Answer:
order pair (2,1) is the solution to the inequality.
What is the function of f and G?
Answer:
f(x) and G(x)
Step-by-step explanation:
When you want to write a function of something, you can write it as the letter followed by "(x)"
for a ride on a rental scooter, bob paid an fee to start the scooter plus cents per minute of the ride. the total bill for bob's ride was . for how many minutes did bob ride the scooter?
The total cost for Bob's ride is C = x + m and no. of minutes of the ride is
m = C - x.
What is a numerical expression?A mathematical statement expressed as a string of numbers and unknowable variables is known as a numerical expression. Statements can be used to create numerical expressions.
Given, A ride on a rental scooter, bob paid a fee to start the scooter plus cents per minute of the ride.
Let, 'x' be the fee in cents to start the scooter and 'm' be the no. of minutes of riding.
Therefore, The total bill(C) for Bob's ride is,
C = x + m.
The no. of minutes Bob ride the scooter is simply,
m = C - x.
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How do you check the function is continuous or discontinuous?
A function is continuous if it is defined for all values of the independent variable and there are no breaks, jumps, or gaps in its graph. In other words, a function is continuous if you can draw its graph without lifting your pen from the paper.
To check whether a function is continuous at a particular point, you can use the following methods:
The two-part definition of continuity: A function is continuous at a point if the following two conditions are met:
The limit of the function as it approaches the point from the left and the right exists and is equal to the function's value at that point.
The function is defined at the point.
The Epsilon-Delta definition of continuity: A function is continuous at a point if, for every epsilon (a small positive number) there exists a delta (also a small positive number) such that, for all points x within delta units of the point in question, the function's value at x is within epsilon units of the function's value at the point.
The graph of the function: You can also check the continuity of a function by looking at its graph. If the graph is a continuous curve with no breaks or jumps, then the function is continuous. If the graph has breaks or jumps, then the function is discontinuous.
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The Epsilon-Delta definition of continuity states that a function is continuous at a point if there is an epsilon (a small positive number) and a delta (also a small positive number) such that the value of the function at x is within epsilon units of the value of the function at the point for all points x within delta units of the point in question.
The function's graph: Additionally, you can examine a function's graph to see whether it is continuous. The function is continuous if the graph displays a continuous curve without any interruptions or leaps. The function is discontinuous if the graph has breaks or jumps.
Cuánto es?
35
— –1
10
Answer:
145
Step-by-step explanation:
Cuánto es means what is the answer
35 - (-110)
Two negative signs equal a positive sign
35 + 110 = 145
Calculate. Then, write a situation to match this expression and explain what 48.78 ÷ 0.9 the quotient means in your situation.
Answer:
Calculate: 48.78/0.9 = 54.2
Write a situation: Richard has 48.78 ounces of grape juice that he wants to ration out for his friends at his birthday party. Each cup the friends get can hold 0.9 ounces of grape juice.
What does the quotient mean: The quotient, 54.2, means that Richard had given 54.2 ounces of grape juice to all of his friends combined.
The equation P = 0.00892t^2 + 1.1149t + 78.4491 models the
United States population, P, in millions since 1900. If t
represents the number of years after 1900, then what is
the estimated population in 2025 to the nearest tenth of a
million?
343.9
219.0
356.9
217.8
The estimated population in 2025 is 356.9
What is estimation ?
In math, estimating can be used to roughly calculate an answer (getting a "rough response") or to verify its accuracy (getting the "proper answer"). Even when estimating large numbers or decimal numbers, you shouldn't need to utilize a calculator or other documented techniques.
Estimation is frequently performed by sampling, which involves counting a small sample of a given thing and extrapolating that number to a wider population. Calculating the number of sweets of a particular size that are contained in a glass jar serves as an illustration of estimation.
There are 125 years from after 1900 to 2025
P = 0.00892t^2 + 1.1149t + 78.4491
P= (0.0089x125x125)+(1.1149x125)+78.4491
=139.0625+139.3625+78.4491
=356.87
=356.9
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boulder is flung out of the top of a 3,000 m tall volcano. The bouIders height, y, in meters, is a function of the horizontal distance it travels, x, in meters. The slope of the line representing the volcano's hillside is -5/3 At what height above the ground will the boulder strike the hillside?
