ralph records the time it takes for each of his classmates to run around the track one time. as he analyzes the data on the graph, he locates the mean and median time. which component of data analysis is ralph utilizing?

Given:

Focus of a parabola = [tex]\left(1,\dfrac{1}{2}\right)[/tex]

Directrix: [tex]y=3[/tex]

To find:

The equation of the parabola.

Solution:

The equation of a vertical parabola is:

[tex]y-k=\dfrac{1}{4a}(x-h)^2[/tex]            ...(A)

Where, [tex](h,k)[/tex] is center, [tex](h,k+a)[/tex] is focus and [tex]y=k-a[/tex] is the directrix.

On comparing the focus, we get

[tex](h,k+a)=\left(1,\dfrac{1}{2}\right)[/tex]

[tex]h=1[/tex]

[tex]k+a=\dfrac{1}{2}[/tex]           ...(i)

On comparing the directrix, we get

[tex]k-a=3[/tex]              ...(ii)

Adding (i) and (ii), we get

[tex]2k=\dfrac{7}{2}[/tex]

[tex]k=\dfrac{7}{4}[/tex]

Putting [tex]k=\dfrac{7}{4}[/tex] is (i), we get

[tex]\dfrac{7}{4}+a=\dfrac{1}{2}[/tex]

[tex]a=\dfrac{1}{2}-\dfrac{7}{4}[/tex]

[tex]a=\dfrac{-5}{4}[/tex]

Putting [tex]a=\dfrac{-5}{4},h=1,k=\dfrac{7}{4}[/tex] in (A), we get

[tex]y-\dfrac{7}{4}=\dfrac{1}{4\times \dfrac{-5}{4}}(x-1)^2[/tex]

[tex]y-\dfrac{7}{4}=\dfrac{-1}{5}(x^2-2x+1)[/tex]

[tex]y-\dfrac{7}{4}=-\dfrac{1}{5}(x^2)-\dfrac{1}{5}(-2x)-\dfrac{1}{5}(1)[/tex]

[tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x-\dfrac{1}{5}+\dfrac{7}{4}[/tex]

On further simplification, we get

[tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{35-4}{20}[/tex]

[tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{31}{20}[/tex]

Therefore, the equation of the parabola is [tex]y=-\dfrac{1}{5}x^2+\dfrac{2}{5}x+\dfrac{31}{20}[/tex].

Note: Option C is correct but the leading coefficient should be negative.

Step-by-step explanation:

A=s2

100=5×5

100/25=25x/25

x=4

Answer:

d=2m

area(A)=196m

l=60m

now,

A=d(l+b-d)

196=2(60+b-2)

196=2(58+b)

196=116+2b

2b=196-116

2b=80

b=40m

Answer: 14.5 feet

Step-by-step explanation: that’s he correct answer delta math gave me AFTER I got it wrong

Answer:

14.5

Step-by-step explanation:

Answer:

13260 square inches

Step-by-step explanation:

In DEF e = 100 inches f = 740 inches and angle D = 159°. Find the area of DEF to the nearest square inch

The formula to solve the above question is

1/2absinθ

a = 100 inches

b = 740 inches

θ = 159°

The area of the triangle =

1/2 × 100 × 740 × sin 159°

= 13259.61 square inches

Approximately = 13260 square inches

Therefore, the area of DEF = 13260 square inches

Answer:

8. 12 in

9. 30 ft

10. 87.92 in

Step-by-step explanation:

Answer:

12in, 30ft, 87.92in

Step-by-step explanation:

question 8: 24/2 = 12in

question 9: 15(2) = 30ft

question 10:

C = 2πr

C =2(3.14)(14)

C= 87.92in

Answer:

the answer would be 3.4 + 4 = 7.4 .

Answer:

the answer would be 3.4 + 4 = 7.4 .

Step-by-step explanation:

Answer:

It’s b

Step-by-step explanation:

Just think

Answer:

a. $250

b. 50x + 200

Step-by-step explanation:

a. For the first month, you have to account for the cost to start which is $200, and the adition of the $50 for each month.

b. the 200 is only a one time fee so you add it on to months(x)

Answer:

a. 250$

b. 200+50x

Step-by-step explanation:

#1 What is the total cost to use the cell phone plan for one month?

GIVEN:

Startup price=$200

Charge per month=50$

SOLVE:

The total cost for one month will be the startup price+ charging price for one month.

