Mathematics Middle School

The rest of the students in the play are from Mr. Logan’s class and Ms. Gardner’s class.
Mr. Logan has 23 students in his class, and 7 of them are in the play. There are 4 more students from Ms. Gardner’s class than from Mrs. Cho’s class in the play.
The number of students in the play from Mr. Logan’s class is greater than the number from Mrs. Cho’s class and fewer than the number from Ms. Gardner’s class.
In all, 30% of the students in these three classes are in the play.

Show or explain why there must be exactly 23 students in Ms. Gardner’s class. As part of the explanation, determine how many students from Ms. Gardner’s class are in the play.

Answers

Answer 1

There should be 23 students from Ms. Gardner’s class in the play.

To determine why there must be exactly 23 students in Ms. Gardner's class and to find out how many students from Ms. Gardner's class are in the play, let's break down the problem step-by-step.

Define Variables:

  - Let L be the number of students in Mr. Logan's class.

  - Let G be the number of students in Ms. Gardner's class.

  - Let C be the number of students in Mrs. Cho's class.

  - Let [tex]P_L[/tex] be the number of students from Mr. Logan's class in the play.

  - Let [tex]P_G[/tex] be the number of students from Ms. Gardner's class in the play.

  - Let [tex]P_C[/tex] be the number of students from Mrs. Cho's class in the play.

Given Information:

  - L = 23

  - [tex]P_L[/tex] = 7

  - There are 4 more students from Ms. Gardner's class in the play than from Mrs. Cho's class: [tex]P_G[/tex] = [tex]P_C[/tex] + 4

[tex]P_G[/tex]

  - The number of students in the play from Mr. Logan's class is greater than the number from Mrs. Cho's class and fewer than the number from Ms. Gardner's class: [tex]P_C[/tex] < 7 < [tex]P_G[/tex]

  - 30% of the students in these three classes are in the play.

Calculate Total Students and Students in the Play:

  - Total students in these three classes: L + G + C

  - Total students in the play: [tex]P_L[/tex] + [tex]P_G[/tex] + [tex]P_C[/tex]

30% of the Students are in the Play:

  - 0.30 (L + G + C) = [tex]P_L[/tex] + [tex]P_G[/tex] + [tex]P_C[/tex]

Substitute L = 23 and [tex]P_L[/tex] = 7:

0.30 (23 + G + C) = 7 + [tex]P_G[/tex] + [tex]P_C[/tex]

Using [tex]P_G[/tex] = [tex]P_C[/tex] + 4 :

0.30 (23 + G + C) = 7 + ([tex]P_C[/tex] + 4) + [tex]P_C[/tex]

0.30 (23 + G + C) = 7 + [tex]P_C[/tex] + 4 + [tex]P_C[/tex]

0.30  (23 + G + C) = 11 + 2[tex]P_C[/tex]

Simplify the equation:

0.30 (23 + G + C) = 11 + 2[tex]P_C[/tex]

0.30 × 23 + 0.30G + 0.30C = 11 + 2[tex]P_C[/tex]

6.9 + 0.30G + 0.30C = 11 + 2[tex]P_C[/tex]

Rearrange the equation:

0.30G + 0.30C = 11 + 2[tex]P_C[/tex] - 6.9

0.30G + 0.30C = 4.1 + 2[tex]P_C[/tex]

Divide by 0.30:

G + C = [tex]\frac{4.1 + 2P_C}{0.30}[/tex]

G + C = [tex]\frac{4.1}{0.30} + \frac{2P_C}{0.30}[/tex]

G + C = [tex]\frac{41}{3} + \frac{20}{3}P_C[/tex]

G + C = [tex]\frac{41 + 20P_C}{3}[/tex]

From the constraints [tex]P_C[/tex] < 7 < [tex]P_G[/tex] and [tex]P_G[/tex] = [tex]P_C[/tex] + 4:

[tex]P_G[/tex] = 7

[tex]P_C[/tex] = [tex]P_G[/tex] - 4 = 7 - 4 = 3

So,

G + C = [tex]\frac{41 + 20 \cdot 3}{3} = \frac{41 + 60}{3} = \frac{101}{3}[/tex]

G + C = 33.67

Since G and C must be integers and they add up to 33.67, we need to check for plausible values of G and C. However, considering our assumptions and given constraints, we should use consistent integer values:

For:

[tex]P_G[/tex] = 7

[tex]P_C[/tex] = 3

Using the total students equation:

0.30(23 + G + C) = 7 + 7 + 3

0.30(23 + G + C) = 17

Thus:

23 + G + C = [tex]\frac{17}{0.30}[/tex]

23 + G + C = 56.67

So:

G + C = 56.67 - 23 = 33.67

Given [tex]P_C[/tex] < 7 < [tex]P_G[/tex], by resolving as integers:

G = 23

C = 11

Thus, Ms. Gardner's class must have 23 students.