Using the linear function y = -5/3x + 3000, the boulder will touch the ground at 1800m
Linear FunctionA linear function has one independent variable and one dependent variable. The independent variable is x and the dependent variable is y.
A model of a linear function is given as y = mx + c
where m is the slope or rate of change of the function and c is the constant value or y - intercept
In this function;
The slope is - 5/3 and the constant is 3000
m = -5/3c = 3000The linear function can be written as
y = -5/3x + 3000
The height at which the boulder will strike the ground, the value of y = 0
0 = -5/3x + 3000
5/3x = 3000
x = 1800
The point is at 1800m
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Find the indicated z-scores shown in the graph The graph is bell shaped, both ends are shaded. The number on the right is 0.0322 and the number on the left is 0.0322. The z-scores are (____,_____) use comma to seperate answers as needed. Round to two decimal places as needed
The z-scores are (-1.85, 1.85)
What is Z- score?An illustration of a standardised score is the z-score. A z-score calculates how far a data point deviates from the distribution's mean by standard deviation.
If a Z-score is 0, it indicates that the data point's score is identical to the mean score
Given:
If we look at the z score table we will get the value of z- score.
The value 0.0322 lies in horizontal row 1.8 and column 0.05.
Then, for left value 0.0322 is -1.85
and, for right value 0.0322 is 1.85.
Hence, the z-scores are (-1.85, 1.85)
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A ditributor of computer oftware want to obtain ome cutomer feedback concerning it newet package. Three thouand cutomer have purchaed the package. Aume that 600 of thee cutomer are diatified with the product. Twenty cutomer are randomly ampled and quetioned about the package. Let X denote the number of diatified cutomer ampled. (a) Find the denity for X. (b) Find E[X] and Var X. (c) Set up the calculation needed to find P[X ? 3]. (d) Ue the binomial table to approximate P[X ? 3]
(a) The distribution of X is binomial with parameters n = 20 and p = 600/3000 = 1/5 since we are randomly selecting 20 clients without replacement and interested in the proportion of happy consumers. Given below is the probability density function for this binomial distribution.
f(x) is equal to (n pick x) * p * x * (1-p) (n-x)
Where p and 1-p are the probability of success and failure, respectively, and n pick x is the binomial coefficient, which is equal to n!/(x! * (n-x)!).
(b) The formula for the anticipated value of X, or E[X], is
E[X] = np = 20 * (1/5) = 4
Var X, the variance of X, is defined as follows:
Var X = np(1-p) = 20*1/5*4/5=3.2
(c) The cumulative distribution function of the binomial distribution's formula can be used to get P[X >= 3]:
Sum(i=3 to n) f for P[X >= 3] (i)
Summarizing from I = 3 to 20 and substituting the values from the density function, we obtain:
Sum(i=3 to 20) = P[X >= 3] [(20 pick I (1/5)*i*4/5*(20-i)]
(d) We must determine the value of the cumulative distribution function at x = 3, which is equivalent to the likelihood of receiving three or fewer successes out of 20 trials, in order to approximate P[X >= 3] using the binomial table. By using n = 20 and p = 1/5 to calculate the value of the cumulative distribution function at x = 3 in the binomial table, it is possible to determine this probability. P[X >= 3]'s estimated value is 0.586.
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How do you find the domain of A?
Take the function y = f(x), with the independent variable x as well as the dependent variable y, to determine the domain of a. If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.
What is a domain?The collection of all potential inputs for a function is its domain.
For instance, the domain of f(x)=x2 and g(x)=1/x are all real integers with the exception of x=0.
The set of numbers x for which a function is defined in a valid manner is known as the domain of the function.
A function's domain is referred to as a closed interval if it is specified across the interval a ≤ x ≤ b.
So, to find the domain of a, consider the function y = f(x), which has the independent variable x and the dependent variable y.
A value for x is said to be in the domain of a function f if it successfully allows the production of a single value y using another value for x.
Therefore, take the function y = f(x), with the independent variable x as well as the dependent variable y, to determine the domain of a. If a value for x successfully enables the creation of a single value y using another value for x, it is said to be in the domain of the function f.