200+50=250$

#2 What is the total cost for x months?

The total cost for x months will be the startup price+charging price for x months.

200+50x

Hope this helps!! :)

Please let me know if you have any questions

Answer: 4.25 miles

Step-by-step explanation:

The distance he biked on Thursday and Friday combined is:

= 3.5 + 4.25

= 7.75 miles

On Saturday he biked 12 miles. The number of miles he biked over Thursday and Friday is:

= 12 - 7.75

= 4.25 miles

Answer:

1. The probability that she throws a multiple of 3 and flips tails is 1/6

2. The probability that Cymra draws a red marble put it back and draws a red marble again is 25/196

3.  The probability that Cole flips three tails in a row, P(3T) is 1/8

4. The number of shots Linda is expected to make if she takes 175 shots is 56

Step-by-step explanation:

1. The number of sides on the special die Li rolls = 12 sides

The numbers on the die are 1 through 12

The number of faces on the penny = 2 (heads and tails)

The number of multiples of 3 on the die = 3, 6, 9, and 12 = 4

The probability that she throws a multiple of 3, P(3) = 4/12 = 1/3

The probability that she flips tails rather than heads = 1/2

∴ The probability that she throws a multiple of 3 and flips tails = 1/3 × 1/2 = 1/6

2. The number red marbles in the bag = 5

The number green marbles in the bag = 6

The number blue marbles in the bag = 3

The total number of marbles in the bag = 5 + 6 + 3 = 14

The probability that Cymra draws a red marble put it back and draws a red marble again is given as follows;

The probability with replacement of picking two red marbles = 5/14 × 5/14 = 25/196

3. The probability that Cole flips three tails in a row P(3T) = (1/2)×(1/2)×(1/2) = 1/8

The probability that Cole flips three tails in a row, P(3T) = 1/8

4. The percentage of times Linda makes her free throws in the past 5 basketball practices = 32%

The number of shots she is expected to make if she takes 175 shots = 175 × 32/100 = 56.

Answer:

16.33628179866692

Step-by-step explanation:

I dont know how far you wanted me to round so you will have to do that part

Answer:

x=146 degrees

Step-by-step explanation:

A supplementary angle is the conrisponding angle that adds to the other angle so it is 180. So 180-34= 146

Answer:

Yes

Step-by-step explanation:

You will get $279,841.74 in that 50 years.

Answer:

3 solutions:

[tex]\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}} [/tex]

Step-by-step explanation:

So, first of all, we need to figure the angles that cannot be included in our answers out. The only function in the equation that isn't defined for some angles is [tex]tan(\frac{\theta}{2})[/tex] so let's focus on that part of the equation first.

We know that:

[tex]tan(\frac{\theta}{2})=\frac{sin(\frac{\theta}{2})}{cos(\frac{\theta}{2})}[/tex]

therefore:

[tex]cos(\frac{\theta}{2})\neq0[/tex]

so we need to find the angles that will make the cos function equal to zero. So we get:

[tex]cos(\frac{\theta}{2})=0[/tex]

[tex]\frac{\theta}{2}=cos^{-1}(0)[/tex]

[tex]\frac{\theta}{2}=\frac{\pi}{2}+\pi n[/tex]

or

[tex] \theta=\pi+2\pi n[/tex]

we can now start plugging values in for n:

[tex] \theta=\pi+2\pi (0)=\pi[/tex]

if we plugged any value greater than 0, we would end up with an angle that is greater than [tex]2\pi[/tex] so,  that's the only angle we cannot include in our answer set, so:

[tex]\theta\neq \pi[/tex]

having said this, we can now start solving the equation:

[tex]tan(\frac{\theta}{2})=sin(\theta)[/tex]

we can start solving this equation by using the half angle formula, such a formula tells us the following:

[tex]tan(\frac{\theta}{2})=\frac{1-cos(\theta)}{sin(\theta)}[/tex]

so we can substitute it into our equation:

[tex]\frac{1-cos(\theta)}{sin(\theta)}=sin(\theta)[/tex]

we can now multiply both sides of the equation by [tex]sin(\theta)[/tex]

so we get:

[tex]1-cos(\theta)=sin^{2}(\theta)[/tex]

we can use the pythagorean identity to rewrite [tex]sin^{2}(\theta)[/tex] in terms of cos:

