The value of a comic book in dollars has been found to be 0.20y + 1.50, where y is the number of years since it was released. is
(a) [tex]0.2$[/tex]
(b) [tex]1.5$[/tex]
[tex]0.2 y+1.5 \longleftarrow \text { initial value }[/tex]
[tex]when $y$ increase one. the value increase $\$ 0.2$[/tex]
Travelling to movies and television programmes. An element of a comic book being in a popular film or television programme is a major factor in its value rising. Characters' comic book appearances have become far more valuable as they are integrated into the Marvel Cinematic Universe.
Marvel's first comic book just sold for $1.26m. Movies have contributed to the enduring popularity of superheroes, bringing in new audiences. The printed comic is still big business, worth over $1bn in North America alone.
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Find the lengths of segments AD and BD. Then check your answers using a different method.
Answer: BD = 5
Step-by-step explanation:
Using the Pythagorean theorem [tex]a^{2} + b^{2} =c^{2}[/tex] where c is the hypotenuse, we can solve for BD[tex]a^{2} +12^{2} =13^{2}[/tex]
[tex]a^{2} =13^{2}-12^{2}[/tex]
[tex]a = \sqrt{25}[/tex]
[tex]a = 5[/tex]
Therefore BD = 5
r(x) = x^2 + 5x + 4 write r(x) in factored form. I would like an explanation as to how you get the answer please!
Answer: (x+1)(x+4)
Step-by-step explanation:
Step 1: Use the sum-product pattern
x^2 + 5x + 4
x^2 + 4x + x + 4
Step 2: Common factor from the two pairs
x(x+4) + x+4
Step 3: Rewrite in factored form
(x+1)(x+4)
Graph the inequality on the axes below.
3x + y ≤ -3
Answer:
y ≤ -3x - 3
Step-by-step explanation:
The graph crosses the y axis at -3. The slope is -3. (0, -3) . From that point do down vertical 3 spaces and horizontally 1 space. You will be at the point (1,-6) Draw a line to join those 2 points. The inequality is ≤ that means the solutions are the points on the line and below the line. This is shown in the pink shading.
y ≤ -3x - 3
Step-by-step explanation:
The graph crosses the y-axis at -3. The slope is -3. (0, -3) . From that point do down vertical 3 spaces and horizontally 1 space. You will be at the point (1,-6) Draw a line to join those 2 points.
The inequality is ≤ which means the solutions are the points on the line and below the line. This is shown in the pink shading.
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In a video game, a player follows a certain path that can be partially modeled by the functionf(x)=x(x−5)(x−3) . This function can be graphed on a coordinate plane.
The graph of the function f(x) = x(x - 5)(x - 3) is given by the image shown at the end of the answer.
How to draw the sketch of the graph?To draw the sketch of the graph, we need to consider these three following features:
The x-intercepts.The y-intercept.The end behavior.The function in this problem is defined as follows:
f(x) = x(x - 5)(x - 3).
From the factor theorem, the x-intercepts are taken from the linear factors, as follows:
x = 0.x - 5 = 0 -> x = 5.x - 3 = 0 -> x = 3.The y-intercept is the value of y when the graph of the function crosses the y-axis, that is, the value of y when x = 0, hence:
f(0) = 0(0 - 5)(0 -3) = 0.
In the problem, we have a cube function, hence:
At the left tail(negative infinity) it goes to negative infinity.At the right tail(positive infinity) it goes to positive infinity.More can be learned about functions at https://brainly.com/question/24808124
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question 5: on a given day, there is a car accident reported at the intersection of victory blvd and richmond avenue with a probability 0.05. what is the probability that there are at most 2 car accidents reported thoughout a month?
The formula for the cumulative probability of a Poisson distribution can be used to calculate the likelihood that there will be at most 2 reported car accidents over the course of a month:
Cumulative probability is equal to (number of events * e)/(average number of events per time period).
(Number of events / (-average number of events per time period)!)
In this instance, there are typically 0.05 events per time period (the likelihood that a car accident is reported at the intersection on any given day), and there are typically between 0 and 2 events per time period (at most 2 car accidents). With these values entered into the formula, we obtain:
Cumulative probability is equal to (0.05 * e(-0.05)) / 0, (0.05 * e(-0.05)) / 1, and (0.05 * e(-0.05)) / 2, respectively.
