The table represents a quadratic function. Write an equation of the function in
standard form.

Answer:

21

Step-by-step explanation:lol

This is based on a survey conducted by the American Customer Satisfaction Index (ACSI) in 2020 that surveyed 1,097 passengers who had flown on U.S. airlines in the past 12 months.

A survey is a research method used to collect quantitative and qualitative data from a specific population. Surveys are often used to assess attitudes, opinions, and behaviors of a given group of people. They are typically administered in the form of a questionnaire, which can be administered in person, over the phone, or online. Surveys are often used in market research, political polling, social science research, and other types of research.

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The effective interest on £2000 at a 3% interest rate compounded quarterly over a period of 4 years is approximately £245.15.

To calculate the effective interest, we need to use the formula for compound interest:

A = P(1 + r/n)^(nt)

Where:

A = the future value of the investment (including interest)

P = the principal amount (initial investment)

r = the annual interest rate (as a decimal)

n = the number of compounding periods per year

t = the number of years

In this case, the principal amount (P) is £2000, the annual interest rate (r) is 3% (or 0.03 as a decimal), the compounding is done quarterly (n = 4), and the investment period (t) is 4 years.

Plugging the values into the formula:

A = £2000(1 + 0.03/4)^(4*4)

= £2000(1 + 0.0075)^16

= £2000(1.0075)^16

≈ £2000(1.126825)

Calculating the future value:

A ≈ £2253.65

To find the effective interest, we subtract the principal amount from the future value:

Effective Interest = £2253.65 - £2000

≈ £253.65

Therefore, the effective interest on £2000 at a 3% interest rate compounded quarterly after 4 years is approximately £253.65.

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Answer:

4

Step-by-step explanation:

y = kx

Use point (3, 12).

12 = k * 3

k = 12/3 = 4

y = 4x

Answer: 4

Divide y by x:

12/3 = 4

36 / 9 = 4

The constant of variation is 4

An equation can either have a solution, no solution or infinite many solution.

The equation has infinite many solutions.

The equation is given as:

\(\mathbf{3x + 21 = 3(x + 7)}\)

Open bracket

\(\mathbf{3x + 21 = 3x + 21}\)

Collect like terms

\(\mathbf{3x -3x = 21 - 21}\)

Evaluate like terms

\(\mathbf{0= 0}\)

There are no traces of variable x in the above equation, and the equation is true.

This means that: the equation has infinite many solutions.

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The probability of event A given event B, denoted as P(A | B), is 0.750. The probability of event B given event A, denoted as P(B | A), is 0.900. A and B are not independent events because the conditional probabilities P(A | B) and P(B | A) are not equal to the marginal probabilities P(A) and P(B), respectively.

To find P(A | B), we use the formula:

P(A | B) = P(A ∩ B) / P(B)

In this case, P(A ∩ B) = 0.45 and P(B) = 0.60.

Plugging these values into the formula, we get

P(A | B) = 0.45 / 0.60 = 0.750.

To find P(B | A), we use the formula:

P(B | A) = P(A ∩ B) / P(A)

Here, P(A ∩ B) = 0.45 and P(A) = 0.50.

Substituting the values, we find

P(B | A) = 0.45 / 0.50 = 0.900.

A and B are not independent because the probabilities of A and B are affected by each other. If A and B were independent, then P(A | B) would be equal to P(A), and P(B | A) would be equal to P(B). However, in this case, both P(A | B) and P(B | A) differ from their respective marginal probabilities. Therefore, A and B are dependent events.

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1) Considering this data set, we need to rewrite them orderly:

4,7,8,10, 11, 14, 16, 19

2) Note that there are 8 data points. So the Median can be found this way:

Answer: 2^7

Step-by-step explanation: 4 is equal to 2^2

32 is equal to 2^5

If you multiply the two, you get 2 to the power of the sum of the exponents which in this case is 2+5 or just 7.

It will take approximately 3.9 hours from noon for 90% of the population to hear the rumor, which means they will have heard it by approximately 3:00 PM.

By noon, half of the town's population, which is 3500/2 = 1750, has heard the rumor. This means that 1750 - 280 = 1470 people heard the rumor between 8AM and noon. Therefore, the number of people who have yet to hear the rumor is 3500 - 1750 = 1750.

