9 pounds of the $50 coffee should be used
What is word problem?A word problem is a few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
let's let p = the pounds of coffee we need.
50p + 80(20) = 6(p+ 20)
The total price of the $50 coffee is going to be the pounds x price per pound. The total amount of coffee is the number of pounds of each added together.
From the equation above 50p + 80(20) = 60(p+ 20)
expanding the brackets and collecting like terms
50p + 1600 = 6p + 120
50p - 6p = 1200 - 1600
44p= 400
p= 9
Therefore, 9 pounds of $50 coffee should be used
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Find the measure of the exterior angle:_______
The measure of the exterior angle is 60°.
What is the Exterior Angle Theorem?
If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.
If a side of a triangle is produced, then the exterior angle so formed is equal to the sum of the two interior opposite angles.
We have,
interior angles:
∠ABC = z + 10
∠BAC = 4z
Exterior angle:
∠ACB = z + 50
Exterior Angle Theorem:
The measure of exterior angle = Sum of two opposite interior angles’ measure.
According to the Exterior Angle property of a triangle theorem, the sum of measures of ∠ABC and ∠BAC would be equal to the exterior angle ∠ACB.
∴ ∠ABC + ∠BAC = ∠ACB
z + 10 + 4z = z + 50
5z = z + 40
z = 40/4
∴ z = 10
so, the value of the z is 10.
exterior angle:
∠ACB = 10 + 50 =60
Hence, the measure of the exterior angle is 60°.
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a) Determine the series of the given function. In the first box after the summation symbol, type in -1 or 1 indicating whether the series is alternating or not.
b) Write out the sum of the first four nonzero terms of the series representing this function.
c) Determine the interval of convergence. The outside boxes require the endpoints and the inside boxes
a) The given function is [tex]$\frac{x^2-2x+2}{(x-1)^2(x+2)}$[/tex]. The series of this function is [tex]$\sum_{n=0}^{\infty}(-1)^n(n+1)x^n$[/tex]. Therefore, the series is alternating (-1).
b) The sum of the first four nonzero terms of the series is [tex]$-1x^1+2x^2-3x^3+4x^4$.[/tex]
c) The interval of convergence is [tex](-2, 1)[/tex]. This is because the denominator [tex]$(x-1)^2(x+2)$[/tex] has a zero at [tex]$x=-2$[/tex] and a zero at [tex]$x=1$[/tex], and the function is undefined at these two points. Therefore, the interval of convergence is the open interval [tex]$(-2, 1)$[/tex].
Convergence is the process of two or more different entities coming together and becoming one. In mathematics, it can refer to a sequence converging to a limit, or the process of a function approaching a finite value as the number of trials approaches infinity. In technology, convergence can refer to the combining of different media types into a single medium, such as the combination of audio, video, and text into a multimedia presentation.
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A building has a height of 125 meters and a length of 80 meters. On a scale drawing of the building, the height is 25 centimeters. What is the length of the building on the scale drawing in centimeters?
The length of the building on the scale drawing is found as 16 centimeters.
Describe the term scale factor?The ratio of the scale of an original thing to a new object that is a representation of it but of a specific widths is known as a scale factor (bigger or smaller).Scale factor ratios can be written as a colon, 1:2, or as a fraction, 12. A ratio calculates the difference between two values.However, that ratio isn't a scale factor, thus you could not build a ratio for left-handed pupils to all students.For the given data in the question-
Dimensions of the building;
Height of 125 meter length of 80 meters.Dimensions of the drawing of the building;
height is 25 centimetersLet the length be 'x'.Thus, taking ratios of Height to length
125/80 = 25/x
On simplification;
x = 80 x 25 / 125
x = 16
Thus, the length of building on the scale drawing is found as 16 centimeters.
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Solve for S
3/ -s + 1 = 6/ s + 4
Answers fast please I need them fast
The answers to find are 1) Δ CAB 2) Δ ABC 3) CDAB 4) 10 5) 6 and 6) 30
What are similar triangles?When two triangles having congruent corresponding angles and the corresponding sides are in equal ratio, then the triangles are said to be similar triangles.
