Jorge and Mary are both filling cups with fruit punch in preparation for a party. After 3 minutes, Jorge had 53 cups left to be filled, and after 5 minutes, he had 25 cups left to be filled. Mary’s progress is shown in the table of values below. Assuming that both Jorge and Mary are filling cups at a constant rate, which statement is correct?


Mary’s Cup-Filling Progress
Time (minutes)

0.5

1

1.5

2

2.5
Cups Remaining

99

81

63

45

27

Jorge is filling 14 cups per minute, which is faster than Mary.
Jorge is filling 28 cups per minute, which is faster than Mary.
Mary is filling 18 cups per minute, which is faster than Jorge.
Mary is filling 36 cups per minute, which is faster than Jorge.

Answer:

Mary is filling 36 cups per minute, which is faster than Jorge.

Step-by-step explanation:

Lets get Jorge's time :

As the rate is constant, we can find the slope to know the number of cups he is filling per minute.

Slope is found using: [tex]\frac{y2-y1}{x2-x1}[/tex]

= [tex]\frac{53-25}{5-3}[/tex]

= [tex]\frac{28}{2}=14[/tex]

From the table lets get Mary's time:

[tex]\frac{99-81}{1-0.5}[/tex]

= [tex]\frac{18}{0.5}=36[/tex]

Another data: [tex]\frac{63-45}{2-1.5}[/tex]

=  [tex]\frac{18}{0.5}=36[/tex]

Therefore, we can see that Mary is filling 36 cups in a minute and Jorge is filling 14 cups.

Hence, the correct answer is : Mary is filling 36 cups per minute, which is faster than Jorge.

Answer:

Mary is filling 36 cups per minute, which is faster than Jorge.

Step-by-step explanation:

find the number of liters in 90 gallons

If CDEF ≅ MNPQ, then ≅ DE ≅

a. NP
b. PQ
c. NQ
d. MN

* there's no picture this is all the information the question gives me *

What is the slope of the line that passes through (10,0) and is parallel to y=1/2x+3

30 POINTS!!! HELP PLEASE!
Model each scenario with an equation and a sketch. Solve for the missing value and u. Use complete sentences to interpret the solution. In your final answer, include your equation, sketch, interpretation, and all calculations necessary for the solution.

1.) To get home from school, Bob walks four blocks north and three blocks east. What is the straight line distance between Bob’s house and his school?

2.)One of the requirements of your summer window-washing job is to provide yourself with all of the necessary supplies, including a fourteen foot ladder. When you arrive at your first job, you place your ladder on the ground six feet from the base of the house and lean it towards a second story window, only to realize that the ladder doesn’t reach the window. Given the length of the ladder and its current position, what is one possible height of the second story window? (Hint: There is more than one correct answer.)

3.) In a softball diamond, each of the bases, including home plate, are equidistant from each other. Although the name implies differently, a softball diamond is in the shape of a square. Given that the distance between the bases is unknown, determine an expression for the straight line distance between first and third bases.

4.) A sailboat drifts 600 meters west, makes a turn and sails 800 meters south. How far is the sailboat from its original position?

what are the lengths of the other two sides of the triangle?

Which unit would you use to measure the weight of an elephant? mg g kg km

1
Which mathematical symbol would best fill in the blank to compare the two real numbers? 7.6 repeating____55 squared


<
>
=
≈

2
Convert 11.42424242 … to a rational expression in the form of a/b , where b ≠ 0.

42/999 with 11 whole number
42/9990 with 11 whole number
42/99 with 11 whole number
99/42 with 11 whole number

3
Order the set of numbers from least to greatest: -5/6, -5, -26 squared, -31/6


4
Identify the number that does not belong with the other three. Explain your reasoning
50.1 reapting , -50/2, , -50.1, 50 squared

justin runs at a constant rate, traveling 17km in 2 hours whats the equation

how do you do #8,9,10 ?? thank you !!

