(A) The system of equations is,
6A + 3S = $51
9A + 6S = $90
(B) The price of one adult ticket is $4 and the price of one student ticket is $9.
What is system of equations?
A set of one or more equations involving numerous variables is referred to as a system of equations. The variable mappings that satisfy all component equations are the solutions to systems of equations, or the points where the components of these equations intersect.
Given:
Juan's school is selling tickets to the annual talent show.
On the first day of ticket sales the school sold 6 adult tickets and 3 student tickets for a total of $51.
The school took in $90 on the second day by selling 9 adult tickets and 6 student tickets.
Let A be the number of adult tickets sold.
S be the number of students ticket sold.
⇒ 6A + 3S = $51 ..(1)
9A + 6S = $90 ..(2)
Multiply first equation by (2)
12A + 6S = $102 ..(3)
Subtract equation (2) and (3)
12A + 6S = $102
- 9A + 6S = $90
________________
3A = 12
⇒ A = $4
Plug A = 4 in equation (1)
6(4) + 3S = $51
24 + 3S = $51
3S = $51 - $24
3S = $27
S = $9
Hence,
(A) The system of equations is,
6A + 3S = $51
9A + 6S = $90
(B) The price of one adult ticket is $4 and the price of one student ticket is $9.
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A student has a container with a volume of 1.5 L. She estimates the volume to be 1.8 L. By what percent is the students estimate off?
Answer:
20%
Step-by-step explanation:
You want to know the percentage error in an estimate of 1.8 L for an actual value of 1.5 L.
Percentage errorThe percentage error is the ratio of error amount to actual value, multiplied by 100%.
Error amount = estimate - actual = 1.8 L -1.5 L = 0.3 L
ratio = (error amount)/(actual) = (0.3 L)/(1.5 L) = 0.2
percentage error = 0.2 × 100% = 20%
The error in the student's estimate is 20%.
Which of the following equations represents a line with a positive slope and a negative y-intercept?
The equation represents a line with a positive slope and a negative y-intercept is y = 7.5x - 2
How to determine which equation represents a line with a positive slope and a negative y-intercept?
The slope-intercept form of the equation of a line is y = mx + c
where m is the slope and c is the y-intercept
Given: y = 3.5x, y = 1/4 x + 7, y = 7.5x - 2 and y = -5x - 8
For y = 3.5x:
y = 3.5x
Comparing with y = mx +c
m = 3.5 and c = 0
For y = 1/4 x + 7:
y = 1/4 x + 7
Comparing with y = mx +c
m = 1/4 and c = 7
For y = 7.5x - 2 :
y = 7.5x - 2
Comparing with y = mx +c
m = 7.5 and c = -2
For y = -5x - 8 :
y = -5x - 8
Comparing with y = mx +c
m = -5 and c = -8
Thus, y = 7.5x - 2 has a positive slope (7.5) and a negative y-intercept (-2)
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Order ³√97, 78/9, √45 from greatest to least.
³√97, 78/9, √45
78/9, √45, ³√97
³√97, √45, 78/9
78/9, ³√97, √45
78/9, √45 , ³√97 is the order of numbers from greatest to least.
Given,
The numbers;
³√97, 78/9, √45
We have to order these numbers from greatest to least.
Ordering of numbers;
A series of numbers can be arranged in numerical order. Both ascending and descending orders are possible. For instance, suppose you arranged a group of numbers in ascending order as 2, 55, 103, 256, and 802, for instance. This can make it much simpler to look through a large collection of numbers.
Here,
First we have to find the values of the numbers.
The value of ³√97 = 4.59
The value of 78/9 = 8.66
The value of √45 = 6.71
So,
The greatest one is 78/9 and the least one is ³√97
Therefore,
The order of numbers from greatest to least is 78/9, √45 , ³√97
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Which fraction of the total area does each shaded section represent?