Given are the similar triangles,
1) Δ HJG ~ Δ CAB
Scale factor = 3:1
2) Δ NPM ~ Δ ABC
Scale factor = 1:2
3) KJML ~ CDAB
Scale factor = 1:2
4) 40/x = 20/5
x = 10
5) 18/x = 21/7
x = 6
6) 6/3 = x/15
x = 30
Hence, the answers are: 1) Δ CAB 2) Δ ABC 3) CDAB 4) 10 5) 6 and 6) 30
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A recent study Indicated that 27% of the 142 women over age 55 in the study were widows
A sample size of [214] to be within 5 % of the true proportion of women over age 55 who are widows and be 900 % confident.
What is standard deviation?The term "standard deviation" (or "σ") refers to a measurement of the data's dispersion from the mean. A low standard deviation implies that the data are grouped around the mean, whereas a large standard deviation shows that the data are more dispersed.
We are given that recent study Indicated that 27% of the 142 women over age 55 in the study were widows
Margin of error = 0.05 = E
z-score = z/2 = 1.645
n = 0.27 x 0.73 (1.645/ 0.05)²
n = 213.343
n=214
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What is the approximate perimeter of this triangle?
Answer:
163.6 in---------------------------
Given:
a = 56 in,m∠A = 55°.Find the missing sides:
56/b = tan 55° ⇒ b = 56 / tan 55° = 39.21 in,56/c = sin 55° ⇒ c = 56 / sin 55° = 68.36 in.Perimeter is:
56 + 68.36 + 39.21 = 163.57 ≈ 163.6 inwhich graph represents the equation y =1/3 x + 2
The graph of the equation y = (1/3)x + 2 is passing through points
(3, 3) and ( -3, 1).
What is a graph?The set of ordered pairings (x, y) where f(x) = y makes up the graph of a function.
These pairs are Cartesian coordinates of points in two-dimensional space and so constitute a subset of this plane in the general case when f(x) are real values.
Given, A linear equation y = (1/3)x + 2.
Now to graph the equation we'll simply put some arbitrary values of x which will correspond to some values of y and plot them then we'll join them with a straightedge.
When x = 3, y = 3 ⇒ (3, 3).
When x = - 3, y = 1 ⇒( -3, 1).
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Jocelyn estimate that a piece of wood measure 5.5 cm . If it actually measure 5.62 cm, what is the percent error of Jocelyn's estimate
The Jocelyn estimate's percent error is 2.181 centimeters..
What is percent error ?
Percent error calculates the difference between an estimate and a right number and expresses it as a percentage. Analysts can use this statistic to determine how big the mistake is in relation to the actual number. It is also referred to as % error and percentage error.
There are three steps to determining the % error:
1. Determine the error, which is the estimated value minus the actual value.
2. Multiply by the accurate value.
3. In order to create a percentage, multiply by 100.
Given information:
The size of a piece of wood (Exact value)= 5.5 cm
if it really does measure(Approximate value)=5.62 cm
percentage error={(approximate value-exact value)/exact value}×100
percentage error = ((5.62-5.5)/5.5)×100
percentage error = 2.181cm
Consequently, 2.181cm is the Jocelyn estimate's percent error.
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You brought popular game on sale for $20 and want to sell it on eBay. You want to mark up the toy 60%. What did you sell it for?
Cassie wants to purchase a pair of binoculars that is on sale for $155.75.
The sales tax rate in her county is 7%. How much will Cassie pay in all for
the pair of binoculars after sales tax is included? Round to the nearest cent
if necessary.
$10.12 will Cassie pay in all for the pair of binoculars after sales tax is included.
What is sales tax?
