Determine the equation of the parabola graphed below. A parabola is plotted, concave down, with vertex located at coordinates negative three and four.

Answers

Answer 1

The equation of parabola from graph is y = a(x + 1)² - 4.

According to the statement

we have to determine the parabola equation from the graphical representation.

So,

For this purpose we know that

Parabola is a symmetrical open plane curve formed by the intersection of a cone with a plane parallel to its side. The path of a projectile under the influence of gravity ideally follows a curve of this shape.

The general equation of parabola is y = a(x-h)2 + k

And The equation of a quadratic function, of vertex (h,k), is given by:

y = a(x - h)² + k

In which a is the leading coefficient.

Considering the vertex given, we have that h = -1, k = -4, hence the equation is:

y = a(x + 1)² - 4

So, The equation of parabola from graph is y = a(x + 1)² - 4.

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Question:

Determine the equation of the parabola graphed below. Note: be sure to consider the negative sign already present in the template equation when entering your answer. A parabola is plotted, concave up, with vertex located at coordinates negative one and negative four.

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Related Questions

The data set below shows the number of tickets sold by the Benson High School Bulldog Basketball team per home game in one
season.
75, 120, 255, 113, 225, 190, 108, 91, 134, 95, 163, 178, 171, 105, 100
Using a box plot, determine which of the following are true regarding the data set above.
1. The data is skewed left.
II. The data is skewed right.
III. The data is symmetric.
IV. The median is 120.
OA. I only
OB. I and IV
OC. II only
OD. III and IV
OE. II and IV

Answers

The correct answer is OE. II and IV: The data is skewed right, and the median is 120.

How to solve

Before identifying the attributes of the data set, it is necessary to organize the data by sorting it and obtaining the median, quartiles, and potential anomalies.

Sorted data: 75, 91, 95, 100, 105, 108, 113, 120, 134, 163, 171, 178, 190, 225, 255

The median (Q2) is 120. Q1 is 100 and Q3 is 178.

The Interquartile Range (IQR) is 78 (Q3 - Q1).

As the median is closer to Q1 than to Q3 and there are larger values towards the higher end, it indicates the data is skewed right.

So, the correct answer is OE. II and IV: The data is skewed right, and the median is 120.

Answers

In a paint-drying situation with a null hypothesis H0: μ = 73 and an alternative hypothesis Ha: μ < 73, a random sample of n = 25 observations is taken. We are given x = 72.3 and σ = 6. We need to determine (a) how many standard deviations below the null value x = 72.3 is, (b) the conclusion using α = 0.005, (c) the value of Φ(70) for α = 0.005, (d) the required sample size to ensure Φ(70) = 0.01, and (e) the probability of a type I error when α = 0.01 and n = 100.

(a) To determine the number of standard deviations below the null value x = 72.3, we calculate z = (x - μ) / σ. Plugging in the values, we have z = (72.3 - 73) / 6, giving us z = -0.12.

(b) To make a conclusion using α = 0.005, we calculate the test statistic z = (x - μ) / (σ / √n) and compare it to the critical value. The critical value for α = 0.005 in a left-tailed test is approximately -2.576. If the calculated test statistic is less than -2.576, we reject the null hypothesis. Otherwise, we fail to reject the null hypothesis.

(c) To find Φ(70) for α = 0.005, we calculate the test statistic z = (70 - μ) / (σ / √n) using the values provided. Then we find Φ(z) using a standard normal distribution table.

(d) To determine the required sample size for Φ(70) = 0.01, we find the z-score corresponding to Φ(70) = 0.01 using a standard normal distribution table. We then rearrange the formula for the test statistic z = (x - μ) / (σ / √n) to solve for n.

(e) To calculate the probability of a type I error when α = 0.01 and n = 100, we find the test statistic z = (x - μ) / (σ / √n) and compare it to the critical value for a left-tailed test. The probability of a type I error is the area under the curve to the left of the critical value.

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An American traveler who is heading to Europe is exchanging some U. S. Dollars for European euros. At the time of his travel, 1 dollar can be exchanged for 0. 91 euros.

