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The quadratic inequality is given as follows:

y ≤ 2/3(x + 9)² - 27.

The equation of a quadratic function, of vertex (h,k), is given by the rule presented as follows:

y = a(x - h)² + k

a is the leading coefficient of the equation.

In the context of this problem, the vertex is at point (-9, -27), hence the parameters are as follows:

h = -9, k = -27.

Hence the rule is:

y = a(x + 9)² - 27.

When x = 1, y = 39.67, hence the leading coefficient is calculated as follows:

39.67  = a(1 + 9)² - 27

100a = 66.67

a = 2/3

Hence the inequality is:

y ≤ 2/3(x + 9)² - 27.

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1) The volume of ice cream that completely fills one cone to the top is 31.4159 cubic inches

2) The surface area of the cone that would be needed for a wrapper is 31.4 square inches.

To find the volume of the waffle cone, we can use the formula for the volume of a cone:

V = (1/3) × pi × r^2 × h

where V is the volume, pi is approximately 3.14, r is the radius of the cone (which is half of the diameter), and h is the height of the cone.

In this case, the diameter of the waffle cone is 5 inches, so the radius is 2.5 inches. The height of the cone is 6 inches. Substituting these values into the formula, we get:

V = (1/3) × 3.14 × (2.5)^2 × 6

V = 31.4159 cubic inches (unrounded)

Therefore, the volume of ice cream that completely fills one cone to the top is approximately 31.4159 cubic inches.

Part 2

To find the surface area of the cone for a wrapper, we can use the formula for the lateral surface area of a cone:

A = pi × r × s

where A is the lateral surface area, r is the radius of the cone, and s is the slant height of the cone.

In this case, we are given that the slant height is 4 inches, and we already calculated that the radius is 2.5 inches. Substituting these values into the formula, we get

A = 3.14 × 2.5 × 4

A = 31.4 square inches

Therefore, the surface area of the cone needed for a wrapper is approximately 31.4 square inches.

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The type of data for the water consumption (liters) by a randomly chosen player on the Celtics roster during a home game would be quantitative continuous data.

This is because the variable, water consumption, is a numerical measurement that can take on any value within a specific range (e.g., 0.5 liters, 1.2 liters, 2.7 liters, etc.), and it can be measured with a high level of precision. The data is continuous because there are no restrictions on the possible values, and it can take on any value within a given range.

what is range?

In statistics, the range refers to the difference between the maximum and minimum values in a dataset. It provides a measure of the spread or variability of the data.

To calculate the range, you simply subtract the minimum value from the maximum value:

Range = Maximum value - Minimum value

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Answer:

x = 2, 4

Step-by-step explanation:

Step 1: Write out quadratic

x² - 6x + 10 = 2

Step 2: Subtract 2 on both sides

x² - 6x + 8 = 0

Step 3: Factor

(x - 4)(x - 2) = 0

Step 4: Find roots

x - 4 = 0

x = 4

x - 2 = 0

x = 2

Answer:

X = 5, -2

Absolute value function

The domain and range of H is  {4, 2 ,-9, 8} and {4, 0, 2, -5}.

Given:

H = {(4,4), (2, 0), (-9, 2), (8,-5)}

Domain = set of x values or inputs.

x values = {4, 2, -9, 8}

Domain = {4, 2 ,-9, 8}

Domain = -9 ≤ x ≤ 4

Range = set of y values or outputs.

y values = {4, 0, 2, -5}

Range = {4, 0, 2, -5}

Range = -5 ≤ x ≤ 4

Therefore he domain and range of H is {4, 2 ,-9, 8} and {4, 0, 2, -5}.

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Answer:

\(x + 6 = - x - 16 + 6x \\ x \: terms \: togather \\ x + x - 6x = - 16 - 6 \\ - 4x = - 22 \\ x = \frac{ - 22}{ - 4} \\ x = 5.5 \\ thank \: you\)

Answer:

\(x + 6 = - x - 16 + 6x \\ x + x - 6x = - 16 - 6 \\ - 4x = - 22 \\ 4x = 22 \\ x = 22 \div 4 = 11 \div 2 = 5.5\)

To determine the sum of money Jeff should invest on January 21, 2020, in order to reach $80000 on August 8, 2020, at an annual interest rate of 5%, we need to calculate the present value of the future amount using the time value of money concepts.

We can use the formula for the present value of a future amount to calculate the initial investment required. The formula is:

Present Value = Future Value / (1 + interest rate)^time

In this case, the future value is $80000, the interest rate is 5% per year, and the time period is from January 21, 2020, to August 8, 2020. The time period is approximately 6.5 months or 0.542 years.

