MATH HELP PLEASE WILL GIVE BRAINLIEST!!
Quadrilateral ABCD is inscribed in this circle.
What is the measure of angle A?
Answers
When you have an inscribed quadrilateral, the opposite angles add up to 180 degrees.
So we can start with angles B and D, and write the equation x + 116 = 180.
Solving that gives us that x = 64.
Now, input 64 for x in the expression for angle A.
2(64) - 40
128 - 40
88
Angle A is 88 degrees.
Good luck,
MrEQ
Related Questions
Noshi ordered a new desk for her office. The desk came in two parts, each shaped like a trapezoid. The height of both part A and part B is 3 feet. Noshi wants to be sure the desk will fit in her office so she calculates the area of the desk. What is the total area of the desk?
Answers
Let me know if I made a mistake any where :)
Answer:
39 ft
Step-by-step explanation:
Can you help me to find the answer
Answers
A formula is expressed as d=a(2+kt). Express k in terms of d, a and t
Answers
k = [tex] \frac{d-2a}{at} = \frac{d}{at} - \frac{2a}{at} = \frac{d}{at} - \frac{2}{t} [/tex]
Explanation:
To get the value of k, we will need to isolate it on one side of the equation.
This can be done as follows:
d = a(2+kt)
1- get rid of the brackets using distributive property:
d = a(2+kt)
d = 2a + akt
2- Subtract 2a from both sides of the equation:
d - 2a = 2a + akt - 2a
d - 2a = akt
3- Divide both sides of the equation by "at":
[tex] \frac{d-2a}{at} = \frac{akt}{at} [/tex]
[tex] k= \frac{d-2a}{at} [/tex]
4- We can further simplify the answer as follows:
k = [tex] \frac{d-2a}{at} = \frac{d}{at} - \frac{2a}{at} = \frac{d}{at} - \frac{2}{t} [/tex]
Hope this helps :)
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]
A team from the Department of Public Works is painting lines on the freeway. The length of road that needs to be lined determines how many hours the project will take.
r = the length of road
h = the number of hours needed
Which of the variables is independent and which is dependent?
Answers
The variable r is a dependent variable, depending upon independent variable h.
What is linear function?The graph of a linear function is a straight line. The following is the form of a linear function.
a + bx = y = f(x).
One independent variable and one dependent variable make up a linear function. x and y are the independent and dependent variables, respectively.
Given:
A team from the Department of Public Works is painting lines on the freeway.
The length of road that needs to be lined determines how many hours the project will take.
r = the length of road
h = the number of hours needed.
Here, r is a dependent variable depending upon independent variable h.
Therefore, r is a dependent variable depending upon independent variable h.
To learn more about the linear function;
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The perimeter of the base of the regular quadrilateral pyramid is P = 30 cm. Find the sum of all edges of this pyramid, if the perimeter of a lateral face is 27.5 cm
Answers
.. 2*(27.5 cm) +(1/2)*(30 cm) = 70 cm
The sum of all edges of the regular quadrilateral pyramid depends on the length of the base edges and the height of the pyramid.
Explanation:To find the sum of all edges of the regular quadrilateral pyramid, we need to find the length of the edges. Let's denote the length of the edge of the base by 'a'. Since the base of the pyramid is a regular quadrilateral, all its sides are equal. Therefore, the perimeter of the base is given by P = 4a = 30 cm.
Dividing both sides of the equation by 4, we get a = 7.5 cm.
Since the perimeter of a lateral face is 27.5 cm, the length of each lateral edge is equal to the height of the pyramid. Therefore, the sum of all edges of the pyramid is 4a + 4h, where 'h' is the height of the pyramid.
So, the sum of all edges is 4(7.5 cm) + 4h = 30 cm + 4h.
Jada has picked 1 cup of strawberries for a cake, which is enough for 3/4 of the cake. How many cups does she need for the whole cake?
Answers
3/4x = 1
We can solve this equation by multiplying both sides of the equation with 4/3, so it cancels out with the 3/4. Make sure to do this to both sides!
So, you get:
x=4/3
Jada needs 4/3 cups of strawberries for the whole cake.
