A total of 800 tickets for the covered pavilion and 700 tickets for lawn seats were sold, solved using a system of equations.
We assume the number of covered pavilion tickets sold to be x and the number of lawn seat tickets sold to be y.
As a total of 1500 tickets were sold, we can form an equation:
x + y = 1500 ... (i),
as we had only those two types of tickets.
The cost of each covered pavilion ticket = $20.
Hence, the total revenue from covered pavilion tickets = $20x.
The cost of each lawn seat ticket = $10.
Hence, the total revenue from lawn seat tickets = $10y.
The total receipts were said to be $23,000.
Thus, we can represent this as an equation:
20x + 10y = 23000 ...(ii).
Combining (i) and (ii), we get a system of equations:
x + y = 1500 ... (i).
20x + 10y = 23000 ... (ii).
Dividing equation (ii) by 10, we get:
2x + y = 2300 ... (iii).
Subtracting (i) from (iii), we get:
2x + y = 2300.
x + y = 1500.
(-) (-) (-)
____________
x = 800.
Substituting x = 800 in (i), we get:
x + y = 1500,
or, 800 + y = 1500,
or, y = 1500 - 800,
or, y = 700.
Thus, a total of 800 tickets for the covered pavilion and 700 tickets for lawn seats were sold, solved using a system of equations.
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The solution to an absolute value inequality is shown on the graph below.
-5-4-3 -2 -1 0 1 2 3 4 5
What is another way to show the solution?
x> -3 or x < 2
{x|x <-3 orx <2}
[-3, 2]
O (-3, 2).
The solution to the absolute value inequality is (-3,2).
What is absolute value inequality ?Absolute Value Inequality is the expression which contains absolute function as well as inequality signs .
The absolute value inequality is represented in the form of a line
Interval of the function is -3 to 2
As the intervals are represented by open circles, so -3 and 2 are exclusive of the values of the inequality.
Therefore the another way to show the solution is
-3 < x < 2
or
(-3,2)
Therefore, the solution to the absolute value inequality is (-3,2).
The complete question is attached with the answer.
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Find the area of each rhombus.
PLS HELP!! Geometry!!!!
Answer:
A) 384
B) 576
Step-by-step explanation:
the area of a rhombus is
pq/2
First Rhombus
we have p but to find q we can cut the triangle in half to form a right triangle, that allows us to use the Pythagorean theorem
20² = 12² + b²
400 - 144 = b²
b² = 256
b = 16
since the height (b) is half the rhombus, we double it to get q
p = 24
q = 32
a = [tex]\frac{24*32}{2}[/tex]
a = 384
Second Rhombus
Since rhombuses are parallelograms, we can use its area formula (b)(h)
a = (24)(24)
a = 576
If we have five decisions to make and four choices for each decision, how can we represent the number of potential outcomes?
4 to the power of 5
5 to the power of 4
4 to the power of 4
5 to the power of 5
Using the Fundamental Counting Theorem, the number of potential outcomes is given by: [tex]4^5[/tex]
What is the Fundamental Counting Theorem?It is a theorem that states that if there are n things, each with [tex]n_1, n_2, \cdots, n_n[/tex] ways to be done, each thing independent of the other, the number of ways they can be done is:
[tex]N = n_1 \times n_2 \times \cdots \times n_n[/tex]
There are five decisions, each with four options, hence:
[tex]n_1 = n_2 = n_3 = n_4 = n_5 = 4[/tex]
The number of options is:
[tex]N = 4 \times 4 \times 4 \times 4 \times 4 = 4^5[/tex].
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Please Help Asap Please And Thank You!
Answer:
Rate of change: 4/3
Step-by-step explanation:
Number of sodas/Total cost
pick a number
24/18 = 4/3
Answer:
4/3
Step-by-step explanation:
Rate of change is also known as slope.
To find slope, you have to find the change in y divided by the change in x.
y2-y1 / x2-x1
The variable y in this situation is the number of sodas.
The variable x in this situation is the total cost.
28 - 24 / 21 - 18
= 4 / 3
The rate of change in this problem is 4/3.
00
What is the volume of the following rectangular prism?
2
units
Volume=
27
5
units2
units
The volume of the rectangular prism is 27/2 square units
How to determine the volume?The volume is calculated as:
Volume = Base area * Height
This gives
Volume = 27/5 * 5/2
Evaluate the product
Volume = 27/2
Hence, the volume of the rectangular prism is 27/2 square units
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The general form of the equation of a circle is ax2 by2 cx dy e = 0, where a = b 0. if the circle has a radius of 3 units and the center lies on the y-axis, which set of values of a, b, c, d, and e might correspond to the circle?