Find the amount of money in euros that the American traveler would get if he exchanged 100 dollars.

euros

What if he exchanged 500 dollars?

euros

Write an equation that gives the amount of money in euros, e, as a function of the dollar amount being exchanged, d.

e = d

Upon returning to America, the traveler has 42 euros to exchange back into U. S. Dollars. How many dollars would he get if the exchange rate is still the same?

dollars

Listen to the complete question

Part B

Write an equation that gives the amount of money in dollars, d, as a function of the euro amount being exchanged, e

Answers

If the American traveler exchanges $100, they would receive approximately 91 euros. If they exchange $500, they would receive approximately 455 euros. The equation e = d

To calculate the amount of money in euros that the American traveler would receive, we multiply the dollar amount being exchanged by the exchange rate of 0.91 euros per dollar.

For $100, the amount in euros would be:

e = 100 * 0.91 = 91 euros.

For $500, the amount in euros would be:

e = 500 * 0.91 = 455 euros.

Therefore, if the traveler exchanges $100, they would receive 91 euros, and if they exchange $500, they would receive 455 euros.

To calculate the amount of dollars the traveler would receive when exchanging back 42 euros, we divide the euro amount by the exchange rate:

dollars = 42 / 0.91 = $46.15.Therefore, if the exchange rate remains the same, the traveler would receive approximately $46.15 when exchanging 42 euros back into U.S. Dollars.

The equation e = d represents the amount of money in euros (e) as a

function of the dollar amount being exchanged (d). It implies that the amount in euros is equal to the amount in dollars multiplied by the exchange rate.

Similarly, the equation d = e represents the amount of money in dollars (d) as a function of the euro amount being exchanged (e). It implies that the amount in dollars is equal to the amount in euros multiplied by the reciprocal of the exchange rate.

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(6 points) let s = {1,2,3,4,5} (a) list all the 3-permutations of s. (b) list all the 5-permutations of s.

Answers

(a) The 3-permutations of s are:

{1,2,3}

{1,2,4}

{1,2,5}

{1,3,2}

{1,3,4}

{1,3,5}

{1,4,2}

{1,4,3}

{1,4,5}

{1,5,2}

{1,5,3}

{1,5,4}

{2,1,3}

{2,1,4}

{2,1,5}

{2,3,1}

{2,3,4}

{2,3,5}

{2,4,1}

{2,4,3}

{2,4,5}

{2,5,1}

{2,5,3}

{2,5,4}

{3,1,2}

{3,1,4}

{3,1,5}

{3,2,1}

{3,2,4}

{3,2,5}

{3,4,1}

{3,4,2}

{3,4,5}

{3,5,1}

{3,5,2}

{3,5,4}

{4,1,2}

{4,1,3}

{4,1,5}

{4,2,1}

{4,2,3}

{4,2,5}

{4,3,1}

{4,3,2}

{4,3,5}

{4,5,1}

{4,5,2}

{4,5,3}

{5,1,2}

{5,1,3}

{5,1,4}

{5,2,1}

{5,2,3}

{5,2,4}

{5,3,1}

{5,3,2}

{5,3,4}

{5,4,1}

{5,4,2}

{5,4,3}

(b) The 5-permutations of s are:

{1,2,3,4,5}

{1,2,3,5,4}

{1,2,4,3,5}

{1,2,4,5,3}

{1,2,5,3,4}

{1,2,5,4,3}

{1,3,2,4,5}

{1,3,2,5,4}

{1,3,4,2,5}

{1,3,4,5,2}

{1,3,5,2,4}

{1,3,5,4,2}

{1,4,2,3,5}

{1,4,2,5,3}

{1,4,3,2,5}

{1,4,3,5

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The flight path of a plane is a straight line from city J to city K. The roads from city J to city K run 9. 4 miles south and then 15. 1 miles east. How many degrees east of south is the plane's flight path, to the nearest tenth?

Answers

The plane's flight path is about 59.6 degrees east of the south.

The flight path of a plane is a straight line from city J to city K.

The roads from city J to city K run 9.4 miles south and then 15.1 miles east.

To the nearest tenth, the degree to which the plane's flight path is to the east of the south is approximately 59.6 degrees.

