What is the quadratic regression equation that fits these data?
OA. 9-0.3x+30.3
X
1
2
3
4
5
OB.-29.8(0.99)
OC.9 -0.3x² + 30.3x -0.11
OD.9=2.4x2-14.4x+46.8
y
35
27
24
28
33

The two x-values where the sculpture at sea-level are x = 2.581 and x = -0.581

From the question, we have the following parameters that can be used in our computation:

y = 2x^2 - 4x - 3

When the sculpture at sea-level, the value of y is 0

So, we have

2x^2 - 4x - 3 = 0

When solved graphically, we have

x = 2.581 and x = -0.581

Hence, the x values are x = 2.581 and x = -0.581

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Answer:

  (a)  x = -4y +19

Step-by-step explanation:

You want to know a good first step for solving the system of equations in an efficient manner.

One way to solve these equations is by substitution. To do that, we typically write an expression for one of the variables in terms of the other. It is efficient to choose a variable that already has a coefficient of 1.

Here, a useful first step is to solve the second equation for x:

  x = -4y +19

__

Additional comment

Then the solution proceeds with substitution for x:

  3(-4y +19) +2y = 17

  -10y +57 = 17

  -10y = -40

  y = 4

  x = -4(4) +19 = 3

The solution is (x, y) = (3, 4).

Another reasonable first step is to subtract the second equation from twice the first:

  2(3x +2y) -(x +4y) = 2(17) -(19)

  5x = 15

  x = 3

  3 +4y = 19 . . . . . . substitute for x in the second equation

  y = (19 -3)/4 = 4

The "addition" or "elimination" method shown second is also shown using 5 steps, but these are generally more complicated steps than the ones shown for the "substitution" solution. It appears the substitution solution probably is "the most efficient" in this case.

The value of cost of the perimeter of the lid is, $32.625

Given that;

Dylan is putting a gold ribbon around the lid of a rectangular box. The lid ha a width of 6(1/4) inches and a length of 4(5/8) inches.

Hence, The value of perimeter of the lid is,

⇒ P = 2 (6 1/4 + 4 5/8)

⇒ P = 2 (25/4 + 37/8)

⇒ P = 2 (50/8 + 37/8)

⇒ P = 2 (87/8)

⇒ P =  87/4 inches

Since, The ribbon costs $1.50 per Inch.

Hence, Total cost for lid is,

⇒ 1.50 × 87/4

⇒ $32.625

Thus, The value of cost of the perimeter of the lid is, $32.625

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Answer:

2x2+x+5

Step-by-step explanation:

Applying the formula for the area of triangle using sine, we have:

sin A = 1/3 (A ≈ 19.5°).

Given that a triangle has the following parameters:

Area of triangle ABC = 21 square units

Side b = 14 units

Side c = 9 units

Thus, applying the area of a triangle using the sine rule, we have the following formula:

Area = 1/2 * b * c * sin A

Plug in the values:

21 = 1/2 * 14 * 9 * sin A

2 * 21 = 126 * sin A

42 = 126 * sin A

42/126 = sin A

sin A = 1/3

A = sin^(-1)(1/3)

A ≈ 19.5°

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The missing term of the factorization equation is A = ( -15x - 1 ) ( x + 2 )

Given data ,

Let the equation be represented as A

Now , the value of A is

A = -15x² - 31x - 2

On simplifying , we get

The expanded form of the expression ( -15x - 1 ) ( x + 2 ) can be calculated using the distributive property of multiplication over addition

So , on factorizing , we get

A = ( -15x - 1 ) ( x + 2 )

Hence , the factorized equation is A = ( -15x - 1 ) ( x + 2 )

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The complete question is attached below :

Fill in the missing terms to complete the factorization. 15x² + x - 2 = (? -1) (? + 2)

a- 3x, 5x

b- x, 15x

c- 5x, 3x

d- 15x, x

Answer:

Step-by-step explanation:

[tex]\sf -24=8(y-8)-4y[/tex]

[tex]\sf 8\left(y-8\right)-4y=-24[/tex]

Expand:-

[tex]\sf 4y-64=-24[/tex]

Add 64 to both sides:-

Divide both sides by 4:-

________________________

If 5 is subtracted from the square of a number, the positive solution is √5.