The set of values which might correspond to the circle are A = 1, B = 1, C = 0, D = -8 and E = 7.
The equation of a circle.Mathematically, the general form of the equation of a circle is given by;
(x - h)² + (y - k)² = r²
Where:
h and k represents the coordinates at the center.r is the radius of a circle.Based on the information provided that the center of the circle lies on the y-axis, we have:
(h, k) = (0, 4)
Radius, r = 3 units.
Substituting the given parameters into the formula, we have;
(x - 0)² + (y - 4)² = 3²
x ² + y² - 8y + 16 = 9
x ² + y² - 8y + 7 = 0.
Therefore, the set of values which might correspond to the circle are A = 1, B = 1, C = 0, D = -8 and E = 7.
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Complete Question:
The general form of the equation of a circle is Ax² + By² + Cx + Dy + E = 0, where A = B. If the circle has a radius of 3 units and the center at (0, 4), which set of values of A, B, C, D, and E correspond to the circle?
Triangles F H G and K J G share common point G. The lengths of sides H G and G J are congruent. Angles F H G and K J G are right angles.
Can you conclude that triangle GHF is congruent to triangle GJK? Explain.
yes, by ASA
yes, by AAS
yes, by AAA
not enough information given
Answer:
not enough information given
Step-by-step explanation:
as the rules say, we need at least 3 pieces of information :
2 angles and a side, or 3 angles (or there are other options like 2 sides and one angle or 3 sides).
but here we get 1 side and 1 angle. the shared point does not give us anything in that regard.
so, not enough information.
The number line below is correctly represented by which of the following intervals?
The intervals that represent the number line are given as follows:
b. [tex](-\infty, -5] \cup [8, \infty)[/tex]
What intervals belong to the number line?The first painted interval is of numbers to the left of x = -5(inclusive due to closed circle), hence:
[tex](-\infty, -5][/tex]
The second interval is of numbers to the right of x = 8, also inclusive, hence:
[tex][8, \infty)[/tex]
Hence the union is given by:
[tex](-\infty, -5] \cup [8, \infty)[/tex]
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Answer:
B
Step-by-step explanation:
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Which expression is equivalent?
Answer:
The answer is the 3rd option (2)
Step-by-step explanation:
Hope this helped! :D
Determine which function has a greater initial value and explain how you know.
Function 1: y = 2()*
Function 2:
xy
03
16
2 12
3 24
Answer:
Function 2
Step-by-step explanation:
An initial value of a function, aka y-intercept, is obtained by using x=0 and evaluating the function at that point. Evaluating the two functions given:
Function1: y = 2x(1/3)^x|x=0 = 2*0*1=0
with the chart
xy
03
16
2 12
3 24
Function2 has value 3 for x=0
So, Function 2 has a greater initial value
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what is the side view ? the rest are right like i've tried loads of combinations but they're not right, please say what the shape is you know
Answer:
it will be a rectangle mostly...
FIND R, Interest problem
R, which is the rate is 20%.
What is simple interest?Simple interest is the interest on a sum of money invested or borrowed for a specific period of time.
The sum invested is called the principal.
Analysis:
simple interest (I) = PRT/100 = 300
P = principal = 3000
R = rate = ?
T = 0.5 year
300 = 3000 x R x 0.5/100
R = 20%
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Explain how to decide when a normal distribution can be used to approximate a binomial distribution.
A normal distribution can be used to approximate a binomial distribution when n* p and n * q are greater than 5.
What is a normal distribution?A probability distribution that is symmetric about the mean is the normal distribution, sometimes referred to as the Gaussian distribution. It demonstrates that data that are close to the mean occur more frequently than data that are far from the mean.
A probability bell curve is more properly described as the normal distribution.
The mean and standard deviation of a normal distribution are 0 and 1, respectively. It has a kurtosis of 3 and zero skew.
Not all symmetrical distributions are normal, but all normal distributions are symmetrical.
Natural occurrences frequently resemble the usual distribution.
However, most price distributions in finance are not exactly normal distributions.
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Absolute value of -6.2 is _________.
1. 6.2
2. 6
3. 7
4. -6
[tex]\Large\maltese\underline{\textsf{A. What is Asked}}[/tex]
What is the absolute value of -6.2? It's _____________.
[tex]\Large\maltese\underline{\textsf{B. This problem has been solved!}}[/tex]
No matter what the number is, its absolute value is always positive.
The number -6.2 is not an exception, there's nothing special about that number. Its absolute value is also positive.