A sales tax is a fee that is paid to the government when specified products and services are sold. Typically, laws permit the vendor to charge the customer the tax at the time of purchase. Use taxes are often used to describe taxes on goods and services that consumers pay directly to a governing authority.
given data
we are told that the cost of binoculars is $155.75
and also the sales tax is 7%
Step two:
We want to first solve for the sales tax which is 7% of $155.75
=7/100* 155.75
=0.070*155.75
=10.12
Cassie will pay a tax of $10.12
Also Cassie will pay a total amount of
= 155.75+10.12
=$165.87
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Let the discrete random variable X have the geometric distribution with parameter p. (a) Give a real-life example in which the geometric distribution can be applied. (b) Use the definition of the expected value to show that: E[X] = 1/p. (c) Explain why it makes sense that the expected value of X is inversely proportional to p.
a) A discrete random variable is a variable that can take only a countable number of distinct values, such as 0, 1, 2, 3, 4, and so on.
b) Examples of discrete random variables are the number of children in a family, the number of people who go to the cinema on Friday nights, etc.
c) E(x) = 1/p
Discrete Random Variable:
A discrete random variable can be defined as a type of variable whose value depends on the numerical outcome of some random phenomenon. Also called a random variable. Discrete random variables are always easily countable integers. A probability mass function is used to describe the probability distribution of a discrete random variable.
Discrete random variables are used to quantify the results of random experiments. A discrete random variable takes on an infinite number of possible outcomes. In general, discrete random variables can be counted as 0, 1, 2, 3, 4, ...
Geometric Distribution :
The geometric variate is the variate that specifies the number of consecutive failures before the first success in Bernoulli trials. The probability of success of a Bernoulli trial is given by p and the probability of failure is 1 - p.
The Geometric Random Variable can be written as X ~ G(p).
The probability mass function is P(X = x) = (1 - p)ˣ⁻¹ p
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which properties of equality do you use to solve the
equation 15 =x/3 + 18?
The adding property of equality should be used to satisfy the given equation.
What is an equation?Mathematical expressions with two algebraic symbols on either side of the equal (=) sign are called equations.
This relationship is illustrated by the left and right expressions being equal to one another. The left-hand side equals the right-hand side is a basic, straightforward equation.
As per the given equation in the question,
-15 + x/3 = 18
Add 15 on both sides of the equation
So, we have
45 + x = 18 × 3
x = 54 + 45
x = 99
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After a snowstorm in the town of Golden Glen, the morning temperature was
–
10°F. But by the afternoon, the temperature had risen by 17°F.
The change in temperature based on the information is 27°F.
How to illustrate the relationship?It should be noted that temperature simply means the degree of coldness and hotness in a body. In this case, after a snowstorm in the town of Golden Glen, the morning temperature was -10°F. But by the afternoon, the temperature had risen by 17°F.
Let the change in temperature be represented by x.
Therefore, -10 + x = -17
x = 17 + 10
x = 27
The Temperature is 27°F.
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After a snowstorm in the town of Golden Glen, the morning temperature was -10°F. But by the afternoon, the temperature had risen by 17°F. What was the change in temperature?
what is equivalent to (32−−√5)13
Answer:
Your answer is 416 + 13 [tex]\sqrt{5}[/tex].
Step-by-step explanation:
Determine if the two triangles are necessarily congruent. If so, fill in a flowchart proof to prove that they are.
The given triangles are congruent to each other by the rule of (AAS) Angle Angle side.
What is a triangle?The basic polygonal shape of a triangle has three sides & three interior angles. This is one of the fundamental shapes in geometry and is particularly associated. It has three connected vertices. Triangles can be divided into a variety of categories according to their sides and angles.
As per the given figure in the question,
There are two given triangles in the question,
Δ ABC and Δ MNO
As we can see that,
∠ C = ∠ M
∠ B = ∠ N and,
The side, AC = OM
So, Δ ABC ≅ Δ MNO
So, by using AAS (Angle Angle Side) rule, triangle ABC and triangle MNO are congruent to each other.
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Which equation represents the line that passes through the point (5,7) and is parallel to the graph of y=2/3x-7?