That amounts to:
Probability total = 1 + 0.05 + 0.0025
which translates to 1.0525 percent, or 105.25%. It's crucial to keep in mind that this probability exceeds 1, which is impossible. This is because the formula for cumulative probability makes the assumption that each event is independent, which means that the occurrence of one event has no bearing on the probability of the occurrence of another. The cumulative probability calculated using this formula may not accurately reflect the probability of at most 2 car accidents occurring throughout a month because in reality, the probability of a car accident occurring on a given day may be influenced by the number of car accidents that have already occurred. You would need to account for the dependencies between the events in order to calculate this probability precisely.
Find the inverse of f(x) = 2(x-2) ^2 +1
Find the inverse of y = ^3√x-3
Answer:
f^-1(x) = 2(x-2)^2 + 1
f^-1(x) = (x+3)^3
Step-by-step explanation:
The inverse of a function is found by switching the roles of the dependent and independent variables. In other words, we can find the inverse of a function by interchanging the x and y values in the equation. So, the inverse of the function f(x) = 2(x-2)^2 + 1 can be written as f^-1(x) = 2(x-2)^2 + 1.
1. To find the inverse function explicitly, we can use the following steps:
2. Replace f(x) with y in the original function to obtain y = 2(x-2)^2 + 1.
3. Solve for x in terms of y to obtain x = +/- sqrt((y-1)/2) + 2.
The inverse function f^-1(x) can then be written as f^-1(x) = +/- sqrt((x-1)/2) + 2.
Note that this inverse function is not a one-to-one function, because for some values of x (namely, x < 1), the function has two possible values of y (i.e. it has two solutions). Therefore, the inverse function is not a function in the strict mathematical sense, but it is still a useful concept in certain contexts.
To find the inverse of a function, we switch the roles of the dependent and independent variables, so the inverse function can be written as x = ^3√y-3.
1. To find the inverse function explicitly, we can use the following steps:
2. Replace y with x in the original function to obtain x = ^3√y-3.
3. Solve for y in terms of x to obtain y = (x+3)^3.
The inverse function can then be written as f^-1(x) = (x+3)^3.
Note that this inverse function is a one-to-one function, meaning that for every value of x, there is only one corresponding value of y. Therefore, the inverse function is a function in the strict mathematical sense.
Sam wants to build a wooden deck on his patio, which is in the shape of a parallelogram. The
area of the patio is 350 ft2. Find the base. Round your answer to the nearest foot.
Hint : Use A = bh.
We may calculate our answer using fractions and the fact that the base is 18.3 feet.
What are fraction ?The components of a whole or group of items are represented by fractions. A fraction consists of two components.
The numerator is the figure at the top of the line. It details the number of equal portions that were taken from the total or collection.
The denominator is the figure that appears below the line. It displays the total number of identical objects in a collection or the total number of equal sections the whole is divided into.
There are three different methods to express a fraction: as a fraction, as a percentage, or as a decimal. Let's examine each of the three representational styles.
According to our question-
The patio is 280 square feet in size. locate the base.
Height = 5x Area = 280 feet square
Base = 6x
The parallelogram A's area can be expressed mathematically as;
Base + height equals area.
A = b×h
the values of area, base, and height are substituted.
280 = 5x × 6x = 30x^2 \sx^2 = 280/30 \sx = √(280/30)
Given that the base is 6x,
swapping out x's value.
Base = 6x = 6(√(280/30))
Base=18.3 feet
18.3 ft tall is the base
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Answer:
At short 18.7 ft is the answer
Tires A mechanic checked the tire pressures on each car that he worked on
for one week. The random variable x represents the number of tires that
were underinflated.
0
P(x) 0.30
1
2
0.25 0.25
3
0.15
4
0.05
The expected value for the given problem is E(x) = 1.4.
What is expected value?
The expected value is a generalization of the weighted average in probability theory. Informally, the expected value is the arithmetic mean of a significant number of outcomes of a random variable that were independently chosen.
A projected average value for an investment at some point in the future is known as the expected value (EV).
Investors use expected value to gauge an investment's merit, frequently in relation to how risky the investment is.
The formula for to find the expected value is given as,
E ( X ) = μ = ∑ x P ( x ) .
E(x) = 0*0.30 + 1*0.25 + 2*0.25 + 3*0.15 + 4*0.05
E(x) = 1.4
Hence, the expected value for the given problem is E(x) = 1.4.
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Hello can someone help me out with these two questions!?!?! This will help me a lot thank you! :D
The solution to the first inequality is x ≥ -2. Option 1 is correct. The solution to the second inequality is x ≤ -7. Option 1 is correct.