Jessique sells handbag for $50 each she spends $4 per handbag for materials and $1000 to rent a store each month write an expression that shows how much profit jessique will earn in 1 month if she sells x amount of handbags
Answers
Answer:
The expression that shows how much profit Jessique will earn in
1 month is ⇒ Profit = 46x - 1000
Step-by-step explanation:
* Lets revise the relation between selling price , cost price and profit
- Profit is the difference between the selling price and the cost price
- Profit = selling price - cost price
- Jessique sells handbag for $50 each
- The selling price of each handbag is $50
- She spends $4 per handbag for materials
- She spends $1000 to rent a store each month
- She sells x amount of handbags in one month
* Lets calculate the cost price of the x handbags in 1 month
∵ She spends $4 per handbag for materials
∴ She spends on the materials of x handbag = 4 × x = 4x
∵ She spends $1000 to rent a store each month
∴ The cost price of x handbags in 1 month = 4x + 1000
∵ She sells x handbags in 1 month
∵ The selling price of 1 handbag is $50
∴ The selling price of x handbags in 1 month = 50 × x = 50x
∵ Profit = selling price - cost price
∴ Profit = 50x - (4x + 1000) ⇒ multiply the bracket by (-)
∴ Profit = 50x - 4x - 1000 ⇒ add like terms
∴ Profit = 46x - 1000
* The expression that shows how much profit Jessique will earn in
1 month is Profit = 46x - 1000
Final answer:
Jessique's profit for selling x handbags in one month is represented by the expression 46x - 1000, where x is the number of handbags sold.
Explanation:
Jessique sells handbags for $50 each. She spends $4 per handbag for materials and $1000 to rent a store each month. To calculate Jessique's profit for selling x handbags in a month, you would subtract both the materials cost and the fixed store rent from her total sales.
The total sales from x handbags is $50 times x, or $50x. The cost of materials for x handbags is $4 times x, or $4x. The fixed store rent is $1000 every month, regardless of how many handbags are sold.
Therefore, to find her profit, the expression is:
Profit = Total Sales - Materials Cost - Fixed Rent
Profit = (50x) - (4x) - 1000
Simplifying this expression, her profit for x handbags in a month would be:
Profit = 46x - 1000
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
Answers
9/25 + 12 - 2
9/25 + 10
It would be 10 and 9 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]
PLZZZ HELP! Best answer gets brainliest! THANK YOU!
Answers
If you were to place a point in the center of the shape, and place a "pin" there, then rotate the shape around that point 180 degrees, the shape would match up. This shape has point symmetry.
Line symmetry: symmetry across the point
If you were to draw a line through the top right and bottom left corner of the shape, and fold the shape over the line, it would match up. This shape has line symmetry.
So, c. This has both point and line symmetry.
an observer on a cliff 1200 feet above sea level sights two ships due East. The angle of depression to the shops are 48° and 33°. What is the distance between the ships?
Answers
The problem involves using trigonometry, specifically the tangent function, to determine the distance between the two ships. By calculating the distance from the observer to each ship separately and finding the difference, we find the distance between the two ships to be approximately 814.61 feet.
Explanation:The problem at hand involves the use of trigonometry, specifically tangent of an angle in a right triangle. Since we are dealing with angles of depression, we must understand that these angles are taken from a horizontal line - in this case, the line of sight from the cliff's edge.
First, let's consider the observer and the further away ship using tangent as follows:
tangent of 33° = height/distance, thus distance to the further ship = height / tangent of 33° = 1200 / tan(33) approximately equals to 1809.54 feet.Similar steps for nearer ship with angle of 48 degrees:
tangent of 48° = height/distance, hence distance to the closer ship = height / tangent of 48° = 1200 / tan(48) approximately equals to 994.93 feet.Therefore, the distance between the ships is the difference between the two distances calculated above, which will be 1809.54 - 994.93 = 814.61 feet.
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To determine the distance between the two ships, use the angles of depression and the observer's height above sea level to find the horizontal distances to each ship with trigonometry and subtract the smaller from the larger.
Explanation:To calculate the distance between two ships using their angles of depression from an observer's viewpoint atop a cliff, we can employ trigonometry. Let us denote the observer's vertical distance above sea level as height (h), which is 1200 feet in this case. The angles of depression to the first and second ship are 48° and 33° respectively.