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23.From the following information, prepare trading account for the year ended 31st March, 2013 Cash purchases Rs. 4,50,000; credit purchases Rs. 27,00,000; returns inward Rs. 60,000; cash sales Rs. 4,80,000; credit sales Rs. 33,00,000; returns outward Rs. 30,000; freight inwards Rs. 9,000; carriage inwards Rs. 9,000; wages and salaries Rs. 12,000; opening stock Rs. 4,50,000; closing stock Rs. 2,64,000 but its market value is Rs.2,52,000
The table showing trading account is given below
What is a trading account for a year?he trading account gives details of total sales, total purchases and direct expenses relating to purchase and sales. Trading account format for the year contains Particulars, Amount, Dr., Cr., Purchases, Sales, etc.
Given here,
Particulars Amount
Cash purchases Rs.4,50,000
Credit purchases Rs.27,00,000
Returns inwards Rs.60,000
Cash sales Rs.4,80,000
credit sales Rs.33,00,000
Returns outward Rs.30,000
freight inwards Rs.9000
carriage inwards Rs.9000
Wages and salaries Rs.12000
Opening stock Rs. 4,50,000
closing stock Rs. 2,64,000
Market value Rs.2,52,000
Hence the trading account for the year ended 31st March, 2013 is given above
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The probability that a person has immunity to a particular disease is 0.8. Find the mean number who have immunity in samples of size 17
The mean number who have immunity in samples of size 17 is 13.6
What is a Mean number?Sample Size =17
Immunity to a Particular disease=0.8
=17*0.8
=13.6
The average of the numbers is the mean. Calculating is simple: add up all the numbers, then divide by the total amount of numbers. To put it another way, it is the total divided by the number. In mathematics and statistics, the concept of mean is crucial. The most typical or average value among a group of numbers is called the mean.It is a statistical measure of a probability distribution's central tendency along the median and mode. It also goes by the name "anticipated value.It is a statistical idea with significant financial implications. The idea is applied in a number of financial areas, such as business appraisal and portfolio management, although not exclusively.To learn more about Mean refer to:
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Which is a graph of y 3x − 1?
The graph of y=3x-1 will be a straight line that does not passes through origin.
What is straight line?A line is a geometry object that extends on both sides and is defined by zero width. Simply put, a straight line is a line devoid of bends. A straight line is one that has no curves and continues to infinity on both sides.
Write standard form of straight line.ax+by=c is the standard form of straight line.
A straight line serves as the visual representation of a linear function's graph.
The given function is as follows:
y=3x-1
A linear function looks like this:
y=mx+c
Where:
m=3: the slope
c=-1: the y-intercept
So given function has a different y-intercept than 0.
So, the resulting graph o does not cross through the origin.
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Which of the following equations represents a proportional relationship? A. x=2.9 B. x+y=2.9 C. y=2.5/x D. y/x=2.5
The equation that represents a proportional relationship is y/X = 2.5. That is option D.
What is proportional relationship?A proportional relationship is the type of relationship that exist when between two variables which can be represented as y and x where a constant of proportionality exists between the two variables as k.
The relationship between these two variables can either be directly proportional or indirectly proportional.
The relationship that exists between X and y is a direct proportional relationship with a constant of proportionality of 2.5.
y = 2.5 X
= y/X = 2.5. Where 2.5 is the constant.
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What is the y-intercept of y =- 5x?
Y- intercept for the line y = 5x is 0. This can be get from the standard equation for a line.
For the The standard equation for a line is,
y = ax + b
y is called the dependent variable because its value depends on the value of x
a is the slope of the line
x is called the independent variable because it can be any value
b is the y-intercept
Here y is a function of x. You could simply write it as y = 5x. Thus if we compare to the standard form equation y = ax + b, a=5 and b=0. Thus the y-intercept is zero. The reason that this is the case is that when you set x=0 the value is plotted on the y axis because the equation for the y axis is the line defined by x=0. Any value in the x, y plane where x is equal to zero plots on the vertical line going through (0,0) or in other words the y axis.