Answer:
are three rectangles with the same measurements and the same area, therefore they are worth 1/3, the whole figure, with three rectangles, is worth 3/3
Step-by-step explanation:
The average number of cars waiting at a drive-up window at 9am follows a Poisson distribution with a mean of 2 cars Calculate the following probability of cars waiting at the drive-up window. X = 1, 2, ..., 10 a. P(x=0) = b. P(x=2)
Probability of cars waiting at the drive-up window is P (X=0) = 0.1353 and P (X=2) = 0.2707
What is probability ?The variety of strategies for achievement. the number of potential outcomes. For instance, the chance of flipping a coin and obtaining heads is 1 in 2, as there is only one method to acquire a head and there are a total of 2 potential outcomes (a head or tail). We specify P(heads) = 1/2.
There are typically 2. chance of automobiles waiting at the drive-up window on any given morning at 9 o'clock, according to a Poisson distribution. a. P(x=0) P(x=0) X = 1, 2,..., 10
X≅ P(2)
a. P(x=0)
P(x=0)
[tex]e^{-2}[/tex] . [tex]2^{0}[/tex] ÷ 0!
[tex]e^{-2}[/tex]
0.1353
b. P(x=2)
[tex]e^{-2}[/tex] .[tex]2^{2}[/tex] ÷ 2!
2[tex]e^{-2}[/tex]
0.2707
So
Probability of cars waiting at the drive-up window is P (X=0) = 0.1353 and P (X=2) = 0.2707
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This design covers the floor of a huge hall. What fraction of the floor is covered by black tiles? What fraction of the floor is covered by white tiles?
The fraction of the floor is covered by white tiles is 1/3.
What fraction of the floor is covered by white tiles?A fraction is simply a piece of a whole. The number is represented mathematically as a quotient where the numerator and denominator are split. In a simple fraction, the numerator as well as the denominator are both integers.
Assumed figure:
Places covered by white tiles = 18
Total tiles = 54
The Fraction covered by white tiles will be:
= Number of whitw tiles / Total tiles
= 18/54
= 1/3
The Fraction is 1/3.
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Liam walks 18 miles in 5 hours. At what unit rate does Liam walk?
О А.
B.
O C.
5 miles
18 hours
18 miles
5 hours
5 hours
18 miles
D. 18/5 miles
1 hour
Answer:
d.
Step-by-step explanation:
it says it in the question 18 miles 5 hours
its not asking you to work out exactly.
I need help on this math problem.
The polynomial p(x) = 3x³ - 5x² - 4x + 4 can be written as a product of linear factor as (x + 1) (3x - 2) (x - 2).
What is a polynomial?A polynomial is a mathematical expression that solely uses the operations of addition, subtraction, multiplication, and positive-integer powers of variables. It is made up of indeterminate (also known as variables) and coefficients.
Given:
p(x) = 3x³ - 5x² - 4x + 4
Factor = (x - 2)
Divide the equation by (x - 2) as shown below,
(3x³ - 5x² - 4x + 4) / (x - 2)
= (3x² + x - 2)
Factorize the above equation,
= 3x² - 2x + 3x - 2
= (x + 1) (3x - 2)
Therefore, the polynomial p(x) = 3x³ - 5x² - 4x + 4 can be written as a product of linear factor as (x + 1) (3x - 2) (x - 2).
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Solving System with 3 variables
Problem 1: Solve for x, y, and z. Show all your work!
x-5y+3=39
3x+8y-z=-19
2x-6y-5z=-29
Answer:
x = 2
y = -2
z = 9
(2,-2,9)
Step-by-step explanation:
Students get two grades for a test in an introductory psychology course: a letter grade, and a numerical equivalent (weighted value). So an A is worth 4 points, a B is worth 3 points, a C is worth 2 points, a D is worth 1 point, and an F is worth 0 points.
The results for the test are listed in the table below.
Score F (=0) D (=1) C (=2) B (=3) A (=4)
Number of students 11 18 52 13 6
Using the numerical equivalents (weighted values), what is the average grade for this test?
Rounded to the nearest hundredth, the average grade is
.
The average grade for this test is given as follows:
1.85.
How to obtain the average grade?The average grade is obtained as the mean of the data-set containing all the grades, which is given by the sum of all grades divided by the number of grades.