Related Questions

Serena is making a model of one of the Egyptian pyramids. The square base has sides that are all 4.4 in. Each of the triangular faces has a base of 4.4 in and a height of 3.8 in. How much paper would it take to cover the entire pyramid?





A.
73.57 sq in
B.
82.78 sq in
C.
52.8 sq in
D.
12.6 sq in


Answers

We can tell that we are solving for area because the question asked "how much paper to cover the entire pyramid". Notice that the image is the net of the pyramid, so we can find the area of the square (base), and then the area of the triangles (walls) and add them all together to find the total area. 

Area of a Square: Length x Width
 
A = 4.4 x 4.4
A = 19.36

Area of a Triangle: [tex] \frac{Base x Height}{2} [/tex]

A = 4.4 x 3.8 ÷ 2
A = 8.36

** We have 4 triangles, and 8.36 is the area for ONE triangle. We can multiply this by 4 to determine the area of all of the triangles together. 

8.36 x 4 = 33.44

Now that we have our area for the base of the pyramid and the walls of the pyramid, we can add them together to determine the total area, and how much paper Serena will need. 

19.36 + 33.44 = 52.8

So, Serena will need 52.8 [tex] in^{2} [/tex] of paper to cover the entire pyramid. 

the circumfrence of a circle is 11 pie inches. what is he the area, in square inches, of the circle? Express your answer in terms of PIE

Answers

Please:  use "pi," this mathematical quantity is not written as "PIE."

Since C=2pi*r, and C=11 inches, r=(11 inches)/(2pi), or
                                                    r^2 = (121 sq in)/(2pi)

Then the area of this circle is A = pi*r^2, or pi*(121 sq in)/(4pi^2).  Reduce this and you will then have the area correct.  Its units of measurement are (inches)^2.

Can ratios have decimals in them or do all the numbers have to be integers? E.g. is 7.8:1.3:6.5 a valid ratio?

Answers

What you have is a valid ratio in theory, but it might be easier to understand if it were simplified to integers:

78:13:65

It also depends on what your teacher is asking of you.

Final answer:

Yes, ratios can include decimals. They can represent quantities in numerous contexts such as scale distances, dimensions, and proportions. The ratio 7.8:1.3:6.5 is, therefore, a valid expression.

Explanation:

Ratios can indeed include decimals in them; they do not need to be limited to integers. Ratios are a way to compare two or more quantities, which can be whole numbers, fractions, or decimals. Just as fractions, ratios express the relationship between parts of a whole or between two quantities in a specific order. For example, the ratio 7.8:1.3:6.5 is valid and represents the relative quantities of three different entities. In many contexts, such as in scale distances or dimensions, the use of decimal ratios is quite common. When dealing with scale factor to find actual dimensions, the ratio could also include decimals, as it compares the scale dimensions to actual dimensions of an object or distance. For example, on a map with a unit scale of 1 inch equals 100 feet, the ratio would be written as 1/100 or in decimal form, 0.01/1.

When Mr. Krumm purchased a tie he paid $9.27, which included the 3% sales tax. How many dollars did the tie cost before the tax was included?

Answers

If $9.27 includes the 3% tax, then 
103% = 9.27

To find the price before tax, we need to find 100% of the price.

103% = 9.27
1% = 0.09
100% = 0.09 x 100 = $9

The price before tax is $9.

I hope this helps :)
the price would be $9

Andrew plays football.On one play,he ran the ball 24 1/3 yards.The following play,he was tackled and lost 3 2/3 yards.The next play,he ran for 5 1/4 yards.Estimate how much farther the ball is down the field after these three plays.Round each mixed numbers to the nearest whole number

Answers

give me a second to recheck my work

Answer: Yes, the team made the third yard goal.