[tex]\cline{1-2}[/tex]
[tex]\bf{Result:}[/tex]
[tex]\bf{=6.2}[/tex]
[tex]\LARGE\boxed{\bf{aesthetic \not1 \theta l}}[/tex]
The absolute value of -6.2 is 6.2 (option 1).
The absolute value of a number represents its distance from zero on the number line, regardless of its sign. For the value -6.2, the distance from zero is 6.2 units. Therefore, the correct answer is 1. 6.2. Option 1 accurately reflects that the absolute value of -6.2 is indeed 6.2.
The other options (2. 6, 3. 7, and 4. -6) do not accurately represent the absolute value of -6.2. The absolute value operation ensures that the result is always a positive value, showing how far a number is from zero. In this case, the absolute value of -6.2 is 6.2.
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Using the following image, find QR given RS=6 and QS=7.
What is QR?
Answer:
1
Step-by-step explanation:
Knowing that the entire number line equals 7, and that the second line segment RS equals 6, we can subtract the two values to find QR.
[tex]7-6=1[/tex]
Therefore, QR equals 1.
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[tex]\quad \huge \quad \quad \boxed{ \tt \:Answer }[/tex]
[tex]\qquad \tt \rightarrow \:QR = 1 \:\: unit [/tex]
____________________________________
[tex] \large \tt Solution \: : [/tex]
[tex] \qquad \tt \rightarrow \: QR + RS = QS[/tex]
Let QR = x
[tex]\qquad \tt \rightarrow \: x + 6 = 7[/tex]
[tex]\qquad \tt \rightarrow \: x = 7 - 6[/tex]
[tex]\qquad \tt \rightarrow \: x = 1[/tex]
Answered by : ❝ AǫᴜᴀWɪᴢ ❞
Please help, i can't figure this out. I'll give a brainliest, but i really need help with how to solve this.
The required linear equation is given by y=10x + 15
The data collected by Harvard Business School plots the linear relationship of business startup success vs. Time.
The statistic is the study of mathematics which deal with relations between comprehensive data.
As clearly, points represents on graph startup success vs Time
part of a straight line
so we take two points on graph at (1,25), (2,35)
now equation of line
[tex]y-y_1=\frac{y_2-y_1}{x_2-x_1} (x-x_1)[/tex]
= [tex]y-25=\frac{35-25}{2-1} (x-1)[/tex]
[tex]y=10x+15[/tex]
Thus, The required expression is given by y=10x + 15 which show the relation ship between startup success Vs time
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A new car costs $34,000 and its value depreciates at 14% of its value each year. What is the decay factor for the value of this car? What will be the price of the car after 10 years?
The price of the car after 10 years is $7524.25 if the new car costs $34,000 and its value depreciates at 14% of its value each year.
What is an equation?An equation is an expression that shows the relationship between two or more variables and numbers.
Let y represent the value of the car after x years. A new car costs $34,000 and its value depreciates at 14% of its value each year. Hence:
y = 34000(0.86)ˣ
After 10 years:
y = 34000(0.86)¹⁰ = 7524.25
The price of the car after 10 years is $7524.25 if the new car costs $34,000 and its value depreciates at 14% of its value each year.
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I Had 150 stickers. I gave 10 stickers to each of the 8 students in my class and kept the rest for myself. How many Stickers will I have
Answer:
70
Step-by-step explanation:
10tickets x 8students = 80tickets
150tickets-80tickets=70tickets
ease help me and thank you so so much u are so amazing!!
[tex] \frac{36 - 40}{2 - 1} = 4[/tex]
2n + 1.6 = 17.6 what is the value of n?
Answer:
n = 8Step-by-step explanation:
2n + 1.6 = 17.6 what is the value of n?
2n + 1.6 = 17.6
2n = 17.6 - 1.6
2n = 16
n = 16 : 2
n = 8
-----------------
check
2n + 1.6 = 17.6
2*8+1.6=17.6
16+1.6=17.6
17.6=17.6
the answer is good
The distance from Capital City to Little Village is 660 miles. From Capital City to Mytown is 310 miles, from Mytown to Yourtown is 200 miles, and from Yourtown to Little Village is 150 miles. How far is it from Mytown to Little Village
The distance from Mytown to Little Village is 350 miles.
The distance from Capital City to Little Village is 660 miles.
The distance from Capital City to Mytown is 310 miles,
The distance from Mytown to Yourtown is 200 miles,
and from Yourtown to Little Village is 150 miles.
Assuming all the places are collinear,
The distance from Mytown to Little Village is
200 + 150 = 350 miles
Hence, The Mytown is 350 miles far from the Little Village
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Lines s and t are parallel. The slope of line s is −32. What is the slope of line t?