Considering the numerical equivalents of each letter, the grades in this problem are given as follows:
11 students with a grade of 0.18 students with a grade of 1.52 students with a grade of 2.13 students with a grade of 3.6 students with a grade of 4.The total number of grades is given as follows:
11 + 18 + 52 + 13 + 6 = 100.
The sum of these grades is given as follows:
11 x 0 + 18 x 1 + 52 x 2 + 13 x 3 + 6 x 4 = 185.
Hence the average grade is of:
185/100 = 1.85.
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PLEASE HELP ME!! 50 POINTS! AND AWARDING BRAINLIEST! :DD
Beginning inventory 38,900 ending inventory 42,100 cost of goods sold 83,500 what is the net purchase?
Answer:
Net Purchase is 86700---------------------------
Given:
Beginning inventory 38900, Ending inventory 42100,Cost of goods sold 83500,Net Purchase = ?The difference in the inventory is same as the difference between cost of goods sold and net purchase.
42100 - 38900 = 3200Net purchase is the sum of the cost of goods and the difference between beginning and ending inventory:
Net Purchase = 83500 + 3200 = 86700Answer:
The difference in the inventory is same as the difference between cost of goods sold and net purchase.
42100 - 38900 = 3200
Step-by-step explanation:
Net purchase is the sum of the cost of goods and the difference between beginning and ending inventory:
Net Purchase = 83500 + 3200 = 86700
Brainliest pls?
:)
For his birthday, Zack and three of his friends went to a movie. They each got a ticket for $8.00 and the same snack from the concession stand. If Zacks mom paid $48 for the groups tickets and snacks how much did each snack set cost?
Answer:
$4.00
Step-by-step explanation:
There is, in total, 4 people attending the movies. [Zack and his 3 friends]
If each ticket costs $8.00, we can use 4 x $8.00 to find out how much the tickets costs.
4 x $8.00 = $32.00
If his mom paid $48 dollars in total, to get the amount of money they spent on snacks, we can use $48 - $32.
$48 - 32 = $16
We can now divide $16.00 by 4, as everyone [Zack and his 3 friends] got the same snack from the concession stand, and that leaves us with the equation: $16/4 [also known as 16 divided by 4]
$16/4 = $4.00
Each snack set cost $4.00
In the parallelogram, m
By the concept of the sum of the adjacent angle in a parallelogram, we determine m∠PQR = 76°.
What is a parallelogram?A basic quadrilateral with two sets of parallel sides is known as a parallelogram. In a parallelogram, the opposing or confronting sides are of equal length, and the opposing angles are of equal size.
The area of a parallelogram is base multiples by height as two triangles form a parallelogram.
We know a parallelogram has opposite angles of equal measure and the sum of adjacent angles is 180°.
Given, m∠QRP = 38° and m∠PRS = 66°.
∴ m∠PQR = 180° - 38° - 66°.
m∠PQR = 76°.
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plsssssssssssss helppppppppppppp ....
Answer:3/4 10
Step-by-step explanation:
PLEASE HELP 70 BRAINLY POINTS IF YOU ANSWER THIS QUESTION
A probability value is listed at the top of each column. Determine the probability for each situation, then drag and drop each situation into the column under its correct probability.
Probability of drawing a even number of dice is 0.5, The probability of flipping a head on a coin is 0.5,The probability of choosing a red block out of a bag containing 1 red, 1 green and 3 green blocks is 0.2, The probability of choosing a soccer ball out of a bag containing 4 soccer balls, 1 playground ball and 3 basketballs is 0.5 and The probability of choosing a tennis ball out of a bag containing 5 rubber balls, 3 tennis balls, 6 bouncy balls and 1 squishy ball is 0.2.
What is Probability?It is a branch of mathematics that deals with the occurrence of a random event.
The probability of drawing a even number of dice.
A dice has 3 even numbers, 2, 4 and 6.
probability of drawing a even number of dice=3/6=1/2=0.5
The probability of flipping a head on a coin =1/2=0.5
The probability of choosing a red block out of a bag containing 1 red, 1 green and 3 green blocks.
1/5=0.2
The probability of choosing a soccer ball out of a bag containing 4 soccer balls, 1 playground ball and 3 basketballs.