Step-by-step explanation:

I‘m not explaining it to you kid so just copy it from the picture.

I would have explained it to ya but the page refreshed when I took the picture in the camera app and cropped it. It’s the one with the circle around the number of the question and if you can’t figure that out, your just plain stupd

A bicyclist heads east at 10km/h. After she has traveled 24.2 kilometers, another cyclist sets out in the same direction going 30km/h. About how long will it take the second cyclist to catch up to the first cyclist?

Answers

We know that the first cyclist has traveled 24.2 km at a speed of 10 km/h. Lets use the equation [tex]time= \frac{distance}{speed} [/tex] to find the time of the first cyclist:
[tex]t= \frac{24.2}{10} [/tex]
[tex]t=2.42[/tex]
So, we know that she has traveled for 2.42 hours.
 
We also know that after she has traveled for 2.42 hours another cyclist sets out in the same direction, so if [tex]t[/tex] represents the time of our first cyclist, the time of our second cyclist will be [tex]t-2.42[/tex].

Now we are going to use the equation [tex]distance=(speed)(time)[/tex] to relate the speeds and times of the two cyclist:
For the first one:
[tex]distance=10t[/tex] equation (1)
For the second one:
[tex]distance=30(t-2.42)[/tex] equation (2)

Replace (1) in (2)
[tex]10t=30(t-2.42)[/tex]
The only thing left now is solve for [tex]t[/tex]:
[tex]10t=30t-72.6[/tex]
[tex]-20t=-72.6[/tex]
[tex]t= \frac{-72.6}{-20} [/tex]
[tex]t=3.63[/tex]

We can conclude that the second cyclist will catch up the first cyclist after 3.63 hours.


What does 60 inches equal

Answers

30 inches it equals I hope this is right because I don't know a lot about inches
#4: 60 inches is 5 feet.


what is 3yr 4mo-1yr 11mo

Answers

The answer is 1 yr 7mo
1 year= 12 months

CONVERT BOTH TO MONTHS
(3 yrs * 12 mos/yr) + 4 mos = 40 mos
(1yr * 12 mos/yr) + 11 mos = 23

SUBTRACT MONTHS
40 mos - 23 mos= 17 mos

DIVIDE TO FIND # YEARS/MONTHS
17 mos ÷ 12 mos/yr= 1 year 5 months

ANSWER: 1 year 5 months

Hope this helps! :)

Regular triangular pyramid has the slant height k=12 cm and lateral area AL = 198 cm2. Find the length of the base edge.

Answers

To find this answer you will use the formula for finding the area of the triangle because that shape is a triangle.  

A = 1/2 bh
198 = 1/2 x b x 12
198 = 6b
b = 33 cm

We know the total area and we know the slant height is 12 cm so we substitute these in and solve for h.

The length of the base edge is 33 cm.  You should substitute this back in to check.

1/2 x 33 x 12 = 198 square cm.

Answer:

The Answer is: 11 cm

which answer choice shows an expression meaning a number plus 13? A)x-13 B)13x C)x+13 D)x÷13

Answers

Let the number be x 

x plus 13 = x + 13

------------------------------------
Answer: x + 13 (Answer C)
------------------------------------

"number plus 13" = x + 13

Answer is C).

What is 1,000 less than 1,416

Answers

Negative 416.

Solved by subtracting 1,000 by 1,416
          
It’s negative 416. hope

what is 4/5 * 2
[tex] \frac{4}5 \times 2 [/tex]

Answers

 4           2         8
----    x  ----  =  ----  =  1  3/5 or [tex]1 \frac{3}{5} [/tex] or 1.6
 5           1          5
So, one thing that we would really want to do in this case would be (always) keeping the bottom denominator always. We would never want to change this hat so ever. So, the first thing that we would do would be sense we know that we are only timing this by only 2, we just add it, to make it ore simple.

4/5+4/5= 1 so far. We now know that we have a whole number.

So then, we subtract 1 from the next fraction. So then, we would then do 1+3/5.

Remember that we took 0.1 from the other fraction.