We will use the tangent of these angles to find the horizontal distances (d1 and d2) from the base of the cliff to each ship:
Using the tangent of the angle of depression 48° to find distance to first ship (d1):tangent(48°) = opposite/adjacent or, h/d1
Thus, d1 = h / tangent(48°)Using the tangent of the angle of depression 33° to find distance to second ship (d2):
tangent(33°) = opposite/adjacent or, h/d2
Thus, d2 = h / tangent(33°)
After finding d1 and d2, we subtract the smaller distance from the larger to get the distance between the two ships:
Distance between ships = d2 - d1
Finally, we convert the answer from feet to the desired unit if necessary.
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Find the total cost for a $579 smartphone with 5% sales tax
Answers
Final cost: $550.05
Final answer:
To calculate the total cost including a 5% sales tax on a $579 smartphone, convert the tax rate to a decimal and multiply it by the price, then add the result to the original price. The total cost would be $607.95.
Explanation:
To find the total cost for a $579 smartphone with a 5% sales tax, you'll need to calculate the amount of sales tax and then add it to the original price of the smartphone. Here's how you would do that step by step:
Firstly, convert the sales tax from a percentage to a decimal by dividing by 100. For 5%, you would calculate 5 ÷ 100 = 0.05.
Next, calculate the sales tax by multiplying the original price by this decimal. You do this by calculating $579 × 0.05 = $28.95 in sales tax.
Finally, add the sales tax to the original price to find the total cost. Add the two amounts together to get $579 + $28.95 = $607.95.
So, the total cost of the smartphone including sales tax would be $607.95.
PLEASE HELP, NEEDS TO BE COMPLETED TODAY!
Drag the system of equation to the point that represents the solution to the system.
Answers
case 1)
2x-y=-13
y=x+9
the solution is the point (-4,5)
see the attached figure N 1
case 2)
y=3x-7
y=2x-5
the solution is the point (2,-1)
see the attached figure N 2
case 3)
3x+2y=10
6x-y=10
the solution is the point (2,2)
see the attached figure N 3
case 4)
y=6
x=-5
the solution is the point (-5,6)
see the attached figure N 4
case 5)
4x-3y=5
3x+2y=-9
the solution is the point (-1,-3)
see the attached figure N 5
case 6)
x+y=7
x-y=-1
the solution is the point (3,4)
see the attached figure N 6
the answer in the attached figure
somebody help me!! anyone
Answers
2 rectangles with length 11 and height 7
2 rectangles with length 11 and height 6
2 rectangles with length 6 and height 7
So, their areas will be (respectively):
[tex]2(11)(7) = 154m^2[/tex]
[tex]2(11)(6) = 132m^2[/tex]
[tex]2(7)(6) = 84m^2[/tex]
Add all of them up:
[tex]154+132+84 = 370 m^2[/tex]
So, your answer is C.
Given the annual interest rate of each, which account will earn the most interest on a $10,000 deposit over 7 years?
Answers
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?
Answers
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.
3x squared -42x+9=-5 for completing the square
Answers
Subtract 9 from both sides
[tex]3x^2 -42x = -5 - 9[/tex]
[tex]3x^2 -42x = -14[/tex]
Divide by 3 through
[tex]x^2 -14x = - \dfrac{14}{3} [/tex]
Add (b/2)^2 to form perfect square
[tex]x^2 -14x + (\dfrac{14}{2})^2 = - \dfrac{14}{3} + (\dfrac{14}{2})^2 [/tex]
Form perfect square
[tex](x -7)^2 = \dfrac{7}{3}[/tex]
square root both sides
[tex](x -7) = \pm \sqrt{\dfrac{7}{3}} [/tex]
Add 7 to both sides
[tex]x = \pm \sqrt{\dfrac{7}{3}} + 7[/tex]
Rewrite the answer into 2 different answers
[tex]x = 7 + \sqrt{\dfrac{7}{3}} \ or \ 7 - \sqrt{\dfrac{7}{3}}[/tex]
At 7:00 AM there were 14,000 gallons of water in Lance’s pool when he noticed there was a leak. After 6 hours there were only 5,000 gallons of water remaining in his pool. Write an equation that describes the number of gallons of water as a function of the time the pool has been leaking.
y = -5,000x + 14,000
y = -1,500x + 14,000
y = -9,000x + 14,000
Is it possible for a vertical line to have a negative slope?
no
yes
Answers
Answer: -5000x + 14,000 = 9000 and yes
Step-by-step explanation:
The equation is y = - 1500x + 14000, then the option B is correct. And yes, the slope of the line is negative.
