

The region of integration is given by {(x,y) | x² + y² ≤ 16, x ≥ 0, y ≥ 0}. This is the upper-right quadrant of a circle centered at the origin with radius 4.

In polar coordinates, the equation of the circle becomes r² ≤ 16, which simplifies to r ≤ 4. Also, since the region lies in the first quadrant, we have 0 ≤ θ ≤ π/2.

Therefore, we can write the integral in polar coordinates as:

∫∫r1√(625-x²-y²) da = ∫θ=0π/2 ∫r=04 r√(625-r²) dr dθ

Now, we can evaluate the integral using these limits of integration:

∫θ=0π/2 ∫r=04 r√(625-r²) dr dθ = ∫θ=0π/2 [-(1/3)(625-r²)^(3/2)]_r=0^4 dθ

= ∫θ=0π/2 [-(1/3)(625-16)^(3/2)] dθ

= (1/3)(609)∫θ=0π/2 dθ

= (1/3)(609)(π/2)

= 320.91

Therefore, the value of the given integral is approximately 320.91.

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Based on the provided graph, the correct statement is that nearly "200 of the cancer cases reported in the U.S. are attributable to smoking".

The graph visually represents statistical data or relationships between variables by drawing lines or bars that connect data points or present information in a graphical format. In this case, the graph likely shows the attribution of cancer cases to smoking in the U.S.

Smoking is a dangerous practice that is known to be one of the leading causes of cancer worldwide. The link between smoking and cancer is well-established, with tobacco smoke containing various harmful chemicals that can damage DNA and increase the risk of developing cancer. It is estimated that nearly 25% of all cancer cases can be attributed to smoking.

The graph likely presents data indicating the number of cancer cases attributable to smoking in the U.S. Based on the information provided, the graph suggests that nearly 200 cancer cases in the U.S. can be directly linked to smoking.

Therefore, the correct statement is that nearly 200 of the cancer cases reported in the U.S. are attributable to smoking.

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120 because when u finish diving it gives u 120

LCL and UCL values of both scenarios are (158.61,161.39),(69.65,70.35) respectively.

To calculate the lower confidence limit (LCL) and upper confidence limit (UCL) for each given scenario, you'll need to use the following formula:

LCL = X - (z * (sigma / √n))
UCL = X+ (z * (sigma / √n))

where X is the sample mean, n is the sample size, sigma is the population standard deviation, and z is the z-score corresponding to the desired confidence level (1 - alpha).

First Scenario:
X = 160, n = 436, sigma = 30, alpha = 0.01

1. Find the z-score for the given alpha (0.01).
For a two-tailed test, look up the z-score for 1 - (alpha / 2) = 1 - 0.005 = 0.995.
The corresponding z-score is 2.576.

2. Calculate LCL and UCL.
LCL = 160 - (2.576 * (30 / √436)) ≈ 158.61
UCL = 160 + (2.576 * (30 / √436)) ≈ 161.39

First Scenario Result:
LCL = 158.61
UCL = 161.39

Second Scenario:
X= 70, n = 323, sigma = 4, alpha = 0.05

1. Find the z-score for the given alpha (0.05).
For a two-tailed test, look up the z-score for 1 - (alpha / 2) = 1 - 0.025 = 0.975.
The corresponding z-score is 1.96.

2. Calculate LCL and UCL.
LCL = 70 - (1.96 * (4 / √323)) ≈ 69.65
UCL = 70 + (1.96 * (4 / √323)) ≈ 70.35

Second Scenario Result:
LCL = 69.65
UCL = 70.35

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Answer:

8

Step-by-step explanation:

If the area is 32 and the formula for area of a triangle is base * height / 2, and you have base = 8 and height = x and area = 32, this would be:

8 * x / 2 = 32

Now, solve:

\(8x/2=32\\4x=32\\x=8\)

Answer:

x=8

Step-by-step explanation:

Area is equal to half of the base times the height. We are told that the area is 32and the base is 8, so we can write this equation:

32=1/2(8)h

Multiply 1/2 by 8:

32=4h

Divide both sides by 4:

h=8

So now we know that x (the height) equals 8.

HTH :)

Answer:

3.95m + 8.95b = 47.65

Step-by-step explanation:

m is the number of magazines, and b is the number of books.  If it costs $3.95 for each magazine, you will get 3.95m.  If it costs $8.95 for each book, you will get 8.95b.  Both of these values add up to the total, which is $47.65.