Plugging these values into the formula, we have:

Present Value = $80000 / (1 + 0.05)^0.542

Evaluating the expression, we find that the present value is approximately $75609. Therefore, Jeff should invest approximately $75609 on January 21, 2020, to amount to $80000 on August 8, 2020, at a 5% annual interest rate.

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Answer:

C

Step-by-step explanation:

f(x).g(x) is

(x+12).(x-5)=x^2-5x+12x-60(add like terms)

=x^2+7x-60, the answer is C

Answer:

£ 90 because

Step-by-step explanation:

4x+x= £ 150

5x =£150

x=£150/5

x=£30

ivan share = 4x=4x£30

=£120

Tanya share =x=£30

difference ,=£120 - £30

=£90

It can be stated that there exist 63,360 ternary sequences of digits selected from {0, 1, 2} with a length of twelve, which contain precisely three 1s and two 0s.

The problem is asking us to find out how many ternary sequences of digits are there that are chosen from {0, 1, 2} of length twelve, and have exactly three 1's and two 0's.

Therefore, there will be a total of 7 digits (12 - 3 - 2 = 7) that could be 1 or 2. So, let's solve it in steps.

Step 1: The number of ways we can choose 3 positions out of 12 for 1s is C (12,3).

Step 2: The number of ways we can choose 2 positions out of 9 (because there are already 3 1s and 2 0s) for 0s is C (9,2).

Step 3: We have three digits left that can be either 1 or 2. So, there will be 2 options for each of these digits, and the total number of options will be

2 × 2 × 2 = 8.

Step 4: So, the total number of sequences will be obtained by multiplying the results of Steps 1, 2, and 3. i.e.

C (12,3) × C (9,2) × 8

⇒ ¹²C₃ × ⁹C₂ × 8

⇒ 220 × 36 × 8 = 63360.

Therefore, there are 63,360 ternary sequences of digits chosen from {0, 1, 2} of length twelve that have exactly three 1s and two 0s.

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Answer:

60% choose the Museum.

Step-by-step explanation:

Add the students who choose the museum and the students who choose the factory to get 95. You would then need to divide the amount of students who choose the museum by the total amount of students. Your answer would be 0.6, or 60%

60% of the students sixth-graders at Jen's school picked the museum.

A percentage is a value per hundredth. Percentages can be converted into decimals and fractions by dividing the percentage value by a hundred.

Given, 57 sixth graders picked the museum and 38 sixth graders picked the factory.

So, the total no. of students is (57 + 38) = 95.

∴ The percentage of the sixth-graders who picked the museum is,

=  (57/95)×100%.

= 60%.

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ANSWER:

+ 4 7/8

STEP-BY-STEP EXPLANATION:

Assuming that we start in week 0, with a total of 0 points, we must operate the changes in each week and the value opposite to that result must be the change necessary to return to the original value.

Just like that:

Which means that to return to the initial value, 4 7/8 points must be added

From the given information provided, the means of x₁, x₂,  and x₃ are 158.28, 41.3, and 43.75 respectively.

a. Handle the missing values using omission strategy:

The omission strategy involves removing any observation with missing values.

The resulting table after the omission strategy is as follows:

Obs x₁ x₂ x₃

1 248 3.5 3.8

2 55 150 74

3 196 4.5 32

4 134 6.2 63

We can see that one observation with missing values was removed, which was observation 5.

b. Handle the missing values using simple mean imputation strategy:

The simple mean imputation strategy involves replacing the missing values with the mean of the non-missing values.

The means of x₁, x₂, and x₃ are calculated as follows:

mean of x₁ = (248 + 55 + 196 + 134) / 4 = 158.25

mean of x₂ = (3.5 + 150 + 4.5 + 6.2) / 4 = 41.3

mean of x₃ = (3.8 + 74 + 32 + 63) / 4 = 43.75

The resulting table after the simple mean imputation strategy is as follows:

Obs x₁ x₂ x₃

1 248 3.5 3.8

2 55 150 74

3 196 4.5 32

4 134 6.2 63

5 158.25 41.3 43.75

We can see that all missing values were replaced, which were x₁ in observation 5 and x₃ in observation 3.

Question - The following table contains 3 variables and 5 observations including some missing values x₁ x₂ x₃ 248 3.5 3.8 55 150 74 196 4.5 32 134 6.2 63 a. Handle missing values using omission strategy. b. Handle missing values using simple mean imputation strategy. How many missing values are replaced? What are means of x₁, x₂, and x₃?