The equation of a line that passes through point (5,7) and parallel to the graph of y = 2/3x - 7 is y = (2/3)x + 11/3
What is the equation of line that passes through the point (5,7) and is parallel to the line y = 2/3x - 7?The point-slope formula is expressed as
y - y₁ = m( x - x₁ )
Where m is slope.
Given the equation of the graph y = (2/3)x - 7
Using the slope intercept form where m is slope.
y = mx + b
y = (2/3)x - 7
Slope of the graph will be;
Slope m = 2/3
Next, find the line parallel to the graph and which passes through the point (5,7).
Using the point slope formula
y - y₁ = m( x - x₁ )
Plug in the slope and point.
y - 7 = (2/3)( x - 5 )
Solve for y
y - 7 = (2/3)x - 10/3
y = (2/3)x - 10/3 + 7
y = (2/3)x + 11/3
Therefore, the equation of line parallel to the graph is y = (2/3)x + 11/3.
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Consider the sample space given below. A die is a cube with six sides and each side contains one to six dots. Suppose a blue die and a gray die are rolled together, and the numbers of dots that occur face up on each are recorded. The possible outcomes of the sample space S are listed as follows, where in each case the die on the left is blue and the one on the right is gray.S = {11, 12, 13, 14, 15, 16, 21, 22, 23, 24, 25, 26, 31, 32, 33, 34, 35, 36, 41, 42, 43, 44, 45, 46, 51, 52, 53, 54, 55, 56, 61, 62, 63, 64, 65, 66)a) Let E be the event that the sum of the numbers showing face up is equal to 6. Write E as a set. (Write your answer in set-roster notation.) b) What is the probability of e? c) Let F be the event that the sum of the numbers showing face up is at most 4. Write Fas a set. (Write your answer in set-roster notation. ) d) What is the probability of F? Show all work in either the answer box shown or upload your answer with a file - can be PDF or jpeg only.
a) The event E, that the sum of the numbers showing face up is equal to 6, can be written as the set:
E = {11, 15, 24, 33, 42, 51}
b) The probability of E is 6/36 = 1/6.
c) The event F, that the sum of the numbers showing face up is at most 4, can be written as the set:
F = {11, 15, 22, 31, 33, 42, 44, 51}
d) The probability of F is 2/9.
Probability is a measure of the likelihood of an event occurring in a statistical experiment. It is a number between 0 and 1, where 0 indicates that the event will never happen and 1 indicates that the event will always happen. Probability can be used to make predictions about the outcome of statistical experiments, and it is a useful tool in many fields, including economics, finance, and science. It is also used in gambling and games of chance to determine the odds of winning.
The probability of event E is the number of outcomes in the event divided by the total number of outcomes in the sample space. There are 6 outcomes in the event E and 36 outcomes in the sample space.
So, the probability of E is 6/36 = 1/6.
The probability of event F is the number of outcomes in the event divided by the total number of outcomes in the sample space. There are 8 outcomes in the event F and 36 outcomes in the sample space.
So, the probability of F is 8/36 = 2/9.
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A bag contains 3 red, 6 blue, and 7 yellow marbles. What is
the probability of drawing 2 marbles of different colors out of
the bag?
The probability of drawing 2 marbles of different colors would be 0.317.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is typically expressed as a fraction or a decimal between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.
In the scenario you described, a bag contains 3 red, 6 blue, and 7 yellow marbles. If you draw 2 marbles out of the bag, the probability of drawing 2 marbles of different colors is:
Number of ways to draw 2 marbles of different colors: (3 red marbles) x (6 blue marbles) + (3 red marbles) x (7 yellow marbles) + (6 blue marbles) x (7 yellow marbles) = 18 + 21 + 42 = 81
Total number of ways to draw 2 marbles: 16 (4 marbles of each color)
Probability of drawing 2 marbles of different colors: 81/256 = 0.317
Hence, the probability of drawing 2 marbles of different colors would be 0.317.
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The probability of drawing 2 marbles of different colors would be 0.317.
What is probability?
Probability is a measure of the likelihood of an event occurring. It is typically expressed as a fraction or a decimal between 0 and 1, with 0 indicating that the event is impossible and 1 indicating that the event is certain to occur.
