The cost function is a linear function
The cost of 10 tickets is $165You can buy 8 tickets with $130The function is given as:
[tex]\mathbf{C(x) = 17.5x - 10}[/tex]
(a) The cost of 10 tickets
This means that: x= 10
So, we have:
[tex]\mathbf{C(x) = 17.5x - 10}[/tex]
[tex]\mathbf{C(10) = 17.5 \times 10 - 10}[/tex]
[tex]\mathbf{C(10) = 175- 10}[/tex]
[tex]\mathbf{C(10) = 165}[/tex]
Hence, the cost of 10 tickets is $165
(b) The number of tickets that costs $130
This means that C(x) = 130
So, we have:
[tex]\mathbf{C(x) = 17.5x - 10}[/tex]
[tex]\mathbf{130 = 17.5x - 10}[/tex]
Add 10 to both sides
[tex]\mathbf{140 = 17.5x}[/tex]
Divide both sides by 17.5
[tex]\mathbf{8 = x}[/tex]
Rewrite as:
[tex]\mathbf{x = 8}[/tex]
Hence, you can buy 8 tickets with $130
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Write an equation for the parabola whose vertex is at (4, 9) and which passes through (5, 24).
Find all the second partial derivatives. w = u9 + v7
Answer:
[tex]w_{uu} = 72u^{7}[/tex]
[tex]w_{uv} = w_{vu} = 0[/tex]
[tex]w_{vv} = 42v^{5}[/tex]
Step-by-step explanation:
We can have the second partial derivatives of w in relation to u, v and uv. So
[tex]w = u^{9} + v^{7}[/tex]
[tex]w_{u} = 9u^{8}[/tex]
[tex]w_{uu} = 72u^{7}[/tex]
[tex]w_{uv} = w_{vu} = 0[/tex]
[tex]w_{v} = 7v^{6}[/tex]
[tex]w_{vv} = 42v^{5}[/tex]
Final answer:
The second partial derivatives of w = u^9 + v^7 are w_uu = 72u^7, w_uv = 0, and w_vv = 42v^5.
Explanation:
To find all the second partial derivatives of w = u^9 + v^7, we need to differentiate twice with respect to each variable. Let's start:
First, find the first partial derivatives:
wu = 9u^8 (differentiating with respect to u)
wv = 7v^6 (differentiating with respect to v)
Now, take the second partial derivatives:
wuu = 72u^7 (differentiating wu with respect to u)
wuv = 0 (differentiating wu with respect to v)
wvv = 42v^5 (differentiating wv with respect to v)
So, the second partial derivatives of w = u^9 + v^7 are wuu = 72u^7, wuv = 0, and wvv = 42v^5.
What is the sum of the series?
Explain what a polynomials is and identify the different parts of a polynomial.
Explain the different labels used to categorize polynomials
Explain how addition and subtraction of polynomials is accomplished
When multiplying polynomials, we are taking every term of one polynomial and multiplying them by every term of the second polynomial, then collecting like terms explain how foil helps us to accomplish this and what category of polynomials foil applies to.
There are tow special case products where the product takes on special patterns explain these two cases and when they occur.
For each of the two special cases, illustrate your explanation with an appropriate exercise from the ( a+b)2=a2+2ab+b2 )(a-b)2=a2-2ab+b2 ) showing how the multiplication is performed using the special pattern formula then also showing the same result using foil.
Write a Multiplication expression that shows 10 sixths
Ling lives 2 miles from school. It took him 15 minutes to bike from school to home. The first half of the distance he biked at a speed of 12 mph. What was his speed for the remaining distance? What was his average speed?
Answer:
First Part: 6 mphSecond Part: 8 mph1. James buys a video game for his Xbox for $49.99, a controller for $34.95, and a walk through manual for $19.99. The sales tax in his area is 8.25%. What will be the total cost of his purchase?
Jack is in hospital and his temperature is recorded every hour one morning. Time Temperature 06:00 40.0 07:00 40.0 08:00 39.5 09:00 39.0 10:00 38.5 11:00 38.0 12:00 38.0 Which is the best type of chart to use to represent this information? scatter diagram, pictogram, pie chart, line graph, tally chart, bar chart?
Here we are given two types of data : Time and Temperature.
We can plot one of these on x axis and the other on y axis.
So we can use a line graph here.
Tom is going to build a fence around his garden which is a rectangle measuring 8 m by 20 m. He will first put in posts which will be 4 m apart. If the posts cost $5.50 each, what will be the total cost for all the posts?
Which of the points listed is the same distance from the x-axis as the point (8, 3.25)?
A- (-8, 4.75) B- (7, -3.25) C- (3.25, 7) D- None of these are correct.
The points listed which has the same distance from the x axis as the point (8, 3.25) is B- (7, -3.25).
What are the Coordinates?Coordinates are the set of points in a geometrical plane or space, which is used to denote the exact point in the coordinate plane or space.
Given is a point in the XY plane with the coordinates (8, 3.25).
We have to find the point in the options which are at a same distance as the given point.
In order for two points to be at a same distance from the x axis, their y coordinates must be same with either same sign or of the opposite sign.