What is inequality?When two expressions are connected by a sign like "not equal to," "greater than," or "less than," it is said to be inequitable. The inequality shows the greater than and less than relation between variables and the numbers.
A number line in elementary mathematics is a representation of a graduated straight line that serves as an abstraction for real numbers, represented by the symbol R." It is assumed that every point on a number line corresponds to a real number and that every real number corresponds to a point.
The inequalities are,
2( x +6 ) > -6( x +1) +2
2x + 12 > -6x - 6 + 2
2x + 6x > -12 - 6 +2
8x > -16
x > -2
-3x - 1 ≥ 20
-3x ≥ 21
x ≥ -7
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suppose that a product is designed to function for 10,000 hours with a 3% chance of failure. find the average number of failures per hour and the mttf.
A product is designed to function for 10,000 hours with a 3% chance of failure , then Average number of failures per hour = 0.03/10000 = 0.000003 and MTTF = 1/0.000003 = 333,333 hours
Given,
Chance Product is designed to function for 10,000 hours
of failure is 3%
To find,
Average number of failures per hour
MTTF
Solution,
Average number of failures per hour = Chance of failure/Total hours of function
= 3%/10000
= 0.03/10000
= 0.000003
MTTF = 1/Average number of failures per hour
= 1/0.000003
= 333,333 hours
The product is designed to function for 10,000 hours with a 3% chance of failure. This means that the average number of failures per hour is 0.000003 and the Mean Time To Failure (MTTF) is 333,333 hours. This means that, on average, the product should last 333,333 hours before it fails.
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on the number line, the distance between x and y is greater than the distance between x and z. does z lie between x and y on the number line?
yes, z can lie between x and y but z can also lie on another side of x in Number lines.
With an example, define number line?
Number lines in mathematics are horizontal straight lines on which numbers are arranged in equal intervals.
A number line can be used to visualize all the numbers in a succession. The endpoints of this line go on forever.
What does the math number line mean?
A horizontal line with uniformly spaced numerical increments is called a number line. How the number on the line can be answered will depend on the numbers that are provided.
How a number is used—for example, to plot a point—depends on the question that goes with it.
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a random sample of size 36 is taken from a population with mean 17 and standard deviation 6. the probability that the sample mean is greater than 18 is?
The probability that the sample mean is greater than 18 as calculated is 0.8413.
Given data,
n = 36, sample size
μ = 17, population mean
σ = 6, population standard deviation
when x = 18
z = (18 - 17)/1 = 1
P(x <18) = 0.8413
Therefore , the probability = 0.8413
A population's standard deviation serves as a gauge for how widely distributed its individual data points are. It's a way to express how dispersed from the mean the data is.
While a large standard deviation indicates that the data is more spread, a small standard deviation indicates that the data points are often close to the mean.
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Using composition of functions, determine if the two functions are inverses of each other. A. No, because the functions contain different operations. B. Yes, for all values x ≥ 0. C. No, because the composition does not result in an answer of x. D. Yes, because F(x) is equal to –G(x).
Yes, for all values x ≥ 0. If the composition of the two functions is equal to the identity function for all values of x in their domain, then the two functions are inverses of each other.
What is composition of functions?Composition of functions is a mathematical operation that involves combining two functions to form a new function. To determine if two functions are inverses of each other using composition of functions, we need to first define the two functions and then determine if the composition of the two functions is equal to the identity function (f(x) = x).If the composition of the two functions is equal to the identity function for all values of x in their domain, then the two functions are inverses of each other. In this case, the correct answer is B: Yes, for all values x ≥ 0.To learn more about composite functions refer :
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You mix 1 fourth cup of crisp wheat cereal with 1 1 half cups of crisp rice cereal. Find and interpret the value of the ratio of crisp wheat cereal to crisp rice cereal.
The amount of crisp wheat cereal is _____ the amount of crisp rice cereal
Response:
Answer:
The value of the ratio of crisp wheat cereal to crisp rice cereal is 1/4 to 1 1/2, which can be simplified to 1/4 to 3/2. This means that for every 4 parts of crisp wheat cereal, there are 3 parts of crisp rice cereal. The amount of crisp wheat cereal is therefore less than the amount of crisp rice cereal. Specifically, the amount of crisp wheat cereal is 1/4 * the amount of crisp rice cereal.
Step-by-step explanation:
The median, or middle value, is 42 48 52 54 59 61 61 64 65 67 68 70 72 75 80
The median or the middle value of 42 48 52 54 59 61 61 64 65 67 68 70 72 75 80 is 64.