Therefore, your correct answer would then be (1) 3/5

I hope this helps you!

the function f(x) varies inversely with x and f(x) = 0.9 when x = 0.5 what is f(x) when x = 1.5 ?

a. 0.02
b. 0.03
c. 0.3
d.0.75

PLEASE HELP ME I WILL MARK BRAINLIEST!!!!!!!!!!!!!

Answers

When x = 0.5, the answer is 0.45
When x = 1.5, the answer is 1.35

You're welcome :)

Answer:

the answer is 0.3

Step-by-step explanation:

The bar graph shows the number of dinner reservations at a restaurant for one week. What percent of the reservations were for Friday or Saturday? Monday 15 Tuesday 5 Wednesday 10 Thursday 25 Friday 40 Saturday 30 Sunday 35

Answers

15 + 5 + 10 + 25 + 40 + 30 + 35 = 160
Friday plus Saturday : 40 + 30 = 70
70 ÷ 160 = 0.4375
 43.75 %

Solve for x.
cx + ax = b

A) b/(c + a)

B) (-b)/(c + a)

C) b - c - a

D) b + c + a

Answers

The answer is A) b/(c+a)
Hope this helps

There are 80 members of the show choir. For a fund raiser 95% of the members raised money, how many members did NOT raise money. PLEASE HELP PLEASE

Answers

To find out how many did not raise money, we need to find the percentage that did not raise money and multiply that by the total number of members.

If 95% raised money, 5% did not raise money.

0.05 x 80 = 4 members did not raise money

Katie painted a wall in her bedroom that is 10.5 feet tall and 23.5 feet wide shoes exactly 3 quarts of paint to cover the wall how many square feet will 1 quart of paint cover

Answers

I believe that the answer is 82.25 because 10.5 x 23.5 is 246.75 feet ^2, and since 3 quarts can cover 246.75 feet^2 all you would have to do is divide 246.75 by 3. When you do that the answer will be 82.25 feet.

ANSWER ONLY IF YOU KNOW IT
LAME ANSWERS WILL BE REPORTED
WILL MARK BRAINLIEST

Suppose you want to buy a bike. The prices are $119, $139, $149, $179, $189, $199, and $209. You want the bike that costs $189. Should you use mean, median, or mode to convince your parents? Explain.

Answers

For mean:
119 + 139 + 149 + 179 + 189 + 199 + 209 = 1183
1183/7 (for the amount you added) = 169

For median: 

119, 139, 149, 179, 189, 199, 209.
Find the middle number: 179 (is your median)

For mode: 

119, 139, 149, 179, 189, 199, 209
Find the number that shows up the most: N/A (they all only show up once)


I believe Median will be your best choice (it has the closest answer to 189)

hope this helps
Hi!

The median would be your best bet at convincing your parents to get you a new bike for $189 because the median which is $179 is the closest value to the one you want.

-ASIAX ∵Frequent Answerer∴

P.S. Give Rohanfighter the brainliest his answer is better.

naomi needs to solve 28 ÷ 7 = ?what related multiplication fact can she use to find the unknown number?

Answers

28/7 =4
7•4 is 28 or
7+7+7+7 is also 28

Explain how you can compare the size of a product to the size of a factor when multiplying fractions without actually doing multiplication including model

Answers

Answer: If you multiply a number by a fraction less than 1, the resulting product will be smaller than the original fraction.

Imagine, if you had half a pizza and you ate one-half of that. You would multiply 1/2 by 1/2 and get an even smaller number. The result would be 1/4.

On the other hand, if you multiply a number by a mixed number that is larger than one, the result would be larger than when you started.

The Comparison size of product and factors is shown below.

What are factors?

A factor is a number that completely divides another number. To put it another way, if adding two whole numbers results in a product, then the numbers we are adding are factors of the product because the product is divisible by them.

For example, 3 and 6 are factors of 12 because 12 ÷ 3 = 4 exactly and 12 ÷ 6 = 2 exactly.

A fraction less than one will result in a smaller product than the initial fraction when multiplied by a number.

Imagine that you only ate half of the pizza you ordered.

You would get a smaller value if you multiplied 1/2 by 1/2. It would come out to 1/4.

On the other hand, the outcome would be more than the starting value if you multiplied a number by a mixed number that is greater than one.