What is the linear system?A Linear system is a system in which the degree of the variable in the equation is one. It may contain one, two, or more variables.
At 7:00 AM there were 14,000 gallons of water in Lance’s pool when he noticed there was a leak.
After 6 hours there were only 5,000 gallons of water remaining in his pool.
Let y be the amount of water in the pool and x be the time.
Then the coordinate will be (0, 14000) and (6, 5000)
We know that the equation of a line is given as
[tex]\rm y - y_1 = \dfrac{y_2 - y_1}{x _2 - x_1} \times (x -x_1)[/tex]
Then we have
[tex]\rm y - 14000 = \dfrac{5000 - 14000}{6 - 0} (x - 0)\\\\y = -1500x + 14000[/tex]
More about the linear system link is given below.
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Ray is x years old. His brother Ron is y years older than Ray.
How old will Ron be in 2 years?
Answers
Ron is [tex]x + y[/tex] years old.
In 2 years, Ron will be two years older than now, so [tex]x + y + 2[/tex] years old.
Ray is years old.
Ron is years old.
In 2 years, Ron will be two years older than now, so years old.
Write an equivalent expression for 1/y^-1/4 using positive exponents
Answers
I hope this helps. God bless
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]
Anastasia had 10 buckets of mulch for her garden. If Colby used 3 2/7 buckets of Anastasia's mulch, how many buckets were left? Leave answer as a mixed number with a space between the whole number and the fraction
Answers
1. Regroup the 10 whole to be able to subtract with common denominators.
10 = 9 7/7
- 3 2/7 = -3 2/7
6 5/7
or
2. Make 10 whole into an improper fraction with a denominator of 7.
10 = 10/1 = 70/7
-3 2/7 = 23/7 = -23/7
47/7
47/7 = 6 5/7
Hope this helps!!
After Colby used 3 2/7 buckets out of Anastasia's 10 buckets of mulch, Anastasia has 6 5/7 buckets left. The subtraction was performed by converting mixed numbers to improper fractions, performing the operation, and then converting back to a mixed number.
Anastasia had 10 buckets of mulch for her garden. After Colby used 3 2/7 buckets, we need to subtract that amount from the total to find out how many buckets are left. To subtract the mixed number, we can convert it into an improper fraction and then perform the subtraction.
First, convert 3 2/7 to an improper fraction:
3 2/7 = 3 x 7 + 2 which is 21/7 + 2/7 = 23/7.
Now subtract the improper fraction from the total number of buckets:
10 - 23/7
Change 10 to a fraction with a denominator of 7 to get 70/7.
Subtract the two fractions:
70/7 - 23/7 = (70 - 23) / 7 = 47/7.
Convert the improper fraction back to a mixed number:
47/7 = 6 5/7 (since 47 divided by 7 is 6 with a remainder of 5).
So, Anastasia has 6 5/7 buckets of mulch left.
If a girl take algebra in 8 grade and she fail , she gonna retake it in 9 grade so that will be affect to the credit high school or same ? I need the answer for algebra
Answers
A circle has an area of 49•3.14 square units. What is the diameter of the circle?
Answers
First we will solve for r, radius, and then double it to find the diameter.
153.86 = (3.14)(r)²
49 = r²
√49 = r
7 = r
Now the diameter:
7*2 = 14
So the diameter is 14 units.
Hope this helps :)
I need help finding the area
Thanks in advance
Answers
The area of the square:
[tex]A_s=3^2=9\ m^2[/tex]
The area of the four half of the circles is equal the area of two circles.
[tex]A_c=\pi\cdot1.5^2=2.25\pi\ m^2[/tex]
The area of the figure:
[tex]A_F=A_s+2A_c\to A_F=9 +2\cdot2.25\pi=(9+4.5\pi)m^2[/tex]
What is 8,663,943,526 rounded to the nearest million? A. 8,663,000,000 B. 8,663,944,000 C. 8,664,000,000 D. 9,000,000,000
Answers
C. 8,664,000,000
The library is having a book sale. Hardcover books sell for $4 each, and paperback books are $2 each. If Connie spends $26 for 8 books, how many hardcover books did she buy?