To find out when 90% of the population will have heard the rumor, we can use the formula:

(people who have heard the rumor) / (total population) = 0.9

Solving for the number of people who need to hear the rumor, we get:

(0.9)(3500) = 3150

To find out how many people need to hear the rumor from noon onwards, we subtract the number of people who have already heard it:

3150 - 1750 = 1400

To find out how long it will take for 1400 more people to hear the rumor, we can use the ratio:

(number of people who hear the rumor per hour) / (total population) = (1400 / 1750)

Solving for the number of people who hear the rumor per hour, we get:

(number of people who hear the rumor per hour) = (1400 / 1750) * (1 / k)

where k is the number of hours it takes for 90% of the population to hear the rumor. Solving for k, we get:

k = (1400 / 1750) * (1 / (number of people who hear the rumor per hour))

Plugging in the value of 280 for the number of people who heard the rumor from 8AM to noon, we get:

\(k = (1400 / 1750) * (1 / ((1470 + 280) / 4))\)

k = 3.86

Therefore, it will take approximately 3.9 hours from noon for 90% of the population to hear the rumor, which means they will have heard it by approximately 3:00 PM.

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The time at which Amanda ends her morning activities is 9:31 A.M.

In the question, we are given that Amanda has recorded how long it takes her to do her morning activities. She does all of the listed activities each day. She starts the first activity at 7:30 a.m. and has a two-minute break between each adjacent pair of activities.

We are asked for the time when she finishes all of her activities each morning.

To find the time at which she finishes, we first calculate the total time period of her activities.

The time that Amanda takes to shower and dress is 15 minutes.

After this she takes a break of 2 minutes.

The time that Amanda takes to prepare and eat breakfast is 20 minutes.

After this she takes a break of 2 minutes.

The time that Amanda takes to chores is 35 minutes.

After this she takes a break of 2 minutes.

The time that Amanda takes to practice piano is 45 minutes.

Thus, the total time spent by Amanda for her morning activities = 15 + 2 + 20 + 2 + 35 + 2 + 45 = 121 minutes or 2 hours and 1 minute.

Amanda's start time = 7:30 A.M.

Thus, Amanda's end time = 7:30 A.M. + 2 hours and 1 minute = 9:31 A.M.

Thus, the time at which Amanda ends her morning activities is 9:31 A.M.

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The provided question had the table missing. The table is attached.

The maximum height achieved by the rider is given by the equation above. You can calculate this value using the given measurements and plug them into the equation to find the maximum height.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.

A. The two quantities you would measure for x and y are the time and height, respectively.

B. The equation that relates time and height for an object in projectile motion is given by:

y = y0 + v0y * t - (1/2) * g * t²

where:

y = vertical height at any time t

y0 = initial vertical height (in this case, the height of the ramp)

v0y = initial vertical velocity (in this case, the vertical velocity of the rider at the top of the ramp)

g = acceleration due to gravity (approx. 9.81 m/s²)

t = time elapsed since the rider left the ramp

To apply this equation to the given image, you can put the picture on a grid with the x-axis representing time and the y-axis representing height.

C. To find the maximum height, you need to determine the point at which the rider's height is greatest. From the plotted points, you can see that the maximum height occurs at the point where the curve reaches its apex. You can find this point by calculating the time at which the vertical velocity of the rider becomes zero (i.e., the highest point of the jump). This occurs at the peak of the curve, where the vertical velocity changes from positive to negative. To calculate this time, you can use the equation for vertical velocity in projectile motion:

v = v0y - g * t

where:

v = vertical velocity at any time t

v0y = initial vertical velocity (in this case, the vertical velocity of the rider at the top of the ramp)

g = acceleration due to gravity (approx. 9.81 m/s²)

t = time elapsed since the rider left the ramp

At the peak of the jump, the vertical velocity becomes zero, so we can set v = 0 and solve for t:

0 = v0y - g * t

t = v0y / g

Substituting this value of t into the equation for height, we can find the maximum height:

y = y0 + v0y * (v0y / g) - (1/2) * g * (v0y / g)²

y = y0 + (v0y² / 2g)

Therefore, the maximum height achieved by the rider is given by the equation above. You can calculate this value using the given measurements and plug them into the equation to find the maximum height.

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Once we have found the vertex, we can determine the maximum height achieved by the rider.

What is statistics?

Statistics is a branch of mathematics that deals with the collection, analysis, interpretation, presentation, and organization of numerical data. It involves the use of methods and techniques to gather, summarize, and draw conclusions from data.

To find the highest point the rider achieved on a jump, we need to measure the rider's height at different points during the jump.

