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.
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.
The measure of an exterior angle of a regular polygon is 15 degrees. What is the sum of the measures of the interior angles of the polygon
It is 360 degrees!
You can see because it is math and yeah..
PLZZZZZZZZZHELP HURRY!!! What is the difference (2x-3) - (x- 1)
x-4
x-2
x+2
x+4
What is the value of the expression shown below?
3 over 5 to the power of 2 + 4 × 3 − 2
10 and 9 over 25
11 and 2 over 25
12 and 9 over 25
13 and 2 over 25
Answer:
[tex]10\frac{9}{25}[/tex]
Step-by-step explanation:
[tex](\frac{3}{5})^2 + 4 * 3 - 2[/tex]
Simplify the given expression
WE use order of operation PEMDAS
Parenthesis, exponents, multiply , divide , add and subtract
LEts start with parenthesis
[tex](\frac{9}{25})+ 4 * 3 - 2[/tex]
now we multiply
[tex](\frac{9}{25})+12 - 2[/tex]
now subtract 2
[tex](\frac{9}{25})+10[/tex]
This can be written as [tex]10\frac{9}{25}[/tex]
in your sock drawer, you have 20 socks. You have two pairs of patterned socks, 4 pairs of gym socks, three pairs of striped socks, and one pair of black socks. What is the probability that you randomly pull a gym sock from the drawer? What are the odds?
At a hardware store, a tool set normally costs $80. During a sale this week, the tool set costs $12 less than usual. What percentage of the usual price is the saving? Explain or show your reasoning.
Which is longer 2 kilometers or 2 meters
Find the surface area of each triangular prism
You plan to paint the outside of this garage, including the roof. Which calculation will help you best decide how much paint you will need? (Omit the floor of the garage in your calculation.) Add the areas of 9 rectangles and 2 triangles. Add the areas of 6 rectangles and 2 triangles. Add the volumes of 1 rectangular prism and 1 triangular prism. Add the perimeters of 4 rectangles and 2 triangles.
Answer:
add the areas of 6 rectangles and 2 triangles
Step-by-step explanation:
what does x equal? Plus can u pls explain cuz I have a test friday
How do you do the midpoint with the same point
Ernie saved $650 in twenty six weeks. He saved the same amount each week. How much did he save each week?
So sorry, I just don’t understand this Please I’m almost done.
Label the percent bar below with the appropriate estimations.
Answer:
it was 25%
Step-by-step explanation:
A circle has an area of 49•3.14 square units. What is the diameter of the circle?
5 Points, Time Limit, Brainliest, Please don't spam, Thanks!
The table shows the number of skirts of different colors in a closet. A fair coin is shown below the table.
Color of Skirt Number
Yellow 5
Blue 8
Green 4
Pink 3
A coin Maria selects a skirt from the closet randomly without looking and then tosses the fair coin. What is the probability that she will select a yellow skirt and that the coin will land tails up?
1 over 20
1 over 10
1 over 8
1 over 5
Answer: [tex]\dfrac{1}{10}[/tex]
Step-by-step explanation:
Given : Number of yellow Skirt Number =5
Total skirt = [tex]5+8+4+3=20[/tex]
The probability that she will select a yellow skirt will be :_
[tex]\dfrac{5}{20}=\dfrac{1}{5}[/tex]
Total faces in coin=2
Number of tails = 1
The probability that the coin will land tails up :-
[tex]\dfrac{1}{2}[/tex]
Since ,both events are independent , then the probability that she will select a yellow skirt and that the coin will land tails up is given by :-
[tex]\dfrac{1}{5}\dfrac{1}{2}=\dfrac{1}{10}[/tex]
What is the value of X in the figure
Write an equivalent expression for 1/y^-1/4 using positive exponents
Answer:
The required exponent is [tex]y^{\frac{1}{4}}[/tex]
Step-by-step explanation:
Consider the provided expression.
[tex]\frac{1}{y^{-\frac{1}{4}}}[/tex]
We need to write the above expression into positive exponent form.
Now apply the exponent rule: [tex]\frac{1}{a^{-b}}=a^b[/tex]
By using the above rule we can rewrite the above expression as shown:
[tex]\frac{1}{y^{-\frac{1}{4}}}=y^{\frac{1}{4}}[/tex]
Hence, the required exponent is [tex]y^{\frac{1}{4}}[/tex]
A formula is expressed as d=a(2+kt). Express k in terms of d, a and t
Answer:
[tex]k=\frac{d}{ta}-\frac{2}{t}[/tex]
Step-by-step explanation:
d=a(2+kt)
WE need to solve for k. our aim is to get K alone
d= a(2+kt)
To eliminate 'a' we divide by 'a' on both sides
[tex]\frac{d}{a} = 2+ kt[/tex]
To eliminte 2 we subtract 2 on both sides
[tex]\frac{d}{a}-2 =kt[/tex]
Now to isolate K we divide by 't' on both sides
When we divide a fraction by 't' then we multiply 't' at the bottom
[tex]\frac{d}{ta}-\frac{2}{t}=k[/tex]
what property is 6x + (9+3x) in? A. Distributive B. Combine like terms C. Associative property of addition D. Commutative property of addition
The expression can be simplified using the distributive property, but it is not in its simplest form, Option A is correct.