What is a median?It is the middle value of the given set of numbers after arranging the given set of numbers in order.
We have,
42 48 52 54 59 61 61 64 65 67 68 70 72 75 80
The given set of numbers is in ascending order.
There are 15 numbers.
The middle number will be the 8th number.
8th number = 64
Thus,
The median is 64.
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Does 0.010110111011110... represent a
rational number or an irrational number?
Explain your reasoning.
Answer:
This is an irrational number.
Step-by-step explanation:
If you see the decimal, it has the values of 1 and 0, but are not constant.
If it were to be 0.010101010... it would be rational.
But this decimal does not look like that, so its irrational.
Hope this helps.
Round 24.07 to the nearest tenths. It’s for an app it got a number line
24.07 rounded to the nearest tenth is 24.1
A school is arranging a field trip to the zoo. The school spends 546.53 dollars on passes for 40 students and 3 teachers. The school also spends 351.60 dollars on lunch for just the students. How much money was spent on a pass and lunch for each student?
There are $21.5 money was spent on a pass and lunch for each student.
What is an expression?Mathematical expression is defined as the collection of the numbers variables and functions by using operations like addition, subtraction, multiplication, and division.
Given that:
The amount spent by school on pass of 40 students and 3 teachers = $546.53
And, the amount spent for the lunch only for students = $351.60
Now,
The money spent for pass of 43 person = $546.53
Then, The amount of pass for each person = 546.53/43
= $12.71
Since, there are 40 student then amount of lunch for each students = ⇒ 351.60/40
⇒ $8.79
Therefore, amount of pass and lunch for each student = 12.71 + 8.79
= $21.5
Thus, $21.5 is the required answer.
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The side of a cube has a length of 4x³y6 cm. The volume of the cube can be found using
the formula V = S³. What is the volume of the cube in cubic centimeters?
PLEASE HELP
Answer:
find my dad
Step-by-step explanation:
What is the distance between points m and n? meters
Answer: 9.8
Step-by-step explanation:
Sonny has 2x + 3 dollars. Allan has 6x + 4 dollars. How much money did Sonny have if they both had $407 all together?
Answer:
$103
Step-by-step explanation:
In order to determine how much money Sonny has, we need to write a mathematical equation to solve for x. We know how much money Sonny and Allan each have in terms of x, and we can add the two expressions together to equal a total amount of $407. This will be represented and simplified as follows:
2x + 3 + 6x + 4 = 4078x + 7 = 407Now we can solve the equation for x.
8x = 400x = 50We know that x is equal to 50, so we can plug it back into Sonny's expression to find out how much money she has.
2(50) + 3 = 100 + 3 = 103Sonny has $103.We can check our work by solving for the amount of money Allan has and then adding up the two amounts to make sure the total is $407.
6(50) + 4 = 300 + 4 = 304CHECK: $103 + $304 = $407Which equation is equivalent to the quadratic equation x^2− 8x +19 = 0 where k represents the absolute value of the maximum value of the function? options:A (x-4)^2+k=0 B:(x-4)^2-k=0 C:(x+4)^2+k=0 D:(x+4)^2-k=0
The equation that is equivalent to quadratic equation x^ 2-8x+19=0 is
(x-4)^ 2+k = 0 using quadratic equation properties .
What is quadratic equation ?
A quadratic equation is a second order equation written as ax2 + bx + c = 0 where a, b, and c are coefficients of real numbers and a ≠ 0.
Properties of graph of quadratic equation :
1. The shape of curve y = f(x) is a parabola.
2. If a>0, the parabola opens upwards.
3. If a<0, the parabola opens downwards.
4.The coordinates of vertex of parabola in all these cases is
(-b/2a , -D/4a).
The given equation is x^ 2-8x+19=0
a = 1,
b = -8,
c = 19.
As a>0, 2nd property is correct i.e. no maximum value , only minimum value can be find that will be at vertex.
So, the vertex = (4,3)
The minimum value = 3 at 4.
So, the value of k = 3,
Given equation can be written as x^ 2-8x+16+3 = 0.
= (x-4)^ 2 +3 = 0.
The option A is correct.
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A quadratic function has roots at 2 and 4 and a vertex at (3, −2). What is the equation of the function in vertex form?
Answer:
Step-by-step explanation:
Word Problems: (please write out the equations and solve it)
1. David is going out for a pizza. The Pizza costs $10.50 plus $1.50 for each extra
topping ,x. Write an equation to represent the total cost of the pizza, t.