A. The two quantities we would measure for x and y would be:

x: the horizontal distance the rider travels during the jump

y: the vertical height of the rider at different points during the jump

B. The equation that describes the rider's motion during the jump would be a quadratic equation in the form of:

y = ax² + bx + c

Where:

a is the coefficient of the quadratic term and represents the acceleration due to gravity

b is the coefficient of the linear term and represents the initial velocity of the rider

c is the constant term and represents the initial height of the rider

C. To find the maximum height, we need to find the vertex of the parabola that represents the rider's motion.

The vertex is the highest point on the parabola and is located at the point (-b/2a, c - b²/4a).

To find the vertex, we need to measure the rider's height at least two different points during the jump.

The two points should be on either side of the vertex to ensure that we have captured the shape of the parabola correctly.

hence, Once we have measured the rider's height at these two points, we can plug the values into the equation and solve for the vertex. Once we have found the vertex, we can determine the maximum height achieved by the rider.

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A larger sample size may be necessary to achieve a more representative sample.

If the grocery stores are similar in terms of the demographics of their customers, the variety and quantity of vegetables they stock, and their geographic location within the city, then it's possible that Zach's sample of 20 vegetables from each store could be representative of the city as a whole.

If the grocery stores differ significantly in any of these factors, then Zach's sample may not be representative.

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Given that

Then

Step-by-step explanation:

2(x-2)⅓=x+2

so we first cube each side,such that...

(2(x-2))⅓•³=(x+2)³

we get...

2(x-2)=(x+2)³

expanding...

2x-4=x³+6x²+12x+8

grouping....

x³+6x²+12x+8-2x+4=0

solving...

x³+6x²+10x+12=0

now you can use you calculator to solve for the possible values of x

I hope this will help

Answer:

x=4

Step-by-step explanation:

y=2x+50

58=2x+50

8=2x

x=4

This is used to calculate the height of the object at any time t during its flight.

The equation you provided represents the height of an object (in meters) at time t (in seconds) when it is thrown or projected upward with an initial velocity of v (in meters per second) from an initial height of hi (in meters) above the ground.

The acceleration due to gravity is taken to be -9.8 m/\(s^2\) (negative since it acts downward), and the formula for the height is derived from the equation of motion:

h(t) = -1/2 \(gt^2\) + vt + hi

Where:

g = 9.8 m/\(s^2\) (acceleration due to gravity)

t = time (in seconds)

v = initial velocity (in meters per second)

hi = initial height (in meters)

The coefficient -4.9 in the equation you provided is simply half of the acceleration due to gravity (-9.8/2 = -4.9).

This is because the object is thrown upward and experiences a deceleration due to gravity that decreases its upward velocity by 9.8 m/\(s^2\) until it reaches the maximum height and then starts to fall back down.

So, for any given initial velocity and height, this equation can be used to calculate the height of the object at any time t during its flight.

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The length of the metal tray can be determined by adding the given dimensions of the tray, which are 20 inches and 14 inches, along with the unknown dimensions represented by "X."

To find the length of the metal tray, we need to consider the given dimensions and the unknown dimensions represented by "X." Let's assume that the length of the metal tray is L. From the given diagram, we can observe that the 20-inch dimension corresponds to one end of the tray, and the 14-inch dimension corresponds to the other end of the tray. In between, there are three sections denoted by "X."

Therefore, the expression for the length of the metal tray can be written as L = 20 + X + X + X + 14, which simplifies to L = 54 + 3X. Thus, the length of the metal tray can be calculated by adding the fixed dimensions and three times the value of "X."

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The required length of the other leg is \($\sqrt{5}$\) cm. If we need to round to the nearest tenth, we get: \($b \approx 2.2$\) cm

Let's use the Pythagorean theorem to solve this problem. The Pythagorean theorem states that in a right triangle, the square of the length of the hypotenuse is equal to the sum of the squares of the lengths of the legs. So we have:

\($c^2 = a^2 + b^2$\)

where c is the length of the hypotenuse, a and b are the lengths of the legs.

We are given that the length of the hypotenuse is 3 cm and the length of one leg is 2 cm. Let's substitute these values into the equation above:

\($3^2 = 2^2 + b^2$\)

\($9 = 4 + b^2$\)

\($b^2 = 5$\)

\($b = \sqrt{5}$\)

So the length of the other leg is \($\sqrt{5}$\) cm. If we need to round to the nearest tenth, we get: \($b \approx 2.2$\) cm (rounded to one decimal place).