What is Expression?An expression is combination of variables, numbers and operators.
The expression 6x + (9+3x) is in the distributive property.
To see why, we can apply the distributive property of multiplication over addition, which states that a(b + c) = ab + ac. In this case, we have:
6x + (9+3x) = 6x + 9 + 3x
Here, the expression 6x is being distributed over the parentheses, which contain 9 and 3x. We can combine the constants 6x and 9, as well as the like terms 6x and 3x, using the commutative and associative properties of addition:
6x + 9 + 3x
= 6x + 3x + 9
= (6x + 3x) + 9
= 9x + 9
So, the expression can be simplified using the distributive property, but it is not in its simplest form.
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when she got to school she saw that the school has nine buildings each having 30 classrooms how many classrooms does the school have
It took Yuik (1/6) of a hour to water get flowers and (4/6) of an hour to weed her garden. What fraction of an hour did Yuik work in her yard
The required fraction of an hour is 5/6 Yuik work in her yard.
What is the fraction?A fraction is defined as a numerical representation of a part of a whole that represents a rational number.
It took Yuik (1/6) of an hour to water the flowers and (4/6) of an hour to weed her garden, so in total, she worked for (1/6) + (4/6) = 5/6 of an hour in her yard.
To add the two fractions, we need to have a common denominator, which is 6. Then we can add the numerators (1 + 4) to get 5.
⇒ 5/6
Thus, the final fraction is 5/6.
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0.5 as a repeating decimal to a fraction
show your work
also 0.7 as a repeating decimal to a fraction
show your work
The decimal 0.5 converts to the fraction 1/2 and the decimal 0.7 converts to the fraction 7/10.
Explanation:To convert the decimal 0.5 and 0.7 into fractions, we use the definition of a decimal. A decimal is a representation of a fraction in terms where we have a power of 10 in the denominator. For instance:
To convert 0.5 into a fraction, we can think of it as 0.5/1 which equals to 5/10 or simplifies to 1/2. Converting 0.7 into a fraction, would give us 0.7/1 which is equal to 7/10.
So, 0.5 as a decimal is 1/2 as a fraction and 0.7 as a decimal is 7/10 as a fraction.
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Which of the following is equivalent to √20
A. 4
B. 5√2
C. 2√5
D. 20
is (8,3) solution to 3x-4y>12
Kelly is making ice cream cones for her 6 friends. 1/3 of her friends asked for sprinkles on their ice cream. How many ice cream cones should kelly make with sprinkles
Suppose g(x)=f(2x) when f(x)=x^2-4x-5. Find the standard expression for g(x).
Please show steps.
I need help finding the area
Thanks in advance
The back-to-back stem-and-leaf plot below shows the ages of patients seen by two doctors in a family clinic in one day. Compare the ages of the patients of doctor 1 and doctor 2 using the mean and the median of each data set. Doctor 1 Doctor 2 | 3 | 5 9 2 0 | 2 | 0 0 2 3 6 8 7 5 | 1 | 3 7 9 7 3 2 1 1| 0 | 2 2 3 9 Key: means 29 9|2|3 means 23
I don't quite know how to do this, so if someone could guide me through it that would be nice..!
Answer:
The mean of the ages of Doctor 1's patients is 13.54 and the median is 15. The mean of the ages of Doctor 2's patients is 16 and the median is 19.
Step-by-step explanation:
Jackson is playing a video game that has 3 castles to conquer within each level. Jackson has completed 5 levels so far. If x represents the number of remaining levels to complete, which of the following equations can be used to find the total number of castles Jackson will have conquered once he completes the final level?
The equation to find the total number of castles conquered by Jackson is 15 + 3x, where x represents the remaining levels. Jackson has conquered 15 castles in 5 levels and will conquer 3 more for each additional level he completes.
Explanation:The question relates to creating an equation to find the total number of castles Jackson will have conquered after completing all levels in a video game. Jackson has completed 5 levels, and there are 3 castles within each level. If x represents the remaining levels to complete, we can create the equation by considering the total number of castles conquered in the levels completed (5 levels × 3 castles/level = 15 castles) and adding it to the castles that will be conquered in the remaining levels (x levels × 3 castles/level). The equation representing the total number of castles Jackson will have conquered once he completes the final level is:
Total castles = (5 × 3) + (x × 3) = 15 + 3x
As a separate example unrelated to Jackson's equation, there is the classical problem involving grains of rice and a chessboard that demonstrates exponential growth. In this example, one grain of rice is placed on the first square of a chessboard, and the number of grains is doubled on each subsequent square. By the 64th square, you are placing a very large number of grains, and the total number minus one grain would be 264 - 1. However, the actual number of grains needed is a separate calculation from the equation for Jackson's video game question.