MATHEMATICS HIGH SCHOOL

Derive the equation of the parabola with a focus at (−5, 5) and a directrix of y = -1f(x) = −1/12 (x − 5)2 + 2
f(x) = 1/12 (x − 5)2 + 2
f(x) = −1/12 (x + 5)2 + 2
f(x) = 1/12 (x + 5)2 + 2

Answers

Answer 1
Answer: From the given information, the parabola is a regular parabola facing up with vertex at (-5, 2).
Required equation is (x + 5)^2 = 4p(y - 2)

But 2 + p = 5 => p = 5 - 2 = 3

Therefore, required equation is (x + 5)^2 = 4(3)(y - 2)
(x + 5)^2 = 12(y - 2)
y - 2 = 1/12 (x + 5)^2
y = 1/12 (x + 5)^2 + 2
f(x) = 1/12 (x + 5)^2 + 2

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PLEASE HELP !The graph shows the ages of different concertgoers who have backstage passes.

Which statement is true about the graph?

A) A late arrival who is 21 years old with a back-stage pass will make the mean greater than the median.
B) The two holders of back-stage passes whose ages are above 40 make the mean age higher than the median age.
C) The ages of concert-goers with backstage passes are skewed left, so the mean age is less than the median age.
D) A concert-goer who is 18 years old and wins a back-stage pass will pull the mean more than 2 years less than the median.

Answers

In the given graph, we calculate the mean by dividing the product of the midpoint of each age interval and the frequency by the total frequency. Mean = [13.5(3) + 16.5(6) + 19.5(8) + 22.5(6) + 25.5(5) + 28.5(4) + 31.5(3) + 43.5 + 46.5] / (3 + 6 + 8 + 6 + 5 + 4 + 3 + 1 + 1) = 856.5 / 37 = 23.15 The median is given by the middle age interval (i.e. the age interval which falls in the (37 + 1) / 2 = 38 / 2 = 19th position) which is the 21 - 24 age inteval. To get the value of the median we use the formular Median = L1 + C[n/2 - summation (Fl)] / Fm where: L1 is the lower class boundary of the median class, C is the class size, n is the total frequency, summation (Fl) is the summation of all frequencies below the mediam class and Fm is the median class frequency. Median = 21 + 4[37/2 - (3 + 6 + 8)] / 6 = 21 + 4[18.5 - 17] / 6 = 21 + 4(1.5) / 6 = 21 + 6 / 6 = 21 + 1 = 22. Thus the mean of 23.15 is greater than the median of 22. Calculating the mean without the two numbers above 40 gives Mean = (856.5 - 43.5 - 46.5) / 35 = 766.5 / 35 = 21.9 Therefore, the statement that is true about the graph is "The two holders of back-stage passes whose ages are above 40 make the mean age higher than the median age." (option B)

The two holders of back-stage passes whose ages are above 40 making the mean age higher than the median age is correct about the graph.

What is a Graph?

This can be defined as pictorial representation of data or values in an organized manner.

From the graph we can calculate mean.

Mean = [13.5(3) + 16.5(6) + 19.5(8) + 22.5(6) + 25.5(5) + 28.5(4) + 31.5(3) + 43.5 + 46.5] / (3 + 6 + 8 + 6 + 5 + 4 + 3 + 1 + 1)

= 856.5 / 37

= 23.15

Median = (37 + 1) / 2 = 38 / 2 = 19th position between 21 - 24 age interval. Median = L1 + C[n/2 - summation (Fl)] / Fm

where L1 = lower class boundary of the median class, C = class size, n = total frequency, summation (Fl) = summation of all frequencies below median class, Fm= median class frequency.

Median = 21 + 4[37/2 - (3 + 6 + 8)] / 6

= 21 + 4[18.5 - 17] / 6

= 21 + 4(1.5) / 6

= 21 + 6 / 6 = 21 + 1 = 22.

Mean of 23.15 is greater than the median of 22.

Mean without two numbers above 40

= (856.5 - 43.5 - 46.5) / 35 = 766.5 / 35 = 21.9.

Therefore the  two holders of back-stage passes whose ages are above 40 make the mean age higher than the median age which makes option B the most appropriate choice

Read more about Graph here brainly.com/question/25184007

Pete earns $8.50 per hour plus tips. On Tuesday, he received $16 in tips.How many hours did Pete work if he earned a total of $50 on Tuesday?


Help me plz

Answers

Answer:

Pete worked for 4 hours.

Step-by-step explanation:

If you subtract his tips from his overall total (50-16) you get 34. Now you divide what's left of his total by his hourly wage (34/8.5) which gets you 4.

What is bigger 11/14 or 3/4?

Answers

Step 1: Reduce (simplify) entered fractions to lowest terms, if the case:
Fraction: 3 / 4 it's already reduced to lowest terms
Fraction: 11 / 14 it's already reduced to lowest terms

Step 2: Calculate LCM (lowest common multiple) of the reduced fractions' denominators, it will be the common denominator of the compared fractions:
Denominator 4, factored = 22
Denominator 14, factored = 2 * 7
LCM (4, 14) = 22 * 7 = 28

Step 3: Calculate each fraction's expanding number (LCM divided by each fraction's denominator):
For fraction: 3 / 4 is 28 : 4 = (22 * 7) : 4 = 7
For fraction: 11 / 14 is 28 : 14 = (22 * 7) : 14 = 2

Step 4: Expand fractions to bring them to the common denominator (LCM):
3 / 4 = (7 * 3) / (7 * 4) = 21 / 28
11 / 14 = (2 * 11) / (2 * 14) = 22 / 28

An animal shelter has a ratio of dogs to cats that's 3:2. If there are 30 cats at the shelter, how manydogs are there?
A. 15
B. 90
C. 20
D. 45

Answers

In the question "An animal shelter has a ratio of dogs to cats that's 3:2. If there are 30 cats at the shelter, how many dogs are there" the correct answer is 45 (option D). To solve the problem, let the number of dogs be x, then dogs / cats = 3 / 2 = x / 30. i.e. 2x = 3(30) = 90. x = 90 / 2 = 45. Therefore, there are 45 dogs in the animal shelter.

An animal shelter has a ratio of dogs to cats that's 3:2. If there are 30 cats at the shelter, 45 dogs are there . 3/2 = x/30 , x= 30*3/2 =45

1. How can you use an equation to make a prediction from a pattern? 2. Pizza costs $1.50 per slice. Use a table and an equation to represent the relationship between the number of slices of pizza bought and the total cost.

Answers

So for question 1, Well, using an equation to make a prediction for patterns is pretty easy, really. It is also very efficient. When you look at the pattern, you should be able to make an equation based upon the pattern, or any previous patterns, and using that, you can make an equation to solve or figure out other parts of the pattern. 


The area of a sector of a circle with a radius of 4 centimeters is 2.512 square centimeters. The estimated value of ╥ is 3.14. The measure of the angle defining the sector is

Answers

The equation for the area of a sector of a circle is expressed as the product of pi, square of the radius and the ratio of the angle of the sector and 360 degrees.

Area = πr^2 (α / 360°)

We obtain the angle by manipulating the equation.

α = (Area x 360°) / πr^2 
α = (2.512 cm^2 x 360°) / (π x 4^2)
α =35.98°
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