3.95m + 8.95b = 47.65

Answer:) 3.95m+8.59b=47.65

Step-by-step explanation:) edge 2023

The time that Nagma takes to complete five rounds is 0.4 hours or 24 minutes.

Travel time is the total time required to pass a certain length of road.

Given,

Length = 180m

Width = 120 m

Speed = 7.5 km/hr

Time of five rounds?

Steps,

The first step that must be done is to find the travel time for one round

Distance of one round = 2(length + width)

Distance of one round = 2(180 + 120)

Distance of one lap = 3 (300)

Distance of one round = 600 m = 0.6 km

Time needed to reach 5 rounds

Time = 5 (distance : speed)

Time = 5 (0.6 : 7.5)

Time = 0.4 hours = 24 minutes

So, the time needed to complete five rounds is 0.4 hours or 24 minutes.

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Answer:

20 h

Step-by-step explanation:

120/30 = 4

4(5) = 20

Answer:

its 1%

Step-by-step explanation:

Explanation:

Shape P is a triangle with the base of 4 units across the horizontal portion up top.

The height of the triangle is 6 units. Count the spaces down the middle of the triangle and you should get 6 spaces.

Area = base*height/2

Area = 4*6/2

Area = 24/2

Area = 12 square cm.

The value of tensions are:

T₁ = 231/74

T₂ = -329/66

T₃ = 8/33

We can use Gaussian elimination to solve the system of equations:

5T₁ + 3T₂ + 5T₃ = 70

T₁ + 2T₂ + 4T₃ = 24

4T₁ + 2T₂ = 40

First, we'll use the third equation to eliminate T₂ from the first two equations:

4T₁ + 2T₂ = 40   (equation 3)

T₁ + 2T₂ + 4T₃ = 24   (equation 2)

Multiplying the third equation by 2 and subtracting it from the second equation:

T₁ + 2T₂ + 4T₃ = 24   (equation 2)

- 8T₁ - 4T₂ = -80   (2 × equation 3)

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

-7T₁ + 4T₃ = -56

Now we have two equations:

5T₁ + 3T₂ + 5T₃ = 70   (equation 1)

-7T₁ + 4T₃ = -56   (from previous step)

Multiplying the first equation by 7/5 and adding it to the second equation:

5T₁ + 3T₂ + 5T₃ = 70   (equation 1)

-7T₁ + 4T₃ = -56   (from previous step)

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

T₁ + 7T₃ = 14

Now we can use the third equation to eliminate T₂ from the first equation:

4T₁ + 2T₂ = 40   (equation 3)

5T₁ + 3T₂ + 5T₃ = 70   (equation 1)

Multiplying the third equation by 3/2 and subtracting it from the first equation:

4T₁ + 2T₂ = 40   (equation 3)

-11T₁ - T₃ = -35   (3 × equation 3 - 5 × equation 1)

Now we have two equations:

T₁ + 7T₃ = 14   (from previous step)

-11T₁ - T₃ = -35   (from this step)

Multiplying the second equation by -7 and adding it to the first equation:

T₁ + 7T₃ = 14   (from previous step)

74T₁ = 231

Therefore, T₁ = 231/74.

Substituting this value back into the equation T₁ + 7T₃ = 14, we get:

(231/74) + 7T₃ = 14

7T₃ = (74/231) × 20

T₃ = 8/33

Finally, substituting T₁ = 231/74 and T₃ = 8/33 into the equation -11T₁ - T₃ = -35, we get:

-11(231/74) - (8/33) = -329/66

Therefore, T₂ = -329/66.

So, the tensions are: T₁ = 231/74 T₂ = -329/66 T₃ = 8/33

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To find two numbers whose sum is 11 and whose product is maximum, we can use a mathematical approach.

Let's denote the two numbers as x and 11 - x, where x represents the first number. The sum of these numbers is 11, so we can write the equation x + (11 - x) = 11. Simplifying this equation gives us 2x = 11, and solving for x results in x = 11/2 or 5.5. Therefore, the two numbers are 5.5 and 5.5.

To explain this answer, we can consider the properties of quadratic functions. When we multiply two numbers, their product is maximized when the numbers are equal. By representing one number as x and the other as 11 - x, we ensure that their sum is 11. We then set up an equation using the sum constraint and solve for x. In this case, we find that x = 5.5, indicating that both numbers are 5.5. As a result, their product is maximized at 30.25.

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