Dependent variable:
Independent variable:
Equation:
Use your equation to determine the total cost of the pizza with 3 extra
toppings.
The total cost of the pizza is
Dependent variable: t (total cost of the pizza)
Independent variable: x (number of extra toppings)
Equation: t = 10.50 + 1.50x
To determine the total cost of the pizza with 3 extra toppings, plug in x = 3 into the equation:
t = 10.50 + 1.50(3)
t = 10.50 + 4.50
t = 15.00
So the total cost of the pizza with 3 extra toppings is $15.00.
What is Dependent Variables?
The dependent variable is the variable that is being measured or studied in a statistical or scientific research study. It is called the dependent variable because it is believed to depend on the value of one or more other variables, known as the independent variables.
What is Independent Variables?
Independent variables are variables that are manipulated or controlled by the researcher in a scientific or statistical study. They are called independent variables because they are believed to have an effect on the dependent variable, which is the variable being measured or studied.
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STEP BY STEP please help me asap please !!!???
Answer:
(A) 19 times, 16 people.
Step-by-step explanation:
There are 374 people in line and 16 people leave the line without riding, so there are 374 - 16 = <<374-16=358>>358 people who want to ride the Caterpillar.
The Caterpillar seats 18 people, so it must run 358/18 = <<358/18=19.89>>19.89 times to accommodate all the riders.
Since the Caterpillar cannot run a fraction of a time, it must run 19 times.
There are 358 people who want to ride and the Caterpillar can accommodate 19 x 18 = <<19*18=342>>342 of them, so there are 358 - 342 = <<358-342=16>>16 people on the last ride.
Therefore, the Caterpillar runs 19 times and there are 16 people on the last ride, so the answer is (A) 19 times, 16 people.
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A police officer is estimating the distance from one side of a street to the other. The actual distance is 13.4 m. The police officer’s estimate is 14 m. Find the absolute error and the percent error of the police officer’s estimate.
PLEASE HELP
The absolute error and the percent error of the police officer’s estimate will be 4.29%.
What is the percentage?The amount of any product is given as though it was a proportion of a hundred. The ratio can be expressed as a quarter of 100. The phrase % translates to one hundred percent. It is symbolized by the character '%'.
The percentage is given as,
Percentage (P) = [Final value - Initial value] / Initial value x 100
A cop is assessing the separation from one side of a road to the next. The genuine distance is 13.4 m. The cop's gauge is 14 m.
The absolute error and the percent error of the police officer’s estimate are calculated as,
%error = [(14 - 13.4) / 14] x 100
%error = (0.60 / 14) x 100
%error = 4.29%
The outright mistake and the percent blunder of the cop's gauge will be 4.29%.
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7. Use the Division Property of Equality to write an equation that is
equivalent to 5x = 14.
Answer: x = 14/5 or x = 2.8
Step-by-step explanation:
Step 1: Divide both sides of the equation by five: a common nonzero real number.
(5x)/5= 14/5
Step 2: Simplify
x = 14/5
Please help if possible.
Answer:
$1020.00000$1020.15050$1020.18436$1020.19742$1020.20078Step-by-step explanation:
You want to find the effect of compounding 2% annual interest on $1000 at different intervals for a year. The intervals are ...
1 per year4 per year12 per year52 per year365 per yearCalculatorThe attached calculator display shows the result:
yearly: $1020.00000quarterly: $1020.15050monthly: $1020.18436weekly: $1020.19742daily: $1020.20078question in screenshot (need help ASAP)
a plane, 50 miles away from its destination, is flying toward the airport at an altitude of 30,500 feet. later, this same plane is 20 miles from the airport and has descended to an altitude of 18,000 ft. how far has the plane flown?
Using the geometry from the question and using the Pythagorean theorem with the distance provided, The answer is 30.09 miles.
What is unit conversion?By definition, unit conversion refers to the division or multiplication operation used to convert measurements of the same quantity between various units.
What is Pythagorean theorem and it's formula?The Pythagorean theorem, sometimes known as Pythagoras' theorem, is a basic relationship between a right triangle's three sides in Euclidean geometry.
It's formula is:
[tex]h^{2} = p^{2} +b^{2}[/tex]
h1=30500 feet = 5.77 miles
d1= 50 miles
h2= 18000 feet = 3.4 miles
d2= 20 miles
for right angle triangle,
height = h1-h2 = 2.37 miles
distance = 50-20 = 30 miles
plane flown = [tex]\sqrt{2.37^{2}+30^{2}}[/tex]
=30.09 miles
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