Using the Pythagorean Theorem,

we can calculate the length of the hypotenuse (the flight path) of the right triangle

9.4-mile southern segment

15.1-mile eastern segment as follows:

a² + b² = c²

where a = 9.4 and b = 15.1

c² = 9.4² + 15.1²c²

= 88.36 + 228.01c²

= 316.37c

= √316.37c = 17.8 miles

Therefore, the length of the flight path is 17.8 miles.

To determine how many degrees east of south the plane's flight path is, we must use trigonometric ratios.

We will use tangent (tan) since we are given the lengths of the adjacent and opposite sides of the right triangle.

tanθ = b / a = 15.1 / 9.4 θ = tan⁻¹(15.1 / 9.4) θ ≈ 59.6°

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Find the work done by F in moving a particle once counterclockwise around the given curve. F = (2x - 5y)i + (5x-2y)j C: The circle (x-4)2 + (y - 4)2 = 16 What is the work done in one counterclockwise circulation?

Answers

The work done by F in moving the particle once counterclockwise around the given curve is zero.

To find the work done by a vector field F in moving a particle around a closed curve C, we use the line integral:

W = ∮C F · dr

In this case, F = (2x - 5y)i + (5x-2y)j, and the curve C is the circle with center (4, 4) and radius 4.

To evaluate the line integral, we need to parameterize the curve C. We can use the parametric equations for a circle:

x = 4 + 4cos(t)

y = 4 + 4sin(t)

where t ranges from 0 to 2π.

Next, we need to find the differential vector dr along the curve C:

dr = dx i + dy j

Taking the derivatives of x and y with respect to t, we get:

dx = -4sin(t) dt

dy = 4cos(t) dt

Substituting dx and dy into the line integral formula, we have:

W = ∮C F · dr

= ∫(0 to 2π) [(2(4 + 4cos(t)) - 5(4 + 4sin(t))) (-4sin(t)) + (5(4 + 4cos(t)) - 2(4 + 4sin(t))) (4cos(t))] dt

Simplifying the expression inside the integral, we get:

W = ∫(0 to 2π) [-20sin(t) + 40cos(t) - 20sin(t) + 20cos(t)] dt

= ∫(0 to 2π) (20cos(t) - 40sin(t)) dt

Integrating the terms, we have:

W = [20sin(t) + 40cos(t)] (from 0 to 2π)

= (20sin(2π) + 40cos(2π)) - (20sin(0) + 40cos(0))

= (0 + 40) - (0 + 40)

= 0

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the joint moment generating function for two random variables x and y is: \displaystyle m_{x,y}(s,t)=\frac{1}{1-s-2t 2st}\,\text{ for }\,s<1\,\text{ and }\,t<\frac{1}{2} calculate e[xy].

Answers

The expected value of the product of x and y is -1.

The joint moment generating function for two random variables x and y is a mathematical function that allows us to calculate moments of x and y. The moment of a random variable is a statistical measure that describes the shape, location, and spread of its probability distribution.

The expected value of the product of two random variables, E[xy], is one of the moments of the joint distribution of x and y. It can be calculated using the joint moment generating function as follows:

E[xy] = ∂^2 m(x,y) / ∂s∂t |s=0,t=0

where m(x,y) is the joint moment generating function.

In this problem, we are given the joint moment generating function for x and y, which is:

m(x,y) = 1 / (1 - s - 2t + 2st)

We are asked to calculate E[xy], which is the second-order partial derivative of m(x,y) with respect to s and t, evaluated at s=0 and t=0.

Taking the partial derivative of m(x,y) with respect to s, we get:

∂m(x,y)/∂s = [(2t-1)/(1-s-2t+2st)^2]

Taking the partial derivative of m(x,y) with respect to t, we get:

∂m(x,y)/∂t = [(2s-1)/(1-s-2t+2st)^2]

Then, taking the second-order partial derivative of m(x,y) with respect to s and t, we get:

∂^2 m(x,y)/∂s∂t = [4st - 2s - 2t + 1] / (1-s-2t+2st)^3

Finally, substituting s=0 and t=0 into this expression, we get:

E[xy] = ∂^2 m(x,y) / ∂s∂t |s=0,t=0 = (400 - 20 - 20 + 1) / (1-0-20+20*0)^3 = -1

Therefore, the expected value of the product of x and y is -1.