In this exercise, you are required to determine or solve for an unknown number as follows. First of all, we would assign a variable to the unknown number and then translate the word problem into an algebraic expression as follows;

Assuming the unknown number is represented by the variable x.

Therefore, the required algebraic expression is given by;

x² - 5

In order to determine the positive solution, we would have to equate the algebraic expression to zero as follows;

x² - 5 = 0

x² = 5

x = ±√5

x = √5 (positive solution)

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Answer:

Step 3: Divide both sides of the equation in Step 2 by a to get x² + (b/a)x = -c/a.

Answer:

By using the formula down below you can find the area of a trapezoid

A = [tex]\frac{a+b}{2}[/tex]h

↑ Area

A = Base

B = Base

H = Height

Example.

A = 12

B = 4

H = 2

First “ A “ + “ B “ =

12 + 4 = 16

16 / 2 = 8

8 x “ h “

8 x 2 = 16

Answer is 16

Thus the answer is, above

So if you look that up then it will show you how to find the area of a trapizoid

The requried, there is only 1 possible lineup of 6 songs from a list of 6 songs.

To determine how many different lineups are possible, we can use the formula for combinations, which is:

nCk = n! / (k!(n-k)!)

where n is the total number of items, k is the number of items being selected, and the exclamation mark denotes the factorial function.

In this case, we have n = 6 (the total number of songs) and k = 6 (the number of songs to be selected). So we can plug these values into the formula:

6C6 = 6! / (6!(6-6)!) = 6! / (6!0!) = 1

Therefore, there is only 1 possible lineup of 6 songs from a list of 6 songs.

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Answer:

144ft^3

Step-by-step explanation:

To start, we have your formula: [tex]V=\frac{1}{2} (bh) (l)[/tex]
b = base length of the triangle.
h = height of the triangle.
l = length of the prism

Fill in for each of those values:
[tex]V = \frac{1}{2} (6x6)(8)[/tex]

[tex]V=\frac{1}{2} (36)(8)[/tex]

[tex]V=(18)(8)[/tex]

[tex]V=144[/tex]

Your answer, because it is a 3D shape, should be cubed, so:
[tex]V=144ft^{3}[/tex]

A line on the graph which could represent this scenario is: C. g(x), the third line is labeled g(x) and passes through (negative 2, negative 7), (0, negative 3), (1, negative 1) and (2, 1).

In Mathematics and Geometry, the slope-intercept form of the equation of a straight line is given by this mathematical expression;

y = mx + c

Where:

Based on the information provided about Janelle when she woke up, the temperature can be modeled by this equation:

y = mx + c

y = 2x + (-3)

y = 2x - 3

Therefore, the table of values can be generated as follows;

x      y

0     -3

1       -1

2       1

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By using the head to tail, the addition of the vectors [tex]\vec a + \vec b[/tex] is (3, -5).

In Geometry, a vector is typically composed of two end points. First, is the starting point which is commonly known as a "tail" and the second (ending) point that is commonly known as a "head."

Additionally, the head to tail method of adding two vectors requires drawing the first vector ([tex]\vec a[/tex]) on a graph and then placing the tail of the second vector ([tex]\vec b[/tex]) at the head of the first vector. Finally, the resultant vector would be drawn from the tail of the first vector ([tex]\vec a[/tex]) to the head of the second vector ([tex]\vec b[/tex]).

Next, we would add the two (2) vectors algebraically as follows;

[tex]\vec a + \vec b[/tex] = (4, -3) + (-1, -2)

[tex]\vec a + \vec b[/tex] = [(4 + (-1)), (-3 + (-2))]

[tex]\vec a + \vec b[/tex] = [(4 - 1), (-3 - 2)]

[tex]\vec a + \vec b[/tex] = (3, -5).

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Answer:B

Step-by-step explanation:i did the quiz

Savings Account B will have more money after 9 years because it is modeled by the exponential equation, and the investment grows exponentially with time

We have,

To determine which savings account has more money after 9 years, we can evaluate the amount of money in each account using the given equations.

For Savings Account A, the equation is:

A = 21.09t + 1125

Substituting t = 9 (since we're interested in the amount after 9 years), we get:

A = 21.09(9) + 1125 = 1300.81

So, after 9 years, Savings Account A will have $1300.81.