Here the point with the same y coordinate as the given point is B- (7, -3.25)
Hence option B is correct.
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In playing Monopoly, rolling doubles three times in a row sends you to jail. What is the probability of rolling three consecutive doubles? a. 0.167 b. 0.5 c. 0.00463 d. 18.0
An amusement park ride rotates around a fixed axis such that the angular position of a point on the ride follows the equation: θ(t) = a + bt2 – ct3 where a = 0.3 rad, b = 0.85 rad/s2 and c = 0.035 rad/s3
At t = 2 seconds, the angular position of the point on the amusement park ride is approximately 3.42 radians.
We have,
The equation θ(t) = a + bt² - ct³ represents the angular position of a point on the amusement park ride as a function of time.
Given:
a = 0.3 rad
b = 0.85 rad/s²
c = 0.035 rad/s³
In this equation,
θ(t) represents the angular position of the point on the ride at time t.
The term a is the initial angular position when t = 0, which is 0.3 radians.
The term bt² represents the angular displacement due to the linearly increasing angular velocity.
The coefficient b determines the rate of change of the angular displacement over time.
The term -ct³ represents the angular displacement due to the cubic decrease in angular acceleration.
To find the angular position at a specific time t, substitute the given values of a, b, c, and the desired value of t into the equation
θ(t) = a + bt² - ct³.
For example, if we want to find the angular position at t = 2 seconds:
θ(2) = 0.3 + 0.85 * (2²) - 0.035 * (2³)
= 0.3 + 0.85 * 4 - 0.035 * 8
= 0.3 + 3.4 - 0.28
= 3.42 radians
Therefore,
At t = 2 seconds, the angular position of the point on the amusement park ride is approximately 3.42 radians.
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The angular position of a point on a ride is given by the equation θ(t) = a + bt² - ct³. Factors such as the moment of inertia can change the angular acceleration in the system. When a child is on the merry-go-round, the moment of inertia increases, leading to a decrease in angular acceleration.
Explanation:The angular position of a point on an amusement park ride can be described by the equation θ(t) = a + bt² - ct³. In this equation, angular position is represented by θ(t), 'a' represents the initial angular position (0.3 rad), 'b' represents the angular velocity (increase in angular position per unit time - 0.85 rad/s2) and 'c' is the rate of change in angular velocity or the angular acceleration (0.035 rad/s3).
The angular acceleration can change due to factors such as a change in the moment of inertia. For example, when a child is on a merry-go-round, the combined moment of inertia is greater, therefore reducing the angular acceleration. The moment of inertia depends on factors such as the mass and the location of that mass relative to the axis of rotation. The child can be approximated as a point mass at a distance of 1.25 m from the axis of rotation.
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Find the number, if 5/7 of it is 15
The number is 21.
What is an expression?An expression is a way of writing a statement with more than two variables or numbers with operations such as addition, subtraction, multiplication, and division.
Example: 2 + 3x + 4y = 7 is an expression.
We have,
Number = M
5/7 of M = 15
This can be written as,
(5/7)M = 15
M = 15 x 7/5
M = 3 x 7
M = 21
Thus,
The number is 21.
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el area de un rectangulo de lados 0,0005m y 0,003m es
What methods can be used to solve quadratic equations?
Melvin has 1/2 of a cake. He shares the cake equally with each of 2 friends and himself. Show me how u got your answer
Melvin and each of his 2 friends get [tex]\( \frac{1}{6} \)[/tex] of the cake each.
Sure! If Melvin has [tex]\( \frac{1}{2} \)[/tex] of a cake and he wants to share it equally with each of his 2 friends and himself, we need to find out how much each person gets.
First, we need to find out how many people are sharing the cake. Melvin himself plus his 2 friends make a total of 3 people.
Now, to divide [tex]\( \frac{1}{2} \)[/tex] of the cake equally among 3 people, we divide [tex]\( \frac{1}{2} \)[/tex] by 3:
[tex]\[ \frac{1/2}{3} = \frac{1}{2} \times \frac{1}{3} \][/tex]
To multiply fractions, we multiply the numerators together and the denominators together:
[tex]\[ = \frac{1 \times 1}{2 \times 3} \][/tex]
[tex]\[ = \frac{1}{6} \][/tex]
So, each person gets [tex]\( \frac{1}{6} \)[/tex] of the cake.
Therefore, Melvin and each of his 2 friends get [tex]\( \frac{1}{6} \)[/tex] of the cake each.
Find the missing term of the following sequence. . . . –2, __, 456, . . .
The answer should be
228
It is estimated that approximately one-half of all aluminum cans will be recycled each year. If a soft drink company produces 350,000 cans one year, how many cans are still in use after 4 years of recycling and re-using, using this function?
