Let f be defined as shown on the graph. Which statement is true?

1: The inverse of f exists
2: The inverse of f does NOT exist

Answer:

y=6

Step-by-step explanation:

Point O is the center of the circle passing through points D, E, and F because it is equidistant from all these points. This is proven by the construction of the perpendicular bisectors of DE and EF and their intersection at point O.

The point O is the center of the circle that passes through the three points D, E, F because it is equally distanced from each of them. Here's why: When you draw perpendicular bisectors of lines DE and EF, you're effectively finding the midpoint of each line. Then, when these bisectors intersect at point O, point O is equidistant from points D and E (due to being on the bisector of DE), and from points E and F (due to being on the bisector of EF).

By definition, the center of a circle is a point that is equidistant from all points on the circle's circumference. Hence, because points D, E, and F are on the circumference and are equidistant from O, O is the center of the circle passing through points D, E, and F.

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Point O is the center of the circle passing through points D, E, and F because it is equidistant from the vertices of triangle DEF, which is confirmed by the properties of the perpendicular bisectors of line segments DE and EF that intersect at point O.

To determine that point O is the center of the circle passing through points D, E, and F, we use the properties of perpendicular bisectors in a triangle. When we draw the line segments DE and EF, we are essentially drawing two sides of the triangle DEF. Constructing the perpendicular bisectors of these sides involves finding the midpoint of each side and then drawing a line that is perpendicular to that side at its midpoint.

The point where these two perpendicular bisectors intersect, point O, is equidistant from the vertices of the triangle (D, E, and F). This is because the perpendicular bisector of a line segment has the property that every point on the bisector is equidistant from the two endpoints of the segment. In the case of triangle DEF, point O is equidistant from D and E, since it lies on the bisector of DE, and is also equidistant from E and F, since it lies on the bisector of EF.

Since point O is equidistant from all three vertices of the triangle, it can serve as the circle's center, with the radii to the vertices being equal. This circle that we have created by using this method is also known as the circumcircle of triangle DEF, and point O is referred to as the circumcenter.

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If I am understanding you correctly,  first solve for the whole sector, which you can use this formula. 

[tex] \frac{\Theta}{360} \pi r^2[/tex] 

Once you find the area of the sector, all you have to do is get the area of the triangle and then subtract the area of the triangle from the sector and that will tell you the area of CFD and CED and let you know which one is greater.

For instance, Lets find A

sector area = [tex] \frac{90}{360} \pi 10^2 = 25\pi [/tex] 

Now lets get the area of the triangle, which is 

area triangle = [tex] \frac{1}{2} bh\sin C[/tex]

area triangle = [tex] \frac{1}{2} \times 10 \times 10 \times sin 90 = 50m^2[/tex]

CED =  sector area - area of triangle = [tex] 25\pi - 50 = 28.53m^2[/tex]

Now lets find B

sector area = [tex] \frac{60}{360} \pi 12^2 = 24\pi [/tex] 

Now lets get the area of the triangle, which is 

area triangle = [tex] \frac{1}{2} bh\sin C[/tex]

area triangle = [tex] \frac{1}{2} \times 12 \times 12 \times \sin 60 = 36\sqrt(3)[/tex]

CFD = sector area - area of triangle = [tex] 24\pi - 36\sqrt(3) = 13.04m^2[/tex]

So A has the greater area base.

i checked the answer he had he is right :>

The probability that the first winner is from Pike and the second from Wells is 1/6, found by multiplying the individual probabilities of each event happening in sequence.

The question asks for the probability that the first winner comes from Pike and the second from Wells in a random drawing. With 10 customers in total, 3 from Pike and 5 from Wells, the probability of drawing a Pike resident first is 3/10. If that happens, one less customer is available, leaving 9, with 5 still from Wells.

So, the probability for the second draw is 5/9. Multiplying these probabilities gives the combined probability for both events happening in sequence. Therefore, the required probability is (3/10) * (5/9), which simplifies to 1/6.

The probability that both customers selected are Pike residents is [tex]{\frac{28}{153}}[/tex]

To find the probability that both customers selected are Pike residents, follow these steps:

1. Calculate the probability that the first customer is a Pike resident:

  - There are 18 customers in total.

  - There are 8 Pike residents.

  - So, the probability that the first customer is a Pike resident is:

  [tex]\[ \frac{8}{18} = \frac{4}{9} \][/tex]

2. Calculate the probability that the second customer is also a Pike resident, given that the first one was a Pike resident:

  - After selecting the first Pike resident, there are now 17 customers left.