Learn more about factors here:

https://brainly.com/question/24182713

#SPJ5

A rectangular piece of poster board measurea 60 centimeters by 80 centimeters. Linn draws the net of a box on the poster board and cuts it out. If the box measures 10 centimeters by 16 centimeters by 27 centimeters, what is the area of the poster board left....



Plz help me....
thank you

Answers

To find the answer for that question you have to find the area of rectangle first, so you say 60*80 which equals to 4800 cm squared and then find the area of the box and not its volume so you say: 2(16*10)=2*160=320 cm squared
                                                              4(16*27)=4*432=1728 cm squared 
add 320+1728= 2048 cm squared 
Finally, to find the area of the left poster board you have to subtract the area of the rectangle which is 4800 cm squared by the area of the box which is 2048 cm squared so 4800-2048=2752 cm squared 

Please provide work with your answer pls, 20 point question

Answers

The number 350, would be side A.
The number 1000 would be side b

Tanx = 350/1000
x = 19
19 is your answer

A storage room measures 48 inches by 60 inches.what is the total area in square feet of the closet?

Answers

2880 square feet squared
The answer is 240ft because 48 * 60 = 2880
2880 / 12 = 240

one-half of a number increased by 16 is 4 less than two-thirds of the number what is the number.

Answers

We need to create an equation for this.   Let x be the number we want to find. Then 1/2x  + 16 = 2/3x - 4   Multiplying both sides by the common denominator 6, we have   3x + 96 = 4x - 24 x = 120   Inserting 120 into the equation to check, we have 1/2 (120) + 16 = 2/3 (120) - 4 76 = 76

In this box-and-whisker plot, what is the maximum value of the data?


53

56

60

68

Answers

there is a dot under 68 which is the highest number
 answer is 68

68 The answer will be I know this. The answer 68

The center on a target has a diameter of 5 inches. The whole target has a diameter of 25 inches. The center of the target takes up ____% of the whole target

Answers

4%

To find the percentage, first find the area of both circles. The area formula is [tex] \pi r^{2} [/tex] . After finding the area of the center of the target (19.625) and the area of the large target (490.625), set up a percent proportion to determine the percentage that the center takes up: 

[tex] \frac{is}{of} = \frac{percent}{100} [/tex]


[tex] \frac{19.625}{490.625} = \frac{percent}{100} [/tex]


Cross multiplying and dividing by 490.625 will give a total of 4%.

find the area of a triangle with 4 yd and 8 yd

Answers

The answer would be 16 sq yds!

The formula for finding the area of a triangle is:

a = [tex] \frac{1}{2} [/tex] lh
Where l is the length of the triangle and h is the height.

So the formula would be a = [tex] \frac{1}{2} [/tex] 4*8 which equals 16!
24 hope this helps
Well you have to add
+8 which makes 12 so add 12 and you get 24

MATH HELP LEASE WILL GIVE BRAINLIEST!!!
Quadrilateral ABCD ​ is inscribed in this circle.



What is the measure of angle B?

Enter your answer in the box.

m∠B=
°

Answers

The answer is (22) hope it helps have a great day

4a - 4( 15a - 2) - 8

Answers

Hello!

The problem to solve: 4a - 4(15a - 2) - 8

The first thing to do is to apply the Distributive Property, which is: a(b + c) = ab + ac.

Here we have: -4(15a - 2). We must multiply -4 by 15a and -2. Let's do it.

4a - 4(15a - 2) - 8
4a - 60a + 8 - 8

Now we can go ahead and combine like terms; add the constants and add the a-terms. 4a minus 60a is equal to negative 56a. 8 minus 8 is zero, so the 8's cancel out, and we're left with:

-56a

That's your answer! I hope this helps you. (:
 Hey there!

In order to simplify this expression (notice how it's an expression and not an equation because it's not set equal to something) we can use addition and subtraction, and the distributive property which is defined as:

a(b+c) = ab + ac

Using this property, we can simplify this expression to:

4a - 60a + 8 - 8

Notice how -4(-2) was positive 8.

Simplify "a" terms:

-56a + 8 - 8

Since it's +8 - 8, the 8's cancel out.

Therefore, we just have -56a.

Hope this helps!


Write this number in standard form.


one and four tenths

Answers

7/5 is the answer, glad I could help

[tex]1.4 \: or \: 1 \frac{4}{10} [/tex]
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