Nt = 350,000(0.52)t
A 87,500
B 25,591
C 175,000
D 21,875
Answer: B
Step-by-step explanation:
plato
write an inequality in slope intercept form for the graph below. if necessary use <= or >=
The correct options are:
1. The equation of a given line is y=-x-3 (it is easy to find it using points (0;-3)&(-3;0)).
2. According to the equation of a line: y≥-x-3
What is the inequality in slope-intercept form?You may use the slope-intercept form to graph inequalities. The slope-intercept form is expressed as y = mx + b, where the variable m stands for the slope of the line, and b stands for the y-intercept (or in which the line crosses the y-axis).
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Which interval is the solution set to 0.35x – 4.8 < 5.2 – 0.9x?
The solution to the mathematical inequality equation 0.35x - 4.8 < 5.2 - 0.9x is the interval x < 8.
Explanation:In order to find the solution to the equation 0.35x - 4.8 < 5.2 - 0.9x, you first need to rearrange the terms in the equation such that all terms involving x are on one side of the inequality and the other terms are on the other side. Starting with: 0.35x - 4.8 < 5.2 - 0.9x, if we add 0.9x to both sides we get 0.35x + 0.9x < 5.2 - 4.8, which simplifies to 1.25x < 10.
Next, to isolate 'x' we divide through by 1.25, which gives us: x < 10/1.25 which simplifies to x < 8. Therefore the answer to the equation 0.35x - 4.8 < 5.2 - 0.9x is the interval x < 8.
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y=-2x+1
y=-2x-3
solve and graph
Which of the following criteria are necessary conditions for making a statistical inference?
sample size greater than 30, or an approximately normal data set
sample size greater than 100
convenience sample
simple random sample
systematic sample
Answer:
1 and 4 are correct
Step-by-step explanation:
Jatonia sold n cups of lemonade at her stand for $0.75 each. She made a total of $18.00. Write an expression to express how many cups of lemonade she sold.
the basketball court in the park is rectangle two of the sides are 84 feet long and the other two sides are 50 ft long what is the perimeter of the basketball court
Suppose that with a budget of $100, Deborah spends $60 on sushi and $40 on bagels when sushi costs $2 per piece and bagels cost $2 per bagel. But then, the price of bagels falls to $1 per bagel.
b. At the new prices, how much money would it have cost Deborah to buy those same quantities (the ones that she consumed before the price change)?
c. Given that it used to take Deborah’s entire $100 to buy those quantities, how big is the income effect caused by the reduction in the price of bagels?
Answer:
Part A) The quantities are [tex]30\ piece\ of\ sushi[/tex] and [tex]20\ bagels[/tex]
Part B) [tex]\$80[/tex]
Part C) The income effect is a loss of [tex]\$20[/tex]
Step-by-step explanation:
Part A)
Let
x-----> the number of piece of sushi
y----> the original number of bagels
we know that
[tex]2x=60[/tex] ------> [tex]x=30\ piece\ of\ sushi[/tex]
[tex]2y=40[/tex] ------> [tex]y=20\ bagels[/tex]
Part B) At the new prices, how much money would it have cost Deborah to buy those same quantities (the ones that she consumed before the price change)?
Bagels
[tex]20(1)=\$20[/tex]
Sushi
[tex]30(2)=\$60[/tex] -----> is the same
The total cost is
[tex]\$20+\$60=\$80[/tex]
so
The same quantities would have cost [tex]\$80[/tex]
Part C) Given that it used to take Deborah’s entire $100 to buy those quantities, how big is the income effect caused by the reduction in the price of bagels?
Find the difference
[tex]\$100-\$80=\$20[/tex]
therefore
The income effect is a loss of [tex]\$20[/tex]
which graph represent the equation y - 2 = 3x?
What is the truth value for the following conditional statement? If the snow is white, then the grass is red.
Final answer:
The truth value of the conditional statement 'If the snow is white, then the grass is red' cannot be determined to be true or false without context, as it is a statement that requires evaluation of its antecedent and consequent. In logic, a conditional statement is true unless the antecedent is true and the consequent is false.
Explanation:
The truth value for the conditional statement "If the snow is white, then the grass is red," cannot be evaluated as true or false based solely on the content of the statement. In logic, a conditional statement is considered to be true unless a situation occurs where the first part (the antecedent) is true and the second part (the consequent) is false.
Here, the statement "the snow is white" is true, but the statement "the grass is red" can be false, as grass is typically green. This illustrates an important logical principle where the truthfulness of a conditional does not require that the consequent actually follows from the antecedent. To evaluate the truth of a conditional statement, it would be more appropriate to look for a counterexample that disproves it or involves a scenario where the antecedent is true and the consequent is false.
A 90% confidence interval for the mean percentage of airline reservations being canceled on the day of the flight is (1.1%, 3.4%). what is the point estimator of the mean percentage of reservations that are canceled on the day of the flight?
Find all real numbers X such that 18x-9>9 or 2x-4>-10
A British company is sending you measurements for a table to build in your factory. The table top must be 50 cm × 75 cm. Your machine calibrates in inches. Find the size of the table in inches. (1 cm = .39 in) A. 89 in × 114 in B. 11 in × 36 in C. 19.5 in × 29.25 in D. 128.2 in × 192.3 in
Answer: C. 19.5 in × 29.25 in
Step-by-step explanation: (50 x .39) x (75 x .39)