In the game of​ roulette, a player can place a ​$55 bet on the number 3434 and have a startfraction 1 over 38 endfraction 1 38 probability of winning. if the metal ball lands on 3434​, the player gets to keep the ​$55 paid to play the game and the player is awarded an additional ​$175175. ​otherwise, the player is awarded nothing and the casino takes the​ player's ​$55. what is the expected value of the game to the​ player

Adam wrote a check for $38 to pay his monthly gas bill, but when balancing his checkbook, he accidentally recorded it as credit rather than as a debit. How will his check register compare to his monthly bank statement when he receives it?

find the greatest common factor: 14a^4 + 35a^9

The inverse of f(x)

A 72?? sector in a circle has an area of 16.4?? yd??.

What is the area of the circle?

Use 3.14 for pi.

Enter your answer as a decimal in the box.

A group of kindergartners and first graders were asked whether or not they can ride a bike. This table shows the relative frequencies of the rows for the two-way table representing this situation. Select from the drop-down menus to complete the statement. The percent of kindergartners surveyed who can ride a bike is (choose-greater than ,less than, equal to) the percent of first graders surveyed who can ride a bike. 
                         Can ride a bike    Cannot ride a bike
Kindergartners.         0.32.                  0.68
First graders.             0.56.                   0.44

in the inverse variation function, what happens to the output when the function's input value is divided by 3?

Which equation of the least squares regression line most closely matches the data set?

Note: The variable x represents the years after 1970.

Y= -5.7x-67
Y= -0.98x+65
Y= -0.17x+76
Y= -5.7x +67

How do I find the slope of (2,3) and (5,9) by showing all of my work

The proof that HG ≅ EG is shown. Given: G is the midpoint of KF KH ∥ EF Prove: HG ≅ EG What is the missing reason in the proof? Statement Reason 1. ∠EGF ≅ ∠HGK 1. vert. ∠s are ≅ 2. KH ∥ EF 2. given 3. ∠F ≅ ∠K 3. alt. int. ∠s are ≅ 4. G is the midpoint of KF 4. given 5. FG ≅ KG 5. def. of midpt. 6. △FEG ≅ △KHG 6. ? 7. HG ≅ EG 7. CPCTC SAS ASA AAS HL

20 POINTS!!
In two or more complete sentences, explain what additional information is needed to prove triangle CES congruent to triangle RST.

In order to circumscribe a circle on a triangle, which line must you construct?

a.median

b.altitude

c.diagonal

d.perpendicular bisector

Nina has 2 cups of flour. However, this is only 1/4 of the amount of flour she needs for a bread recipe. How many cups of flour does the recipe call for?

An accountant pays 8% per year simple intrest, in year 1 the amount in the account is $850 how much is the account in year 6?

kangaroo wants to arrange the twelve numbers from 1 to 12 in a circle in such a way that any neighboring numbers always differ by either 1 or 2 which of the following pairs of numbers have to be neighbors

A quadrilateral with two sets of parallel sides and four right angles is a
parallelogram
rhombus
rectangle
trapezoid

The figure below shows triangle NRM with r2 = m2 + n2:

Triangle NRM has legs m and n, and r is the length of its longest side.

Ben constructed a right triangle EFD with legs m and n, as shown below:

Triangle EFD has legs m and n and hypotenuse f.

He made the following table to prove that triangle NRM is a right triangle:


Statement Reason
1. r2 = m2 + n2 Given
2. f2 = m2 + n2 Pythagorean Theorem
3. f2 = r2 Substitution
4. f = r Square Root Property of Equality
5. Triangle NRM is congruent to triangle EFD ?
6. Angle NRM is a right angle CPCTC
7. Triangle NRM is a right triangle Angle NRM is a right angle

Which reason best fits statement 5?
SSS Postulate
SAS Postulate
AAA Postulate
AAS Postulate

Solve for X:
X + 25 = 45

Can someone help me please?

If you take a certain number 2.5 times then add 1.75 and divide the result by 0.8, you’ll get 37.5. What was the original number?

Please show how you did it!

Find the nonpermissible replacement for a in this expression 3/4a