  - There are now 7 Pike residents remaining.

  - So, the probability that the second customer is a Pike resident, given the first was a Pike resident, is:

  [tex]\[ \frac{7}{17} \][/tex]

3. Calculate the combined probability:

  - Since the selections are dependent events (one customer is selected after another without replacement), multiply the probabilities of each step:

  [tex]\[ \left( \frac{4}{9} \right) \times \left( \frac{7}{17} \right) \][/tex]

4. Simplify the multiplication:

  - Multiply the numerators: [tex]\(4 \times 7 = 28\)[/tex]

  - Multiply the denominators: [tex]\(9 \times 17 = 153\)[/tex]

  - So, the combined probability is:

    [tex]\[ \frac{28}{153} \][/tex]

Answer:

Option D. 20 minutes.

Step-by-step explanation:

It has been given in the question that distance between the shore of a lake is 3 miles.

Speed of Jim is 4 mph and speed of John is 5 mph.

Let they meet after time t hours.

Therefore distance traveled by Jim in t hours = 4×t miles

and distance traveled by John in t hours = 5×t miles

Total distance they cover = 3 miles.

Now 4t + 5t = 3

9t = 3

t = 3/9 hours.

t = (3×60)/9 minutes.

t = 20 minutes.

Answer is they will meet after 20 minutes.

Answer:

All boys in each grade.

Step-by-step explanation:

The teacher wants to know specifically about whether the boys in the entire school prefer watching television or playing outdoor games after school. The teacher does not include girls, or specifically people on the football team. The teacher also only wants to know about boy students not teachers.

Final answer:

The taxable earnings column of a payroll register records the amount of earnings that are subject to taxes.

Explanation:

The taxable earnings column of a payroll register records the amount of earnings that are subject to taxes. In payroll, taxable earnings refer to the portion of an employee's wages or salary that is subject to various taxes, such as income tax and Social Security tax.

For example, if an employee earns $1,000 per week and the income tax rate is 20%, the taxable earnings would be $800 ($1,000 - $200).

It's important to note that not all earnings may be taxable. Some types of income, such as certain reimbursements or non-taxable fringe benefits, may be excluded from taxable earnings.

he needs  1/4 gallon total

4 walls so need to divide 1/4 x 4

1/4 / 4/1 = 1/4 * 1/4 = 1/16 gallon on each wall

Answer:

He needs [tex]\frac{1}{16}[/tex] of gallon to paint each wall.

Step-by-step explanation:

Given :  He needs 1/4 of a gallon to paint all four walls .

To Find : How much paint will he need for each of his 4 walls if he uses the same amount of paint on each .

Solution:

He needs 1/4 of a gallon to paint all four walls .

He need paint to color 1 wall = [tex]\frac{\frac{1}{4}}{4}[/tex]

                                               = [tex]\frac{1}{16}[/tex]

Hence he needs [tex]\frac{1}{16}[/tex] of gallon to paint each wall.

I think by 1-5 you mean 1/5??

1/5 = 0.20 = 20%

50% + 20% = 70%

100-70 = 30

 so 30% were sponge cakes

Answer: [tex]6\sqrt{2}\ in[/tex]

Step-by-step explanation:

Given: In a 45-45-90 triangle, the length of one of the legs= 6 in.

Let h be the hypotenuse of the given right triangle.

Since the two angles are equal (45°) in the given right triangle,Moreover in a triangle the side opposite to the equal angles are equal.

Therefore, the other leg of given right triangle = 6 in.

Thus by Pythagoras theorem, we get

[tex]h^2=6^2+6^2=36+36\\\\\Rightarrow\ h^2=72\\\\\Rightarrow h=\sqrt{72}\\\\\Rightarrow h=6\sqrt{2}\ in[/tex]

Hence, the length of its hypotenuse = [tex]6\sqrt{2}\ in[/tex]

The probability of getting the desired outcome is 5/12.

Like "point" and "time," the concept of "the likelihood of anything" is one of those concepts that we can't precisely describe but that are nevertheless helpful. The four most popular approaches to probability are classical, empirical, subjective, and axiomatic.

Given flip a coin and roll a 6-sided die. to find the probability that you will flip a head and roll less than a 6. since there are two events that are separated from each other hence we need to find out the probability of both P(a∪b). hence,

probability of getting head on a coin flip P(a) = 1/2

probability of getting less than 6 on dice roll P(b) = 5/6

Probability of getting both the vent simultaneously = P(a) * P(b)

Therefore, the Probability of getting flipped a head and rolling less than a 6 is 5/12.

Learn more about probability here:

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