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Answer:

1

Step-by-step explanation:

y = 5(2) -9

y= 10 -9

y = 1

(a)The probability that Angus had a latte at Tarbucks is 0.403. (b)The two events are not independent of each other. (c)The probability that he drank at Costly Coffee is 0.260. (d) The probability is 0.767.

a) To calculate the probability that Angus had a latte at Tarbucks, we multiply the probability of going to Tarbucks (0.65) by the probability of having a latte (0.62) given that he went to Tarbucks: 0.65 * 0.62 = 0.403.

b) Two events are considered independent if the occurrence of one event does not affect the probability of the other event. In this case, the events of Angus going to Tarbucks and having a latte are not independent because the probability of having a latte (0.62) is influenced by whether Angus goes to Tarbucks or Costly Coffee.

c) To calculate the probability that Angus drank at Costly Coffee given that he had a latte, we need to consider the complement of the event of having a latte at Tarbucks. The probability of having a latte at Costly Coffee is 1 - 0.403 = 0.597. Given that Angus had a latte, the probability of him drinking at Costly Coffee is the probability of having a latte at Costly Coffee divided by the total probability of having a latte: 0.597 / (0.403 + 0.597) = 0.260.

d) To find the probability that Angus went to Tarbucks or had a latte or both, we can add the individual probabilities of each event: the probability of going to Tarbucks (0.65) plus the probability of having a latte at Tarbucks (0.403) minus the joint probability of going to Tarbucks and having a latte (0.403): 0.65 + 0.403 - 0.403 = 0.65.

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Angus goes to one of two coffee shops in his home town. He goes to Tarbucks 65% of the time and otherwise goes to Costly Coffee. Eithe way, he buys a latte 62%of the time, regardless of which place he chose.

a) You are told that Angus went into town for a coffee today. What is the probability (to 3 decimal places) that he had a latte at Tarbucks?

b) Are the two events that gave the joint probability in (a) independent of each other?

c) Given that Angus had a latte in town, what is the probability (to 3 decimal places) that he drank at Costly Coffee?

d) What is the probability (to 3 decimal places) that Angus went to Tarbucks or had a latte or both?

Airy point can be proven by using the calculus of variations to minimize the functional that represents the sum of the distances from vertices of ellipse. The critical points of functional give us coordinates of Airy point.

The Airy point is a point on the ellipse that minimizes the sum of the distances from the three vertices of the ellipse. To prove the existence of the Airy point, we can use the calculus of variations.

First, we need to define the functional that we want to minimize. Let P be the Airy point and let A, B, and C be the vertices of the ellipse. Then the functional we want to minimize is:

F(P) = PA + PB + PC

We can use the calculus of variations to find the point P that minimizes F(P). We do this by finding the critical points of F(P), which are points where the derivative of F(P) with respect to P is zero.

To find the critical points, we can use Lagrange multipliers. We define a new function G(P, λ) = F(P) + λG(P), where G(P) is the equation of the ellipse. We then find the critical points of G(P, λ) by taking the partial derivatives with respect to P and λ and setting them to zero.

Solving these equations gives us the coordinates of the Airy point. The existence of the Airy point is guaranteed by the fact that the ellipse is a compact and convex set, and the functional F(P) is continuous and coercive. This ensures that the minimum of F(P) exists and is attained at a point P on the ellipse.

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Answer:

(-2, 1). (5,5) is 11.55

Answer:

1/2 x 1/10 = 2/100

1/2 + 1/10 =  6/10

1/2 - 1/10 =  4/10

1/2 divided by 1/10 = 5

Step-by-step explanation:

Answer:

y=-2x+-3

Step-by-step explanation:

y=mx+b

m=slope

b=y-intercept

-2 is our slope

-3 is our y-intercept

Answer:

B a b i e s

Step-by-step explanation:

It makes it goody

Answer:

Mineral Oil, Fragrance, Aloe Barbadensis Leaf Extract*, Tocopheryl Acetate

The distance between the two artifacts is approximately 4.47 units.

The problem statement provides two coordinates (1, 4) and (5, 2).

Here (1,4) and (5,2) are known as position (x1,y1) and position (x2,y2), respectively.

Let's find the distance between the two artifacts.

An archaeologist at a dig sets up a coordinate system using string.

wo similar artifacts are found: one at position (1, 4) and the other at (5, 2).

How far apart were the two artifacts? Round to the nearest whole number if necessary.