4/8=1/2=0.5
The probability of choosing a tennis ball out of a bag containing 5 rubber balls, 3 tennis balls, 6 bouncy balls and 1 squishy ball.
The probability is 0.2
Hence, probability of drawing a even number of dice is 0.5, The probability of flipping a head on a coin is 0.5,The probability of choosing a red block out of a bag containing 1 red, 1 green and 3 green blocks is 0.2, The probability of choosing a soccer ball out of a bag containing 4 soccer balls, 1 playground ball and 3 basketballs is 0.5 and The probability of choosing a tennis ball out of a bag containing 5 rubber balls, 3 tennis balls, 6 bouncy balls and 1 squishy ball is 0.2.
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A soccer team purchased a set of team balls for $184.64. If each ball cost $11.54, how many balls were purchased?
O 13 balls
O 14 balls
O 15 balls
O 16 balls
Which function represents g(x), a reflection of f(x) = 4(one-half) Superscript x across the x-axis?
g(x) = −4(2)x
g(x) = 4(2)−x
g(x) = −4(one-half) Superscript x
g(x) = 4(one-half) Superscript negative x
Answer:
The function that represents g(x), a reflection of f(x) = 4(one-half) Superscript x across the x-axis, is g(x) = −4(one-half) Superscript x. This function is obtained by negating the exponent of the original function, which reverses the direction of the exponential growth and creates a mirror image of the original function across the x-axis. The other options listed do not correctly reflect the original function across the x-axis.
Step-by-step explanation:
A rectangle has vertices (a,b), (c,b), and (a,c). Find the fourth vertex.
The fourth vertex is (
Answer:
the fourth vertex is (3,5) or (6,6)
Step-by-step explanation:
this so ez i dont need to explain it
17 - 39 - (-82) + 65
Answer:
125
Step-by-step explanation:
Lauren visits the park every 4 days and goes to the library every 10 days. If Lauren does both of these today, how many days will pass before Lauren gets to do them both on the same day again?
A.20 days
B. 14 days
C. 6 days
D. 40 days
Answer:
20 days
Step-by-step explanation:
In the picture below, which lines are lines of symmetry for the figure?
A. only 2
B. 1, 2, and 3
C. 2 and 3
D. 1 and 3
(A) only 2 is the line of symmetry of the given figure.
What are lines of symmetry?A form or item is divided into two equal and symmetrical portions by a line of symmetry.
Because it divides the figure symmetrically and the separated portions resemble mirror images of one another, we also refer to this line as the axis of symmetry or the mirror line.
The four lines of symmetry in a square are lines across the opposing vertices and the midpoints of the opposing sides.
Together, these four lines of symmetry make up a square.
Consequently, a square has two diagonal, one horizontal, and one vertical line of symmetry.
So, according to the given figure we can easily observe and tell that line 2 is the only one that divides the diagram into 2 identical parts.
Therefore, (A) only 2 is the line of symmetry of the given figure.
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evaluate 150-(2=x)3 when x=2
The value of the expression 150 - 3x when x =2 is 144.
What is an expression?Expression in mathematics is combination of variables with the use of operations and given rules. It can be in the form of equation, numbers etc.
Given expression,
150 - 3x.
And we have x = 2.
Substituting the value of x to the expression
So,
150 -3x = 150 - 3(x = 2)
= 150 - 3(2)
= 150 - 6
= 144
Therefore, the answer is 144.
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Write an inequality for the graph of (-2,-2) (0,-6)
The answer is 24
sorry if i did not say more its hard to explain sorry again
The graph below shows the number of free throws made by five players on a basketball team.
Weekly Free Throw Numbers for Players
#Free Throws
10+
99876543N
Player 1 Player 2 Player 3 Player 4 Player 5
Week 1 Week 2 Week 3
What was the total number of free throws made for Player 2?
24
17
23
8
Total number of free throws made for player 2 are 23 using histogram.