Answer: Parallel lines have equal slopes
If the slope of line s is -32 or -3/2, then the same applies to line t
Parallel lines have equal slopes but different y intercepts. These lines do not cross or intersect.
Answer: -32
Step-by-step explanation:
The two lines are parallel which means these two lines have the same slope. Therefore, the slope of line t is -32.
Madison drew Triangle D E F. In her triangle, Measure of angle D is represented as x degrees. The measure of Angle E is half the measure of Angle D. The measure of Angle F is 2 degrees less than twice Measure of angle D. What is Measure of angle F?
36 degrees
56 degrees
102 degrees
147 degrees
Answer:
c)102 degrees
Step-by-step explanation:
what is the surface area of a cylinder with a radius of 9 and width of 2
Solve the system of linear equations.
y=−16x+5
x+6y=30
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A food truck did a daily survey of customers to find their food preferences. the data is partially entered in the frequency table. complete the table to analyze the data and answer the questions:
part a: what percentage of the survey respondents do not like both hamburgers and burritos? (2 points)
part b: what is the marginal relative frequency of all customers that like hamburgers? (3 points)
part c: use the conditional relative frequencies to determine which data point has strongest association of its two factors. use complete sentences to explain your answer. (5 points)
will mark brainliest if correct answers
The percentage of the survey respondents that do not like both hamburgers and burritos is 16.09%.
How to compute the percentage?The percentage of the survey respondents that do not like both hamburgers and burritos will be:
= 33/205 × 100
= 16.09%
The marginal relative frequency of all customers that like hamburgers will be:
= 134/205
= 0.65
The data point that has strongest association of its two factors will be:
Those who like hamburger and burrito = 39/134 = 0.29
Those who like hamburger and not burrito = 95/134 = 0.71
Those who like burrito but not hamburger = 38/71 = 0.53
Those who do not like hamburger or burrito = 33/71 = 0.47.
Therefore, the data point that has strongest association of its two factors will be those who like hamburgers but not burritos.
A food truck did a daily survey of customers to find their food preferences. The data is partially entered in the frequency table. Complete the table to analyze the data and answer the questions:
Likes hamburgers Does not like hamburgers Total
Likes burritos 38 77
Does not like burritos 95 128
Total 134 71
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An elevator has 4 passengers and 8 floors. Find the probability that no 2 passengers get off on the same floor considering that it is equally likely that a person will get off at any floor.
The probability is 5/343.
Given :8 floors and 4 passengers.
Passengers will be assumed to start on the first floor, where everyone goes up, and each passenger only gets off on the 2nd floor (no one gets off on the 1st floor!)
Now we need to find the number of all ordered lists of four numbers out of seven, eg 2<3<7<8, 3<6<7<8, 4<5<6o<8, etc.
This can be done in 7C4 ways.
The total numbers of ways 4 passengers can get off at 7 floors (starting at the 2nd!) is [tex]7^{4}[/tex].
Therefore the probability is [tex]\frac{7C4}{7^{4} }[/tex] = [tex]\frac{5}{343}[/tex]
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0.3 y+\dfrac yz0.3y+
z
y
0, point, 3, y, plus, start fraction, y, divided by, z, end fraction when y=10y=10y, equals, 10 and z=5z=5
The required solution to the equation is [tex]0.3y+\frac{y}{z}[/tex] at y=10, z=5 is 5.
As we have the equation [tex]0.3y+\frac{y}{z}[/tex] and find solution At y =10 and z=5
What is equation?
The equation is the relationship between dependent and independent variables through some mathematical operators.
Now,
putting the value of y=10, z=5 in [tex]0.3y+\frac{y}{z}[/tex]
⇒[tex]0.3*10+\frac{10}{5}[/tex]
= 5
Thus the required value of the equation at y=10 and z =5 is 3.
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I don’t understand, please help.
Solve x please explain
Answer:
x = 4
Step-by-step explanation:
co interior angles add up to 180.
this means that: 48 + 34x - 4 = 180
thus 48 + 34x = 184
therefore, 34x = 136
so, x = 4.
The two angles labeled in the given diagram are interior angles on the same side of the transversal. They can also be called interior supplementary angles.
These angles have a sum of 180 degrees.
Solving the QuestionThe two angles given have measures of 48 degrees and (34x-4) degrees.
They have a sum of 180 degrees.
Form an equation:
[tex]48+(34x-4)=180\\48+34x-4=180\\44+34x=180\\34x=180-44\\34x=136\\x=4[/tex]
Answer[tex]x=4[/tex]