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A water pail in your backyard has a small hole in it. You notice that it has drained a total of 2.5 liters in 4 days. What is the average change in water volume each day?
The average change in water volume is (answer here)iter(s) per day.
The average change in the volume of water per day is obtained as 0.625 litres.
What is the rate change of volume?The rate change of volume is the change of volume with respect to time.
For instantaneous change the derivative of the expression of volume can be taken.
The average change in the volume of water can be obtained as follows,
Average change = Volume of water ÷ Number of days
= 2.5 ÷ 4 = 0.625
Hence, the average change in water volume is given as 0.625 liters per day.
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What is * in a math problem?
Answer:
it means multiply like the × symbol
Step-by-step explanation:
What is the median of 35 27 51 31 28 19 33?
Answer:
31
Step-by-step explanation:
What is the median of 35 27 51 31 28 19 33?
Median: center most value when values are arranged in numerical order so:
19 , 27 , 28 , 31 , 33 , 35 , 51
Is 8 a multiple yes or no?
Therefore , the solution to this problem is yes 8 has multiple which are 16,24,32 etc.
What is multiple?A multiple in mathematics refers to the product produced by multiplying two numbers or variable. In this instance, the number 7 is multiple by 56.
The expression is termed as multiple .Fun Facts is an additional example of multiples. 0 is a multiple of all numbers since it produces zero when multiplied by any other number.
Here,
There are eight multiples: 8, 16, 24, 32, 40, 48, 56, 64, 72, and so on.
There are two consecutive results in this sequence, and there is an 8-digit gap between each subsequent number and the one before it.
The results of multiplying any integer by other natural numbers are known as multiples.
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What is the value of b2 4ac for the following equation 2x2 2x 1 0 4120?
The value of b2 - 4ac for the equation 2x2 + 2x - 1 = 0 is 12.
The equation 2x2 + 2x - 1 = 0 can be written in the form ax2 + bx + c = 0, where a = 2, b = 2 and c = -1. The formula for calculating b2 - 4ac for this equation is
[tex]b2 - 4ac = (b2) - (4)(a)(c)= (2)2 - (4)(2)(-1)= 4 - (-8)= 12[/tex]
Therefore, the value of b2 - 4ac for the equation 2x2 + 2x - 1 = 0 is 12.
To calculate this value, the formula first finds the value of b2, which is the square of the coefficient of the x-term (2). Then it multiplies the coefficient of the x2-term (2) by the constant term (-1), and multiplies the result by 4. Finally, it subtracts the result of this multiplication from the value of b2.
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simplify 2√12+3√48-75
To simplify this expression, we can start by simplifying the square roots:
2√12 + 3√48 - 75
= 2√(12) + 3√(48) - 75
= 2√(43) + 3√(412) - 75
= 2√4 * √3 + 3√4 * √12 - 75
= 2 * √3 + 3 * √12 - 75
We can then combine like terms:
= 2 * √3 + 3 * √12 - 75
= (2 * √3 + 3 * √12) - 75
= 5 * √12 - 75
Finally, we can simplify the expression to get our final answer:
= 5 * √12 - 75
= 5 * 2√3 - 75
= 10√3 - 75
= -75 + 10√3
= -75 + 10√3
So the simplified expression is -75 + 10√3.
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Amadou misses 2% of the free throws he attempts in a season. How many total free throws did he attempt if he missed 32?
The total free throws Amadou attempts, if Amadou misses 2% of the free throws he attempts in a season, he missed 32, is 1600.
What is the percentage?As it is clear from the term, percent means measuring anything per hundred. For example, you get marks per 100 marks, so you get the percentage.
Given:
Amadou misses 2% of the free throws he attempts in a season, he missed 32,
Calculate the total number of throws as shown below,
2% of x = 32
Here, x is the total number of throws,
0.02 × x = 32
x = 32 / 0.02
x = 1600
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How do you find a prime number?
A prime number is a positive integer greater than one that has no positive integer divisors other than one and itself. To find if a number is prime or not, if a number is divide by any other positive number other than 1 and itself it is not a prime number.
What is a prime number?A whole number higher than one that cannot be divided exactly by any other whole number than itself and one is a prime number.
What is whole number?Complete numbers, the range of numbers that includes zero and natural numbers and not a decimal or fraction.
8 is not a prime number because 8 is divided by 2 and 4 other than 1 and itself.
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How can you determine if the two angles are congruent by AAS A?
By using the the application of ASA we can determine the two angles are congruent by AAS.
AAS stands for Angle-Angle-Side. When two angles and a non-included side of a triangle are equal to the corresponding angles and sides of another triangle, then the triangles are said to be congruent.
AAS congruence can be proved in easy steps.
Suppose we have two triangles ABC and DEF, where,
Diagram attaches at the end of the solution.
∠B = ∠E [Corresponding angles]
∠C = ∠F [Corresponding angles]
AC = DF [Adjacent sides]
By angle sum property of triangle, we know that;
∠A + ∠B + ∠C = 180 ………(1)
∠D + ∠E + ∠F = 180 ……….(2)
From equation 1 and 2 we can say;
∠A + ∠B + ∠C = ∠D + ∠E + ∠F
∠A + ∠E + ∠F = ∠D + ∠E + ∠F [Since, ∠B = ∠E and ∠C = ∠F] ∠A = ∠D
Hence, in triangle ABC and DEF,
∠A = ∠D
AC = DF
∠C = ∠F
Hence, by ASA congruency, (AAS: the application of ASA)
Δ ABC ≅ Δ DEF
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Olivia is going on a 490 mile journey. So far, she has travelled 1% of her journey. How many miles has she travelled
Answer:
4.9 miles
Step-by-step explanation:
(.01)(490)=4.9
Can a 4 year old count to 100?
Yes, a 4 year old can typically count to 100.
What is counting?Counting is the process of determining the number of elements in a given set or group of objects. Counting is a basic numerical skill that is used in mathematics and other fields. It involves recognizing patterns and comparing numbers to identify how many items are in a given set. Counting is an important part of early childhood education, as it introduces children to the concepts of number and quantity.
Depending on the child's exposure to numbers, they may be able to count even higher. Counting to 100 is a fundamental skill that can be developed through practice and repetition. Teaching a 5 year old to count to 100 can be done through activities such as counting objects, counting steps, and playing counting games.
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What is an example of an inverse variation equation?
y = 3/x equation is an example of inverse variation between the variables x and y .
Now, According to the question:
The equation with the inverse variation between the variables 'x' and 'y' .
Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value.
y = 3/x is an example of inverse variation.
Hence, y = 3/x equation is an example of inverse variation between the variables x and y .
Let's know:
What is an Inverse variation equation?
Inverse variation is the relationships between variables that are represented in the form of y = k/x, where x and y are two variables and k is the constant value. It states if the value of one quantity increases, then the value of the other quantity decreases.
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what is the biggest number to mankind?
Answer:
googolplex
Step-by-step explanation:
it just is
Answer:
A Googolplex
Step-by-step explanation:
It is written as 10^googol and 10^10^100
How do you find the length of a rectangle when given the area?
we will find the length of rectangle when area is divided by the breadth of rectangle.
what are the properties of rectangle?Some properties are rectangle are stated below:
1. rectangle has four right angles
2. rectangles has four sides and equal opposite sides which are parallel to each other.
3.rectangle has two diagonals which are similar in length.
which is the formula for finding the length?The bigger side lengths are called length and the smaller sides are called breadth of rectangle.
if area of rectangle is given, we can find length when area is divided by its breadth.
length = area/breadth
hence, length of rectangle is determined from the value of area and breadth.
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How do you know if an equation is consistent and independent consistent and dependent or inconsistent?
Now, when a system has at least one solution, it's called consistent. When it has only one solution, it's called independent. otherwise inconsistent
The classification which best describes the system of equations is; Consistent and dependent
A linear or nonlinear system of equations as the case may be is termed consistent if there is at least one set of values for the unknowns that satisfies each equation in the system. In essence, when substituted into each of the equations, they make each equation hold true.
Additionally, the system of equations is dependent because the value of each variable is dependent on the others.
Now, when a system has at least one solution, it's called consistent. When it has only one solution, it's called independent.
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