[tex]sin^{2}(\theta)=1-cos^{2}(\theta)[/tex]

so we get:

[tex]1-cos(\theta)=1-cos^{2}(\theta)[/tex]

we can subtract a 1 from both sides of the equation so we end up with:

[tex]-cos(\theta)=-cos^{2}(\theta)[/tex]

and we can now add [tex]cos^{2}(\theta)[/tex]

to both sides of the equation so we get:

[tex]cos^{2}(\theta)-cos(\theta)=0[/tex]

and we can solve this equation by factoring. We can factor [tex]cos(\theta)[/tex] to get:

[tex]cos(\theta)(cos(\theta)-1)=0[/tex]

and we can use the zero product property to solve this, so we get two equations:

Equation 1:

[tex]cos(\theta)=0[/tex]

[tex]\theta=cos^{-1}(0)[/tex]

[tex]\theta={\frac{\pi}{2}, \frac{3\pi}{2}}[/tex]

Equation 2:

[tex]cos(\theta)-1=0[/tex]

we add a 1 to both sides of the equation so we get:

[tex]cos(\theta)=1[/tex]

[tex]\theta=cos^{-1}(1)[/tex]

[tex]\theta=0[/tex]

so we end up with three answers to this equation:

[tex]\theta={0, \frac{\pi}{2}, \frac{3\pi}{2}} [/tex]

Answer:

its D. 3

Step-by-step explanation:

for speed runners

Answer:

The equation of the line is;

y = 0.8x + 1

Step-by-step explanation:

Here, we want to get the equation of the line

The general equation of a straight line is;

y = mx + b

m

is the slope and b is the y-intercept

The y-intercept is simply the point on the y-axis where the line crosses the y-axis

we have this point at (0,1)

so we have;

y = mx + 1

to get m, we get any other point on the line and substitute its coordinates before we solve for m

we can identify the point (-2.5, -1)

substituting the coordinates

-1 = -2.5(m) + 1

-2.5m = -1-1

-2.5m = -2

m= 2/2.5

m= 0.8

so we have the equation of the line as;

y = 0.8x + 1

Answer:

I know. It's a pain. I just put tons of points on and that seems to attract people.

Step-by-step explanation:

Answer:

D. 16

Step-by-step explanation:

You first need to find the total percentage who liked vanilla, then subtract it from the total percentage of chocolate.

To find the total of those who liked vanilla you would have to add the given percentages and then subtract that from 100.

Chocolate: 42%

Strawberry: 18%

Coffee: 14%

Vanilla: x

42 + 18 = 60 + 14 = 74%

100 - 74 = x

Vanilla = x = 26%

To find how many more like chocolate than vanilla, you would subtract the two percentages.

Chocolate: 42%

Vanilla: 26%

42 - 26 = 16

Answer and Step-by-step explanation:

Theoretically, we should expect the coin to flip 250, or very close to 250 times, and land on heads.

This is because the probability of getting heads is [tex]\frac{1}{2}[/tex], or 50%.

There is a 50% chance of landing heads or tails, so that means it would land 250 times on heads out of 500 flips of the coin.

#teamtrees #PAW (Plant And Water)

Answer:

250 times

Step-by-step explanation:

The coins has the heads or tails, with two options there is a 50% probability of landing on heads or tails.

500 x 50% = 250 times

Answer:

117.3

Step-by-step explanation:

7*4=117.29=117.3

Answer:

it will be x < 2

Step-by-step explanation:

Because the circle means greater than or less than. And if the circle isn't fillied up it means it is greater than or equal to or less thanor equal to.

Answer:

Use M a t h W a y

Step-by-step explanation:

it all together

The error interval for x would be (3.65, 3.75), indicating that the true value of x lies within this range.

Given that a number x is rounded to 1 decimal place and its 3.7.

We need to find the error of the interval for x,

To determine the error interval for the rounded number 3.7, we need to consider the possible range of values that could have been rounded to 3.7 when rounded to 1 decimal place.

When rounding to 1 decimal place, we look at the digit immediately to the right of the decimal point. If this digit is 5 or greater, we round up. If it is less than 5, we round down.

In this case, 3.7 is the rounded value, which means the original number could have been rounded up from a value greater than or equal to 3.65 or rounded down from a value less than 3.75.

Therefore, the error interval for x would be (3.65, 3.75).

Learn more about error interval click;

https://brainly.com/question/30473763

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