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Answer:

z=23

Step-by-step explanation:

z=2

Answer:

(3,20)

Step-by-step explanation:

so O must be 0,0 and A is a midpoint of OB

This means B must be (14,12)

B is the midpoint of TS.

This means that the distance of SB is equal to the distance of BT.

This must mean that the coordinate of T must be (3,20)

O: (0,0)    x coordinate increases by 7. y coordinate increases by 6.

A: (7,6)

B: (14,12)

S: (25,4)    x coordinate decrease by 11. y coordinate increases by 8.

B: (14,12)

T: (3,20)

The coordinates of T are (3, 20).

A straight line is an endless one-dimensional figure that has no width.

From the figure, A is the midpoint of OB and B is the midpoint of TS

The coordinates of O are (0, 0) and Coordinates of A are (7,6)

We can find coordinate of B.

(7, 6)=(0+x/2, 0+y/2)

(7,6)=(x/2, y/2)

x/2=7   and    y/2=6

x=14               y=12

So the coordinates of B are (14, 12)

Now we can find the coordinates of T.

(14, 12)=(X+25/2, Y+4/2)

X+25=28

x=3

Y+4=24

Y=20

So the coordinates of T are (3, 20)

Hence, the coordinates of T are (3, 20).

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Step-by-step explanation:

5(r + 9) - 2(1 - r) = 1

5r + 45 - 2 + 2r = 1

7r + 43 = 1

7r = -42

r = -6.

Answer:

r = -6

Step-by-step explanation:

Given equation,

→ 5(r + 9) - 2(1 - r) = 1

Now the value of r will be,

→ 5(r + 9) - 2(1 - r) = 1

→ 5r + 45 - 2 + 2r = 1

→ 5r + 2r + 43 = 1

→ 7r = 1 - 43

→ 7r = -42

→ r = -42/7

→ [ r = -6 ]

Hence, the value of r is -6.

Answer:

10 pounds

Step-by-step explanation:

given ratio weight:added weight=10:1

100:x=10:1

100/x=10/1

solving for x

100=10x

x=10

Answer:4

Step-by-step explanation:12/3=4

Answer: the answer is B!!!!!!!!!!!!!!

Step-by-step explanation:

A

1) Since the sum of the interior angles of any triangle is 180º, and this is an isosceles triangle

2) Then the other angle, has the same measure 50º since this is an isosceles triangle, at least two congruent sides, and two congruent angles.

We can finally write

x+88 +50 +50 = 180

x +188 =180 subtract 188 from both sides

x= 180-188

x= -8

3) So x=-8 is the answer.

The income that's made based on the equation when 1 comb is sold is $0.5.

From the information given, the equation is given as y = x/2. In this case, it was illustrated that the income is depicted based on the combs sold.

Therefore, the income by selling 1 comb will be:

y = 1/2

y = $0.5

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The factoring of the expression x²=-x+6 is (x-2)(x+3)

By ordering the values, we get:

x² + x - 6 = 0

To solve this exercise, we have to follow the rules of factoring:

1. Looking for the a and b number that state the following equations:

Analyzing that (a*b) is a negative number, it means that (a) and (b) have different signs, and due to the results of (a+b) is positive the higher number has to be the positive one.  

The number could be:

a = -2

b = 3

Confirming:

a + b = -2 + 3 = 1

a * b = (-2) * 3 = - 6

2. Rewriting the factored expression (x+a)(x+b) with the obtained values, we get:

(x-2)(x+3)

Is a technique that consist of decomposition of a factor into a product of another factor, which when multiplied together give the original number.

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Answer:

7

Step-by-step explanation:

The start this question by looking at two important things, how much money we have and how much money it costs per person. The friends have a total of $284.25 and we don't know how much it costs per person. To find this we must set up an equation and solve it!

Because each person must pay for parking and a ticket, we can find the cost for one person by adding the parking and ticket cost together.

$9.25 + $27.50 = $36.75

Now that we have solved this equation, we know that it costs $36.75 for one person. To find how many total people can go we dived the total amount of money we have by how much it costs per person. Let's call the number of people that can go 'p'.

p = \(\frac{284.25}{36.75}\)

Once we simplify/solve this equation we get 7 \(\frac{36}{49}\) so essentially, we get the whole number 7 and a long decimal, but the only important part is the 7. We take the whole number from our answer which is 7.

We now know the answer: 7.

Let's check our work!

7 * 36.75 = 257.75

284.25 - 257.75 = 26.5

26.5 < 36.75 so we are correct!

The final answer is 7!

Have an amazing day!