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Asap !!!
given a scatter plot, what do you need to do to find the line of best fit?

a) draw a line that goes through the middle of the data points and follows the trend of the data
b) take a wild guess
c) start at the origin and draw a line in any direction
d) draw a line that only goes through 1 point of the data points

Answers

To find the line of best fit on a scatter plot, the first step is to draw a line that goes through the middle of the data points and follows the trend of the data. The line of best fit is a line drawn through a scatter plot that represents the trend of the data.

To find the line of best fit on a scatter plot, the first step is to draw a line that goes through the middle of the data points and follows the trend of the data. The line of best fit is a line drawn through a scatter plot that represents the trend of the data. This line is also known as the line of regression and is used to help predict future events. To draw the line of best fit, a regression analysis needs to be performed.

Regression analysis is a statistical process that looks at the relationship between two variables. In the case of a scatter plot, it is used to find the relationship between the x and y variables. The line of best fit is determined by calculating the slope and y-intercept of the line that best fits the data. The slope of the line is calculated using the formula: y = mx + b, where m is the slope and b is the y-intercept. The slope represents the change in y for every change in x.

The line of best fit should be drawn in such a way that it goes through as many data points as possible while still following the trend of the data. The line should be drawn so that it minimizes the distance between the line and the data points. This is called the least squares method. The line of best fit should be drawn so that it is the best representation of the data, not just a guess.

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Find the derivative of the function. f(x) = ((2x ? 6)^4) * ((x^2 + x + 1)^5)

Answers

To find the derivative of the given function f(x) = ((2x - 6)^4) * ((x^2 + x + 1)^5), you need to apply the product rule and the chain rule.

Product rule: (u × v)' = u' × v + u × v'
Chain rule: (g(h(x)))' = g'(h(x)) * h'(x)
Let u(x) = [tex](2x - 6)^4[/tex] and v(x) = [tex](x^2 + x + 1)^5[/tex].
First, find the derivatives of u(x) and v(x) using the chain rule:
u'(x) = [tex]4(2x - 6)^3[/tex] × 2 = 8(2x - 6)^3
v'(x) = [tex]5(x^2 + x + 1)^4[/tex] × (2x + 1)
Now, apply the product rule:
f'(x) = u'(x) × v(x) + u(x) × v'(x)
f'(x) = [tex]8(2x - 6)^3[/tex] × [tex](x^2 + x + 1)^5[/tex]+ [tex](2x - 6)^4[/tex] × [tex]5(x^2 + x + 1)^4[/tex] × (2x + 1)
This is the derivative of the function f(x).

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If the standard deviation of a data set were originally 4, and if each value in the data set were multiplied by 1. 75, what would be the standard deviation of the resulting data? O A. 1 B. 4 O c. 7 O D. 3

Answers

The standard deviation of the resulting data would be 7. To understand why the standard deviation would be 7, let's consider the effect of multiplying each value in the data set by 1.75.

When we multiply each value by a constant, the mean of the data set is also multiplied by that constant. In this case, since multiplying by 1.75 increases the scale of the data, the mean is also multiplied by 1.75.

Now, the standard deviation measures the dispersion or spread of the data around the mean. When we multiply each value by 1.75, the spread of the data increases because the values are further away from the mean. Since the original standard deviation was 4 and each value is multiplied by 1.75, the resulting standard deviation is 4 * 1.75 = 7.

Therefore, the standard deviation of the resulting data is 7.

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A professor had a volunteer consume 50 milligrams of caffeine on morning.

Answers

The residuals to the nearest tenth are 0.6, -0.7, 0.1, 0.8, and -0.4.

A scatter plot of the residuals is shown in the image below.

What is a residual value?

In Mathematics, a residual value is a difference between the measured (given, actual, or observed) value from a scatter plot and the predicted value from a scatter plot.

Mathematically, the residual value of a data set can be calculated by using this formula: