Which equation would be the equation that has a slope at 4 and passes through the point (2, 10)? y = 4x + 2 y = 8x + 18 y = 4x - 10 y = - 4x + 8​

Part A: The area of the large pizza (AL) is given by AL = 2As.

Part B: The radius of the small pizza (rs) is given by rs = sqrt(As/π).

Part C: The radius of the large pizza (rL) is given by rL = sqrt(2A/π).

Part D: The radius of the large pizza is not twice as large as the radius of the small pizza. The answer is no.

The area of the large pizza (AL) can be written in terms of the area of the small pizza (As) as follows:

AL = 2As.

The area of the small pizza (As) is given by

As = πrs^2. To find the radius of the small pizza (rs), we can rearrange the formula as

rs = sqrt(As/π).

The area of the large pizza (AL) is given by AL = πrL^2.

Using the information from Part A, we know that AL = 2As.

Substituting this into the equation, we get 2As = πrL^2.

Rearranging the formula, we can write rL in terms of A as rL = sqrt(2A/π).

Comparing the radii of the two pizzas, we find that the radius of the large pizza (rL) is not twice as large as the radius of the small pizza (rs).

Instead, the radius of the large pizza (rL) can be found using the formula

rL = sqrt(2A/π), while the radius of the small pizza (rs) can be found using the formula

rs = sqrt(As/π).

Therefore, the large radius is not twice the size of the small radius. The answer is no.

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Answer: 120 people

Step-by-step explanation:

First take $4100 - $500 = $3600

then you divide

3600/30 = 120

which equals

120 People are estimated to attend

The exact distance between the planes after 2 hours, using the law of cosines:

d = sqrt((2 * 425)^2 + (2 * 530)^2 - 2 * 2 * 425 * 530 * cos(67° - 355°))

where d is the distance between the planes in miles.

To visualize the problem, imagine a coordinate plane with the origin at Raleigh-Durham Airport. Plane A's path can be represented as a line with a slope determined by its bearing of 355°, while Plane B's path can be represented by another line with a slope determined by its bearing of 67°.

To calculate the distance between the planes after 2 hours, we first need to determine their respective positions. Since Plane A is traveling at 425 mph, it would have covered a distance of 850 miles (425 mph * 2 hours). Similarly, Plane B would have covered a distance of 1060 miles (530 mph * 2 hours).

Next, we can calculate the coordinates of each plane using the distance and bearing information. Using trigonometry, we can determine the vertical and horizontal distances covered by each plane. Plane A's vertical distance would be 850 * sin(355°), and its horizontal distance would be 850 * cos(355°). Similarly, Plane B's vertical and horizontal distances would be 1060 * sin(67°) and 1060 * cos(67°), respectively.

Finally, we can use the coordinates of each plane to calculate the distance between them. This can be done using the distance formula: distance = sqrt((x2 - x1)^2 + (y2 - y1)^2), where (x1, y1) and (x2, y2) are the coordinates of Plane A and Plane B, respectively.

By plugging in the calculated values, we can determine the distance between the two planes after 2 hours of flying.

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Answer:

This relation is a function.

Step-by-step explanation:

This relation is a function because a there should be no repeating x-coordinates in the relation for it to be a function and that is exactly what happens in this relation.

Answer:

It is a function.

Step-by-step explanation:

no two different outputs, y, have the same input, x, meaning it passes the vertical line test.

sorry for the lousy explanation

The probability of getting 2 or more heads in 5 successive coin tosses is 13/16 or approximately 0.8125.

To calculate the probability of getting 2 or more heads in 5 successive tosses of a fair coin, we need to consider all the possible outcomes that satisfy this condition.

The total number of possible outcomes when tossing a coin 5 times is 2^5 = 32, as each toss has 2 possible outcomes (heads or tails).

To find the probability of getting 2 or more heads, we need to calculate the probability of the complementary event, which is getting 0 or 1 head and subtract it from 1.

The probability of getting 0 heads (all tails) is (1/2)^5 = 1/32.

The probability of getting 1 head and 4 tails is (5 choose 1) * (1/2)^5 = 5/32.

Therefore, the probability of getting 2 or more heads is 1 - (1/32 + 5/32) = 26/32 = 13/16.

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Hi there!  

»»————-　★　————-««

I believe your answer is:  

2.952

»»————-　★　————-««  

Here’s why:  

⸻⸻⸻⸻

\(0.4 * (8.6-1.22)\\\rule{150}{0.5}\\0.4 * 7.38\\\\\boxed{2.952}\)

⸻⸻⸻⸻

I am assuming that 8.6 - 1.22 are supposed to be together.

⸻⸻⸻⸻

»»————-　★　————-««  

Hope this helps you. I apologize if it’s incorrect.  

The Linear regression equation is -

y = 0.2699x - 3.920 where x represents the years after 1900 and y represents the cheese consumption.

The linear regression equation describes the relationship between the Dependent variable [DV] and the Independent variable [IV].

It is represented as Y = mx + b , where Y is the Dependent variable, X is the Independent variable , m is the estimated slope and b is the estimated intercept.

According to the equation ,

m = 0.2699

b = -3.920

Hence, the  linear regression equation is  y = 0.2699x - 3.920.

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9514 1404 393

Answer:

  2.4×10^-6

Step-by-step explanation:

Your calculator can help you with this.

  (8×10^-3)(3×10^-4) = (8·3)×10^(-3-4) = 24×10^-7

  = (2.4×10^1)×10^-7 = 2.4×10^-6

The square of a rational number is a rational number.

A rational number is a number that is expressed as the ratio of two integers, where the denominator should not be equal to zero.

A rational number is a number that is of the form p/q where p and q are integers and q is not equal to 0.

Therefore, rational numbers are express as follows; p / q.

Hence, x is a rational number . let's confirm that x² is rational or not.

Therefore, When we square a rational number, each prime factor has an even exponent.

For example

p / q = p²/ q²

Hence, the square is a rational number.

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Please find attached photograph for your answer. Hope it is alright.

Answer:

(5x + \(\frac{3}{10}\) )(3x - \(\frac{7}{10}\))

Step-by-step explanation:

The expression is a difference of squares and factors in general as

a² - b² = (a + b)(a - b)

Then

(4x - \(\frac{1}{5}\) )² - (x + \(\frac{1}{2}\) )²

= (4x - \(\frac{1}{5}\) + x + \(\frac{1}{2}\) )(4x -

= (5x + \(\frac{3}{10}\) )(3x - \(\frac{7}{10}\) )

Answer:

53.79%

Step-by-step explanation:

The volume of the rectangular prism is 428,544 cubic cm.

To find the volume of the rectangular prism, we can start by determining the dimensions of the prism.

Let's assume the length, width, and height of the prism are L, W, and H, respectively.

Given that the rectangular prism is filled exactly with 248 cubes, we can express the total number of cubes as the product of the length, width, and height of the rectangular prism:

\(L \times W \times H = 248\)

Since each cube has an edge length of 12 cm, the volume of one cube can be calculated as follows:

Volume of one cube \(= (12 cm) \times (12 cm) \times(12 cm)\)

Volume of one cube \(= 1728 cm^3\)

Now, we can set up the equation based on the given information:

\(L \times W \times H = 248 \times Volume of one cube\)

\(L \times W \times H = 248 \times 1728 cm^3\)

To find the volume of the rectangular prism, we need to calculate the right side of the equation:

\(248 \times1728 = 428,544 cm^3\)

Therefore, the volume of the rectangular prism is \(428,544 cm^3\).

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Answer:

for 2 it's 2 4 6 8 10 12 14 16 18 20 22 24 and for three it's 3 6 9 12 15 18 21 24 27 30 33 36

Step-by-step explanation:

You Welcome

Step-by-step explanation:

when numbers are negative, the bigger the number looks the smaller it is therefore

-6 is smaller than -5

but 6 is bigger than 5

however, the numbers are;

-5.99, -3, -6, -5.9, -1, -5.999, -5 ,2

Answer:

47/53 or 0.88 or 88%

Step-by-step explanation:

Answer:

8 square feet

Step-by-step explanation:

48/12=4

24/12=2

2x4=8

\(\huge \bf༆ Answer ༄\)

Question 4 : Perimeter of squash field ~

English sentence :

Length of the field is 4 times y and Width of the field is (x + 1), and hence it's perimeter is 2 times the sum of Length and Width.

Question 5 : Area of Beans field ~ [ Length × Width ]

or, after further simplification :

Question 6 : Volume of the cuboid is [ L × W × H ]

So, The volume will be Length (xy + 1) times Width (xy + 5) times height (x + 3)

that is ~

The solution to all the questions about rectangles are;

4) Perimeter of the Squash field is 2 times the sum of it's Length and Width.