For Savings Account B, the equation is:

A = 1125(1 + 0.01875/2)^(2t)

Substituting t = 9, we get:

A = 1125(1 + 0.01875/2)^(2(9)) = 1318.98

So, after 9 years, Savings Account B will have $1318.98.

Therefore,

Savings Account B will have more money after 9 years because it is modeled by the exponential equation, and the investment grows exponentially with time

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The value of the side length h is 19.1 cm.

The figure in the image is a right triangle:

Angle θ = 47 degrees

Opposite to angle θ = 14cm

Hypotenuse = h

To solve for side length h, we use trigonometric ratio.

Note that: sine = opposite / hypotenuse

Plug in the values and solve for h.

sin( 47° ) = 14 / h

h = 14 / sin( 47° )

h = 19.1 cm

Therefore, the value of h is 19.1 cm.

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To order enough food for a graduation party with drop-in guests, they should order:

112 + 1.4x pieces of fried chicken

14.64 + 0.183x pounds of meat

41 + 0.5125x pounds of lasagna

If we consider each "drop-in" guest as half a guest, then the total number of guests becomes:

40 + 0.5x, where x is the number of "drop-in" guests.

To determine how much of each food item to order, we can use the recommended amounts as a guide and scale them up based on the total number of guests:

So, to order enough food for a graduation party with drop-in guests, they should order:

112 + 1.4x pieces of fried chicken

14.64 + 0.183x pounds of meat

41 + 0.5125x pounds of lasagna

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With a radius of 20 feet and 10 rounds traversed, the total distance equates to approximately 1256.6 feet.

When calculating the circumference (C) of a circle, the formula 2 * π * radius (R) is employed.

Taking into consideration R = 20 feet, we shall arrive at the following figure:

C = 2 * π * 20

C ≈ 2 * 3.14159265359 * 20

C ≈ 125.66 feet

If we use this calculation to determine the total distance covered after running 10 laps around a track, our equation morphs into Circumference (C) multiplied by the Number of laps (L).

When L equals 10, it follows that:

Total distance ≈ 125.66 feet * 10

Total distance ≈ 1256.6 feet

Therefore, with a radius of 20 feet and 10 rounds traversed, the total distance equates to approximately 1256.6 feet.

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What is the total distance covered after running 10 laps around a circular track with a radius of 20 feet?

Answer:

Step-by-step explanation:

4992223553535

your in school ask a teacher

Solving the system of equations, the number of children, parents, and Grandparents who were in attendance are 190, 140 and 70 respectively.

Let C, P and G denotes the number of children, parents and the grandparents in the function.

We get the system of equations,

C + P + G = 400 [equation 1]

P = 2G  ⇒ G = P/2 [equation 2]

C = P + 50 [equation 3]

Substituting 2 and 3 in 1,

(P + 50) + P + (P/2) = 400

2P + P/2 = 350

5/2 P = 350

P = 140

C = P + 50 = 140 + 50 = 190

G = P/2 = 140/2 = 70

Hence the number of parents = 140, grandparents = 70 and children = 190.

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The magnitude of the vector 4v is 4 times the magnitude of v, which is equal to 4 √29.

Given the vector v = 5i - 2j, we can find the magnitude or norm of the vector ||v|| using the formula:

||v|| = √(v · v)

where · denotes the dot product of the vector with itself.

Substituting the values of the vector v, we have:

||v|| = √((5i - 2j) · (5i - 2j))

Expanding the dot product using the distributive law, we get:

||v|| = √(25i² - 20ij + 4j²)

Since i² = j² = 1 and ij = ji = 0, we can simplify this expression to:

||v|| = √(25 + 4) = √29

Thus, the magnitude of the vector v is √29.

Now, we need to find the magnitude of the vector 4v. Using the property that ||kv|| = |k| ||v|| for any scalar k and vector v, we have:

||4v|| = |4| ||v|| = 4 √29

In summary, the magnitude of the vector v is √29, and the magnitude of the vector 4v is 4 √29.

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Answer:

a₈₁ = - 482

Step-by-step explanation:

the nth term of an arithmetic sequence is

[tex]a_{n}[/tex] = a₁ + (n - 1)d

where a₁ is the first term and d the common difference

here a₁ = - 2 and d = a₂ - a₁ = - 8 - (- 2) = - 8 + 2 = - 6 , then

a₈₁ = - 2 + (80 × - 6) = - 2 + (- 480) = - 2 - 480 = - 482

8.) The inequality that describes the possible number of calories X, you can eat during the rest of the day would be < 1200. That is option A.

9.) The value of X would be = 3.

For question 8.)

The quantity of calories for each day < 2200. That is;

1 day < 2200

The calories consumed for breakfast = 350

The calories consumed for lunch = 650

The total calories consumed = 350+650 = 1000 calories.

The amount of calories needed to be consumed the more = 2200-1000 = 1200

Therefore the quantity of calories needed more < 1200 calories.

For question 9.)

t(X) = 3x - 5

where;

t(X) = 4

That is;

4 = 3x - 5

3x=4+5

3x = 9

X = 9/3 = 3

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The population mean is calculated as the sum of all observations in the population, divided by the number of objects in the population.

The mean of a data-set is given by the sum of all observations in the data-set divided by the number of observations, which is also called the cardinality of the data-set.

Hence the population mean is calculated as the sum of all observations in the population, divided by the number of objects in the population.

The problem is incomplete, hence the procedure to obtain the mean of a data-set, in this case the population, is presented.

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Answer: 550.320 to the nearest whole number is 550.

Step-by-step explanation: If the number if five or more, it rounds up, but if it is four or less, it stays the same. Therefore, because 3 is less than four, the answer is 550. Hope this helps! :)

Answer:

550

Step-by-step explanation:

If we look at the number we see .320, as we can see the number in the front is 3 and behind that is 2, when we are rounding the key thing to always remember is if its greater than 5 we round up if not go down so sense 3 doesn't go over 5 we don't change the number in front of it 0 and the same thing with 2 but we wouldn't change the 3 instead. so sense .320 doesn't qualify as a whole number we do not need it so we get the answer,

550.

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HAVE A NICE DAY :)

The rate of car is 35 mph.

Given that engineer traveled 140 mi by car and then an additional 750 mi by plane. The rate of the plane was three times the rate of the car.

Let c be the rate of wind.

215 + c = rate of plane with wind

215 - c = rate of plane against wind

Therefore, the travel time =distance/rate

⇒ 750/(215+c) = 540/(215-c)

Cross multiplying we get,

540(215+c) = 750(215-c)

116100+540c = 161250-750c

1290c = 45150

c=35

Hence, the rate of car is 35 mph.

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a) For Super Home, the superior (or dominant) tactic is to magnify the size of the store and parking lot. This is, regardless of what Great Home does, Super Home's payoff is amplified when it expands its size ($1m vs $0.4m if Great Home amplifies; $3.2m vs $2m if Great Home passes).

Similarly, for Great Home, the logical (or dominant) strategy is also to expand the size of the store and parking lot. This is because, although unrelated to Super Home's decision, Great Home's payoff is augmented when it enlarges its size ($1.5m vs $0.6m if Super Home magnifies; $3.4m vs $2.5m if Super Home disallows).

b) If both stores implement their authoritative plan, Great Home will witness an annual profit growth of $1.5 million, and Super Home will observe an annual profit growth of $1 million.

A Nash Equilibrium comprehends a state wherein each player chooses their finest ploy given the stratagems selected by the other participant(s), and no player can modify their consequence through exclusively adapting their strategy. In this case, the Nash Equilibrium exists in (Increase, Increase), which spans over the payoffs ($1.5m, $1m).

c) The conjunctive approach both stores should commit to would be for Great Home to amplify the size of its store and parking lot, and Super Home to renounce increasing its size.

Under this harmonized approval, the annual profit growth for Great Home will come out at $3.4 million, and for Super Home, it will arrive at $0.4 million. This system gives rise to a higher collective gain compared to the Nash Equilibrium.

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If the number of bacteria triples every 4 hours, then after 1 day (24 hours), the number of bacteria will triple 6 times.

Tripling a number 6 times is the same as multiplying it by 3 raised to the power of 6, or 3^6.

So, if there are 25 bacteria to start, the number of bacteria after 1 day will be:

25 x 3^6 = 25 x 729 = 18,225 bacteria.

Answer:

Step-by-step explanation:

It is not possible to accurately determine the number of bacteria in the glass after 4 hours without additional information such as the rate of bacterial growth, the environmental conditions, and whether any bacteria were removed or added during that time.