Distance between two points is given by,`\(d = sqrt((x2-x1)^2+(y2-y1)^2)`d\)(rounded to two decimal places)

\(= sqrt((5 - 1)\² + (2 - 4)\²)d \\\)

\(= sqrt((4)\² + (-2)\²)d\)

\(= sqrt(16 + 4)d\)

\(= sqrt(20)d = 4.47\)

Therefore, the distance between the two artifacts is 4.

The distance between the two artifacts, located at coordinates (1, 4) and (5, 2), can be calculated using the distance formula:

\(d = sqrt((x2 - x1)^2 + (y2 - y1)^2)\)

Plugging in the given values:

\(d = sqrt((5 - 1)^2 + (2 - 4)^2)d\)

\(= sqrt(4^2 + (-2)^2)d\)

\(= sqrt(16 + 4)d\)

\(= sqrt(20)\)

d ≈ 4.47 (rounded to two decimal places)

Therefore, the distance between the two artifacts is approximately 4.47 units.

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Answer:

C

Step-by-step explanation:

If you reduce 21/28 you get 3/4 and if you reduce 12/16 you get 3/4 which makes them both proportional.

A permutation is an arrangement of outcomes in which the order does matter.

A combination is an arrangement of outcomes in which the order does not matter.

In this case, for example, the password HI is different from the password IH. In both cases, the outcomes (letters H and I) are the same, but the order of them changes the arrangement (the password). Therefore, the problem involves a permutation because the order of letters selected does matter

Answer:

Step-by-step explanation:

-10.9p + 3.9

-10.9p turns positive.

The (p) is isolated.

10.9 - 3.9= 9.18 = -9.18

Answer

-9.18

Answer: The last one, I would suppose.

a. the equilibrium price is $52 per bushel and the equilibrium quantity is 20 bushels.

b. the new equilibrium price is $42 per bushel and the new equilibrium quantity is 15 bushels.

Equilibrium price and quantity:

The equilibrium is the point where the supply and demand curve intersect each other. The point where the demand and supply curve intersect each other, P and Q determine the equilibrium price and quantity respectively.

The given equations for demand and supply of the bananas in Binghamton are:

P = 92 - 2QP = 12 + 2QThe equilibrium price and quantity can be obtained by equating the demand and supply equations,92 - 2Q = 12 + 2Q⇒ Q = 20P = 92 - 2(20)⇒ P = 52

Therefore, the equilibrium price is $52 per bushel and the equilibrium quantity is 20 bushels.

The given equations for demand and supply of the bananas in Binghamton are:

P = 92 - 2QP = 12 + 2QThe demand for bananas increases due to the National Institutes of Health’s study, which shows that bananas reduce the risk of cancer.

The new demand equation is given by:

P = 132 - 2QAt the original equilibrium price ($52), the quantity demanded exceeds the quantity supplied.

Therefore, there is a shortage.

The shortage can be calculated as follows:

Quantity demanded at equilibrium price (P = $52) = Quantity supplied at equilibrium price (P = $52)Qd = 92 - 2(20) = 52 bushels Qs = 12 + 2(20) = 52 bushels Shortage = Qd - Qs= 52 - 52 = 0

Therefore, the shortage is 0 bushels.

c.  Show graphically.

The new demand equation is given by:

P = 132 - 2QTo find the new equilibrium price and quantity, we need to equate the new demand equation with the original supply equation,P = 12 + 2Q (original supply equation)P = 132 - 2Q (new demand equation)⇒ 12 + 2Q = 132 - 2Q⇒ 4Q = 60⇒ Q = 15P = 12 + 2(15)⇒ P = 42

Therefore, the new equilibrium price is $42 per bushel and the new equilibrium quantity is 15 bushels.

The graphical representation is given below:

Graphical representation of new equilibrium price and quantity.

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Answer:

it doesn't show what your talking about be more specific.

Step-by-step explanation:                                                                                               explain what your talking about.

The value of the investment account after 16 years is $1,254.34.

The final value of the investment account is $1,254.34 after 16 years of earning an annual rate of 6.1%.After 16 years, the value of the investment account can be calculated using the formula: FV = PV × (1 + r)n, where FV is the future value, PV is the present value, r is the annual interest rate, and n is the number of years. Applying the values, we get:FV = $531 × (1 + 0.061)16FV = $1,254.34 . Thus, the value of the investment account after 16 years is $1,254.34.

Investment accounts are those that also contain cash and other assets like stocks, bonds, funds, and other securities. The value of the assets in an investment account might vary and even go down, which is a significant distinction between one and a bank account.

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Answer:

74 , 138

Step-by-step explanation:

12 + 2 = 14

14 + 4 = 18

18 + 8 = 26

26+16 = 42

42+32= 74

74+64 =138

please make my answer as brainelist