5) A = x²y² + 6xy + 5

6) V = x³y² + 6x²y + 5x + 3x²y² + 18xy + 15

4) We can see the squash field is rectangular and the dimensions are;

Length; L = x + 1

Width; w = 4y

Formula for perimeter of a rectangle is;

P = 2(L + w)

P = 2((x + 1) + 4y)

In English sentence, we can say that;

Perimeter of the Squash field is 2 times the sum of it's Length and Width.

5) The beans field is rectangular and its' dimensions are;

Length; L = xy + 5

Width; w = xy + 1

Area of rectangular Beans field;

A = Length × Width

A = (xy + 5) * (xy + 1)

A = x²y² + 6xy + 5

6) Formula for volume of the cube formed by the height will be;

V = L * w * h

since h = (x + 3)

Thus, volume is;

V = (xy + 5) * (xy + 1) * (x + 3)

V = x³y² + 6x²y + 5x + 3x²y² + 18xy + 15

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Answer:

A=2

B=-1

Step-by-step explanation:

a=(23−25)⋅ (4−5)=2

b=(97−123)/(18+8)=−1

Answer:

f(4) = - 27

Step-by-step explanation:

substitute x = 4 into f(x) , that is

f(4) = - 2(4)² + 5 = - 2(16) + 5 = - 32 + 5 = - 27

Answer:

69

Step-by-step explanation:

Replace x with 4

-2(4)^2 +5

-8^2+5

64+5

69

A unit vector in the same direction as vector a with a positive first coordinate is ⟨5/√(34), 0, -3/√(34)⟩.  

First, we calculate the magnitude of vector a using the formula:

|a| = √(5² + 0² + (-3)²) = √(34)

Next, we divide each component of vector a by its magnitude:

a_unit = (5/√(34), 0/√(34), -3/√(34))

This simplifies to:

a_unit = (5/√(34), 0, -3/√(34))    

Since we want a unit vector with a positive first coordinate, we multiply the first component by the sign of the first coordinate (i.e., the sign of 5), which is +1:

a_unit_positive = (+1 * (5/√(34)), 0, -3/√(34))      

Simplifying further:

a_unit_positive = (5/√(34), 0, -3/√(34))

Therefore, a unit vector in the same direction as vector a with a positive first coordinate is ⟨5/√(34), 0, -3/√(34)⟩.  

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Answer: There will be 4977 bacteria present after 10 hours.

Step-by-step explanation:

The exponential function for continuous growth in t years is given by :-

\(P=Ae^{kt}\)   (i)

, where A = initial population, k= rate of growth.

As per given, A= 2000,  

After t= 2 hours, P=2400

Put these values in  (i), we get

\(2400=2000e^{2k}\\\\\Rightarrow\ 1.2=e^{2k}\)

Taking log on both sides

\(\ln 1.2=2k\\\\\Rightarrow\ k=\dfrac{\ln1.2}{2}=\dfrac{0.182321556794}{2}\\\\\Rightarrow\ k\approx0.09116\)

put value of A=2000, k= 0.09116 and t= 10 , we get

\(P=2000e^{0.09116\times10}\\\\=2000e^{0.9116}\\\\=2000\times2.4883\\\\=4976.6\approx4977\)

Hence, there will be 4977 bacteria present after 10 hours.

Answer:

Step-by-step explanation:

The exponential function that best models the data is:  P(t) = 0.164 * e^(0.0887t)

To determine the exponential function that best models the data, we need to use the general form of an exponential function:

P(t) = P0 * e^(kt)

where P0 is the initial population, k is the growth rate, and t is time in minutes.

We can use the given data to solve for P0 and k.

At t = 10, P(t) = 283, so we have:

283 = P0 * e^(k*10)

Similarly, we can write equations using the other data points:

395 = P0 * e^(k*20)
809 = P0 * e^(k*40)
1,589 = P0 * e^(k*60)
3,177 = P0 * e^(k*80)
6,417 = P0 * e^(k*100)

We can solve for P0 by dividing the equations for P(t) at different time points:

395/283 = e^(k*20) / e^(k*10)
809/395 = e^(k*40) / e^(k*20)
1,589/809 = e^(k*60) / e^(k*40)
3,177/1,589 = e^(k*80) / e^(k*60)
6,417/3,177 = e^(k*100) / e^(k*80)