Define histogram.A histogram is a graphical depiction of continuous or discrete data. In a histogram, the frequency is represented by the area of a bar. Frequency density, which is proportional to frequency, is plotted on the y-axis, and intervals representing the range of values are plotted on the x-axis. One common graphing tool is the histogram. It is employed to present interval-scaled summaries of discrete or continuous data. It is frequently used to conveniently depict the main characteristics of the data distribution. A histogram is a graph in which the horizontal axis represents the values of the observations, and the vertical axis represents the density of those observations.
Given,
Histogram given,
Total number of free throws made for player 2 are:
8 + 9 + 6
23
Total number of free throws made for player 2 are 23 using histogram.
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A company loses $80 as a result of a shipping delay. The 4 owners of the company must share the loss equally. Write an expression for the earnings per person. Evaluate the expression
Answer:20
Step-by-step explanation: 80 divided by 4 is 20
Solve for the short leg of the 30-60-90 triangle.
Answer:
b = 2
Step-by-step explanation:
because of the 60° in the corner we know this triangle is the left half of an equilateral triangle (where all 3 sides are equally long, and all 3 angles are 60°).
therefore, b is half of the baseline of that equilateral triangle = 4/2 = 2.
so, b = 2 is the correct answer.
Factor the expression using the GCF.18h+30k The factored from is
The given expression can be factorized to obtain 18h + 30k = 6(3h + 5k).
How to factorize an algebraic expression by GCF method?First find the greatest factor common to all the terms of the given expression. Then, take out that term as a common and the remaining terms are written inside a bracket.
The given expression is 18h + 30k.
The GCF of 18 h and 30 k is 6.
Now, the given expression can be factorized as follows,
18h + 30k
= 6 × 3h + 6 × 5k
= 6(3h + 5k)
Hence, the factored form of the given expression is 6(3h + 5k).
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Eleanor practices piano for ¾ of an hour every day. How long does she practice in a week? (She practices on weekends, too!)
Answer:
5 1/4
Step-by-step explanation:
Hope this helps!
Melissa created a scale drawing of a garden in which 2 inches equals 5 feet. The dimensions of the garden on the scale drawing are 15 inches by 10 inches. What are the dimensions of the actual garden in feet?
The dimensions of the actual garden in feet is 37.5 feet x 25 feet
What is scale factor?A scale factor is defined as the ratio between the scale of a given original object and a new object,
We have,
2 inches = 5 feet.
The dimensions of the garden on the scale drawing.
= 15 inches x 10 inches
Now,
2 inches = 5 feet
15 inches = 15/2 x 5 feet
15 inches = 37.5 feet
10 inches = 10/2 x 5 feet
10 inches = 25 feet
Thus,
37.5 feet x 25 feet are the dimensions of the actual garden in feet.
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Write an equation for a rational function with the given characteristics.
Vertical asymptotes at
x = −3
and
x = 6,
x-intercepts at
(−4, 0)
and
(1, 0),
horizontal asymptote at
y = −3
Answer:
y = -3(x +4)(x -1)/((x +3)(x -6))
Step-by-step explanation:
You want a rational function with vertical asymptotes at -3, 6; x-intercepts at -4, 1; and a horizontal asymptote at y = -3.
Vertical asymptotesA rational function will have vertical asymptotes at the denominator zeros. Vertical asymptotes at -3 and 6 will be had if the denominator has factors (x +3) and (x -6).
X-interceptsA rational function will have x-intercept at the numerator zeros. X-intercepts at -4 and 1 will be had if the numerator has factors (x +4) and (x -1).
Horizontal asymptotesA horizontal asymptote will be found at the y-value that is the (constant) ratio of the highest-degree terms of the numerator and denominator. Here, we can achieve that by multiplying the factors mentioned above by the desired constant (-3).
The equation is ...
[tex]\boxed{y=-3\dfrac{(x+3)(x-6)}{(x+4)(x-1)}}[/tex]
__
Additional comment
A "hole" will be found where a numerator and denominator factor cancel. For example, a hole at x=7 could be achieved by making the function have an additional numerator factor of (x -7) and an additional denominator factor of (x -7).
Effectively, the horizontal asymptote is the quotient of the numerator and denominator (excluding the "remainder"). If that quotient is a linear (or other) function, the graph will asymptotically approach that function as the magnitude of x gets large. A linear function gives a "slant aymptote."