Answers
[tex](5 \times 4) + (3 \times 2) \\ = 20 + 6 = 26[/tex]
The table shows the results of two surveys that randomly sampled 50 families about their preferred ways to travel to a vacation destination.
Plane Car Bus Total
Survey 1 17 27 6 50
Survey 2 21 20 9 50
Which statement can be made about families' preferred ways to travel to a vacation destination based on the information in the surveys?
A)Families prefer to ride the bus when traveling on vacation.
B) More families prefer to travel by car on vacation than by bus.
C) Families prefer to ride the bus over flying when traveling on vacation.
D) Most families fly when going on vacation
PLEASEEEEEEEEEE HELP ME OUT SOMEONE 22 PTS AND I WILL GIVE YOU THE BRAINLEST
Answers
Answer:
B) More families prefer to travel by car on vacation than by bus
Two angles are complementary angles. What is the mean of the complementary angles?
Answers
If you mean the “mean,” it would be 45 degrees. This is the average because complementary angles equal 90 degrees. 90/2=45. If you mean what they are, then they are two angles that add up to 90 degrees.
I hope this helps!
The graph represents the height y, in feet, above the ground of a golf ball x seconds after it is hit.
Which statement is true?
Select each correct answer.
The maximum height of the golf ball occurs at x = 2.
For up to 2.5 s after the ball is hit, its height is increasing.
The maximum height of the golf ball is 100 ft.
It takes 3 s for the ball to fall to the ground after reaching its maximum height.
The golf ball is in the air for 5 s.
Answers
The answer is B. The golf ball is in the air for 5 s.
and
d. The maximum height of the golf ball is 100 ft
The correct statements are, for up to 2.5 s after the ball is hit, its height is increasing, the maximum height of the golf ball is 100 ft, the golf ball is in the air for 5 s, the correct options are B, C, and E.
What is a Graph?Graph is a mathematical representation of relation between two objects.
The graph shows the parabolic motion of a golf ball,
Observing the graph, the statements that can be concluded are
It reaches the maximum height in 2.5 seconds.It attains the maximum height of 100 ft.The height of the ball is increasing for 2.5 seconds.The height starts decreasing after 2.5 seconds.The ball is in the air for 5 secondsTo know more about Graph
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Erma maintains an active blog about her seashell collection. She has 500 white shells, 325 yellow shells, 115 pink shells, and 60 green shells in her jar. She asks Sweet T to reach into her jar and randomly selects a shell. Then she replaces it and shakes up the jar before asking Sweet T to pick another shell. Which model shows the probability of a randomly selecting each color shell from her jar?
A. White 60% Pink: 10% yellow: 20% Green: 10%
B.White: 50% Pink: 11% yellow: 32.5% green: 6%
C. White: 25% Pink: 25% Yellow: 25% Green: 25%
D. White: 100% Pink: 23% Yellow: 65% Green: 12%
Answers
B. White: 50% Pink: 11% yellow: 32.5% green: 6%
I believe there is a small typo here, as the probability of pink should be 11.5%
based on the calculations below.
Explanation:
probability of each color=number of shells of this color/total number of shells
To get it in percentage form, we will then multiply the probability by 100
We have:
number of white shells = 500 shells
number of pink shells = 115 shells
number of yellow shells = 325 shells
number of green shells = 60 shells
total number of shells = 500 + 115 + 325 + 60 = 1000 shells
Now, we will get the probability of each color as follows:
probability of white shells = (500/1000) * 100 = 50%
probability of pink shells = (115/1000) * 100 = 11.5%
probability of yellow shells = (325/1000) * 100 = 32.5%
probability of green shells = (60/1000) * 100 = 6%
Hope this helps :)
If you add the number of seashells Erma has in total, it would sum up to 1000. The probability that you will pick a certain color out of all the seashells is: ((Number of seashells of a certain color)/(Total number of seashells))*100%=The probability that that color will be picked.
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
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.