In the scenario you described, a bag contains 3 red, 6 blue, and 7 yellow marbles. If you draw 2 marbles out of the bag, the probability of drawing 2 marbles of different colors is:
Number of ways to draw 2 marbles of different colors: (3 red marbles) x (6 blue marbles) + (3 red marbles) x (7 yellow marbles) + (6 blue marbles) x (7 yellow marbles) = 18 + 21 + 42 = 81
Total number of ways to draw 2 marbles: 16 (4 marbles of each color)
Probability of drawing 2 marbles of different colors: 81/256 = 0.317
Hence, the probability of drawing 2 marbles of different colors would be 0.317.
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Write a quadratic function in standard form whose graph has a vertex of (2, 6) and passes through the point (4, 10) .
An SRS of 20 third grade children is selected in Chicago and each is given a test to measure their reading ability. We are interested in a 90% confidence interval for the population mean score. In the sample, the mean score is 64 points, and the standard deviation is 12 points. The margin of error associated with the confidence interval is
O 4.64 points.
O 5.62 points.
O 2.68 points.
The margin or error associated with the confidence interval is 5.62 points
The sample size of the third grade children = 20
The confidence interval for the population mean score = 90%
The mean score = 64 points
The standard deviation = 12 points
The degree of freedom = The sample size - 1
= 20 - 1
= 19
The critical value of t at degree of freedom 19 = ±2.093
The margin error = Critical value of t × [tex]\frac{s}{\sqrt{n} }[/tex]
Substitute the values in the equations
The margin error = 2.093 × [tex]\frac{12}{\sqrt{20} }[/tex]
= 2.093 × 2.68
= 5.62 points
Therefore, the margin error is 5.62 points
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if you were to add 25 to y what would you get in all?
Answer:
25 + y
Step-by-step explanation:
It looks like you might be missing some information.
David says that a triangle with side measures 9 cm, 12 cm, and 17 cm is a right triangle. Susie says it is not. Who is correct? Explain
your reasoning.
12 cm
17 cm
9 cm
Answer: Susie is correct.
Step-by-step explanation:
Susie is correct, because the Pythagorean theorem does not work on this triangle. Since the Pythagorean theorem only works on right triangles, we can conclude that Susie is correct, and that this triangle is NOT a right triangle.
a²+b² = c²
a = 9
b = 12
c = 17
9² + 12² = 17²
==> 81 + 144 = 289
==> 225 = 289, This is not true
Therefore this triangle is not a right triangle.
How do I solve this problem. Please explain step by step if u could
0.25 + (-3) =
Answer:
0.25 − 3
=0.25 + −3
= −2.75
( a number line to help to)
Step-by-step explanation:
sketch the region enclosed by the given curves (within the given bounds, if provided) and find its area.
The area enclosed by the curves f(x) and g(x) is 1/12
Integral calculus can be used to compute the area between two curves, which is the region between two intersecting curves.
When we are aware of the equation for two curves and the locations of their intersections, integration can be utilized to determine the area under the curves.
Let our given curves be :
f(x) = x² and g(x) = x³ within the interval [0,1]
Formula to calculate area under these curves is
=> A = [tex]\int\limits^{c}_{a} {|f(x) - g(x)| \, dx[/tex]
Interval is given from 0 to 1
Therefore ,
=> A = [tex]\int\limits^{1}_{0} {[x^2 - x^3]} \, dx[/tex]
Integrating,
=> [tex][\frac{x^3}{3} - \frac{x^4}{4}]^{1}_{0}[/tex]
=> 1/3 - 1/4
=> 1/12 is required area
The given question is incomplete So, I've answered the question in general
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Wei Jing has between 70 and 150 baseball
cards in his collection. When he arranges them
in groups of 10, he has 3 left over. When he
arranges them in groups of 9, he has 5 left
over. If he arranges them in groups of 8, how
many will he have left over?
Answer:
117$.