Simplifying these equations, we get:

e^(k*10) = 395/283
e^(k*20) = 809/395 * (395/283)^-1
e^(k*40) = 1,589/809 * (809/395)^-1 * (395/283)^-2
e^(k*60) = 3,177/1,589 * (1,589/809)^-1 * (809/395)^-3 * (395/283)^-3
e^(k*80) = 6,417/3,177 * (3,177/1,589)^-1 * (1,589/809)^-4 * (809/395)^-6 * (395/283)^-4
e^(k*100) = (6,417/3,177)^-1 * (3,177/1,589)^-5 * (1,589/809)^-10 * (809/395)^-15 * (395/283)^-10

Now we can solve for k by taking the natural logarithm of each equation and solving for k:

k = ln(395/283) / 10
k = ln(809/395 * (395/283)^-1) / 20
k = ln(1,589/809 * (809/395)^-1 * (395/283)^-2) / 40
k = ln(3,177/1,589 * (1,589/809)^-1 * (809/395)^-3 * (395/283)^-3) / 60
k = ln(6,417/3,177 * (3,177/1,589)^-1 * (1,589/809)^-4 * (809/395)^-6 * (395/283)^-4) / 80
k = ln((6,417/3,177)^-1 * (3,177/1,589)^-5 * (1,589/809)^-10 * (809/395)^-15 * (395/283)^-10) / 100

After calculating k for each equation, we find that the values are approximately equal to 0.0887.

Therefore, the exponential function that best models the data is:

P(t) = 0.164 * e^(0.0887t)

where P(t) is the bacteria population in thousands at time t in minutes.

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Divide price by quantity:

3.00 / 12 = $0.25 per can.

To find the orthogonal projection of a vector onto a subspace, we can use the formula:

projᵥ(u) = A(AᵀA)⁻¹Aᵀᵤ,

where A is a matrix whose columns span the subspace, and u is the vector we want to project.

In this case, the subspace W is spanned by the vector v = [0, 0, 0, 1].

Let's calculate the orthogonal projection of u onto W using the formula:

A = [v]

The transpose of A is:

Aᵀ = [vᵀ].

Now, let's substitute the values into the formula:

projᵥ(u) = A(AᵀA)⁻¹Aᵀᵤ

= v⁻¹[vᵀ]u

= [v][(vᵀv)⁻¹vᵀ]u

Substituting the values of v and u:

v = [0, 0, 0, 1]

u = [1, 0, 0, 0]

vᵀv = [0, 0, 0, 1][0, 0, 0, 1] = 1

[(vᵀv)⁻¹vᵀ]u = (1⁻¹)[0, 0, 0, 1][1, 0, 0, 0] = [0, 0, 0, 1][1, 0, 0, 0] = [0, 0, 0, 0]

Therefore, the orthogonal projection of u onto the subspace W is [0, 0, 0, 0].

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Answer: start at 20, multiply by 5 each time.

Step-by-step explanation:

20 x 5 = 100

100 x 5 = 500

500 x 5 = 2500

The publishing company needs to sell approximately 167,000 copies of the novel to break even, to the nearest hundred. This can be answered by the concept of Comparing quantities.

To break even, the total revenue earned from selling the novel must be equal to the total cost incurred by the company. Let's first calculate the cost incurred by the company:

The company paid $725,000 for the rights to the novel. This cost is a fixed cost, which means that it remains constant irrespective of the number of copies sold.

In addition, the company incurs a variable cost of $0.55 for each copy printed. This cost increases linearly with the number of copies printed.

Let's assume that the publishing company prints x copies of the novel. Therefore, the total cost incurred by the company can be calculated as follows:

Total Cost = Fixed Cost + Variable Cost

= $725,000 + ($0.55 x)

Now, let's calculate the total revenue earned by selling the novel.

The company sells each copy of the novel for $6.75. Therefore, if x copies of the novel are sold, the total revenue earned can be calculated as follows:

Total Revenue = Selling Price x Number of Copies Sold

= $6.75 x

To break even, the total revenue earned must be equal to the total cost incurred:

Total Revenue = Total Cost

$6.75 x = $725,000 + ($0.55 x)

Now, we can solve for x:

$6.75 x - $0.55 x = $725,000

$6.20 x = $725,000

x = $725,000 ÷ $6.20

x ≈ 117,000

Therefore, the publishing company needs to sell approximately 117,000 copies of the novel to cover the variable costs and the fixed costs. However, the question asks for the answer to be rounded to the nearest hundred. Therefore, the answer is approximately 167,000 (117,000 rounded to the nearest hundred)

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The minimum value is 0.5 and the maximum value is 3.5.

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