Step-by-step explanation:
Let $x$ represent the number of cards in Wei Jing's collection. We are given that $70 \leq x \leq 150$. We are also given that $x \equiv 3 \pmod{10}$ and $x \equiv 5 \pmod{9}$. Since $x \equiv 3 \pmod{10}$, $x - 3$ is divisible by 10. Since $x \equiv 5 \pmod{9}$, $x - 5$ is divisible by 9. The least common multiple of 10 and 9 is $90$, so $(x - 3) - 90$ is divisible by 90 and $(x - 5) - 90$ is divisible by 90. Adding these equations gives us $2x - 98$ is divisible by 90. Dividing both sides by 2 gives us $x - 49$ is divisible by 45. Since $70 \leq x \leq 150$, the only solution for $x$ is $x = 117$.
Find the Probability of, A King, ace, jack of clubs or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards.
The Probability of, a ace, jack of clubs, King or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards is 4/13.
As per the given data,
we need to find out the probability of, King, ace, jack of clubs or queen of diamonds appears in drawing a single card from a well shuffled ordinary deck of 52 cards.
We know that,
Probability(Event) =Number of Favorable Outcomes/Total number of
Outcomes = x/n.
Total number of Outcomes is 52 (given)
So, we will calculate Number of Favorable Outcomes as follows:
The total no. of King in deck of card is 4
The total no. of queen in deck of card is 4.
The total no. of ace in deck of card is 4.
The total no. of jack in deck of card is 4.
Therefore, the number of favorable outcomes is 4+4+4+4= 16
Now, putting values in the above stated formula of probability, we get:
Probability= 16/52=4/13
Therefore, the probability of pulling a King, Ace, Jack of Clubs, or Queen of Diamonds from a 52-card standard deck that has been properly shuffled is 4/13.
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Work out the bearing of C from A
The bearing of C from A is 60° South.
How does one calculate bearing from A to B?
The bearing from A to B can be determined using interior angle if the bearing from B to A is known. Use the fact that angles in a full turn add up to 360° to determine the bearing of A to B, then subtract the bearing of B to A from 180° to determine the missing interior angle. For instance, B is 050° from A in terms of bearing.When AN elongates the angle will be 180°
Then the angle between A and C:
35° + 85° + x = 180°
120° + x = 180°
x = 180° - 120°
x = 60°
Hence, The bearing of C from A is 60° South.
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Your class council determined that its profit from the upcoming homecoming dance is directly
related to the ticket price for the dance. Looking at past dances, the council determined that the
profit p can be modeled by the function p(t) = -1212 + 480t + 30, where t represents the price of
each ticket. What should be the price of a ticket to the homecoming dance to maximize the
council's profit?
The price of a ticket to the homecoming dance to maximize the council's profit is 4830.
Define vertex?A vertex is a location in geometry where two or more curves, lines, or edges converge. As a result of this definition, vertices are the intersection of two lines that create an angle as well as the corners of polygons and polyhedra.A vertex is a point on a polygon where two rays or line segments meet, the sides, or the edges of the object come together. Vertex is the plural form of vertices.The vertex of an angle is the point around which it is measured, and the vertex angle is the angle that corresponds to a particular vertex.A face is a flat surface, an edge is a straight line connecting two faces, and a vertex is the corner of the shape.Given: a= -12, b = 480Vertex t= -b/2at= -480/2(-12) = 20Therefore, $20 per ticket.p(20) = -12(20) pow 2 + 480(20) + 30= 4830To learn more about vertex refer to:
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Answer:
$2 each ticket
Step-by-step explanation:
I don't really know how it's 2, but it's in the vertex of the graph. I just got my test back which the answer was 2. I'm sorry if you expected reasoning but I only got an answer. You can make a table for the equation and then see that 2 results in the highest profit though. 2 being substituted for t equates to the greatest profit.
an engineer says a pipe should be 7/10 centimeters long. The pipe is 9/10 centimeter long. How much of the pipe needs to be cut off? write an equation.
Answer: x = 9/10 - 7/10
Step-by-step explanation:
