if O represents number of integers between 10,000 and 100,000 all of whose digits are odd, and E represents number of integers between 10,000 and 100,000 all of whose digits are even, what is the value of O - E?
Module 04.03 Exponential Functions and Models: Essential Questions:
1) How do the properties of exponents apply to exponential functions?
2)How are key features of graphs and tables used to model relationships between two quantities?
3)How can the average rate of a change be identified for a function?
*PLEASE HELP! NEED TO KNOW THIS.*
Properties of exponents are used to simplify and manipulate exponential functions. In graphing, growth rate, intercept, and asymptotes model relationships. The average rate of change for a function is calculated based on changes in output divided by input changes over an interval.
Explanation:Understanding Exponential Functions and ModelsExponential functions are mathematical expressions where a constant base is raised to a variable exponent. The properties of exponents, such as product, quotient, and power rules, apply to these functions and are used to simplify and manipulate expressions.
When modeling relationships between two quantities using graphs and tables, key features like the growth rate, y-intercept, and asymptotes are important. The growth rate can be understood from the steepness of the graph or how quickly the y-values increase as x increases. The y-intercept represents the starting value of the quantity being modeled when x equals zero.
The average rate of change for a function is identified by calculating the change in the function's output values (y-values) divided by the change in the input values (x-values) over the interval of interest. For exponential functions, this rate of change is not constant, but increases or decreases at a rate proportional to the function's current value.
An example of exponential growth in a natural population might be the rapid increase in a bacteria population in an ideal lab condition, where it doubles every fixed amount of time. In contrast, a logistic growth pattern occurs when the growth rate decreases as the population reaches carrying capacity, such as the population of sheep in a field with limited grass for food.
Exploring the Exponential DistributionThe exponential distribution is typically used to model the time between events in a memoryless process, where the probability of an event occurring is the same at any moment. In an exponential distribution, outcomes are not equally likely as not all intervals of time are equally likely to occur before the next event. The mean (m), often referred to as the expected value, and the standard deviation can be derived from the rate parameter, which is the reciprocal of the mean.
Understanding how to manipulate a linear equation, as well as interpret and compute growth rates, is foundational in various applications including those in economics, biology, and environmental science. The ability to read and manipulate graphs is crucial for clearly presenting data and drawing accurate conclusions.
If there are 11 apples and I eat one and split half of the rest with my friend. How many do i have?
jackson bikes 2 miles in 15 minutes. At this rate, how many miles will he bike in 45 minutes?
For three consecutive years, Sam invested some money at the start of the year. The first year, he invested x dollars. The second year, he invested $2,000 less than 5/2 times the amount he invested the first year. The third year, he invested $1,000 more than 1/5 of the amount he invested the first year.
During the same three years, Sally also invested some money at the start of every year. The first year, she invested $1,000 less than 3/2 times the amount Sam invested the first year. The second year, she invested $1,500 less than 2 times the amount Sam invested the first year. The third year, she invested $1,400 more than 1/4 of the amount Sam invested the first year.
If Sam and Sally invested the same total amount at the end of three years, the amount Sam invested the first year is $ and the amount Sally invested the last year is $ .
Please help me :) Thanks!
The sum of 74 and four times a number is 258. Find the number
The unknown number is 46.
What is a word problem?A word problem is a verbal description of a problem situation. It consists of few sentences describing a 'real-life' scenario where a problem needs to be solved by way of a mathematical calculation.
For the given situation,
Let the number be x.
The sum of 74 and four times a number is 258,
⇒ [tex]74+4x=258[/tex]
⇒ [tex]4x=258-74[/tex]
⇒ [tex]x=\frac{184}{4}[/tex]
⇒ [tex]x=46[/tex]
Hence we can conclude that the unknown number is 46.
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Which of these expressions is equal to 6 + (2 + 3) × 5
Select the factors of 6ab + 3ay − 2bx − xy.
A. (3a − x)(2b + y)
B. (3a − y)(2b + x)
C. (2a − x)(3b + y)
D. (2a − y)(3b + x)
I need the answer I don't get it ...and this is a really long test ..but so far I only need help on this one . thanks to whoever helps me and give correct answer
Answer:
The factors of given expression is (3a-x)(2b+y)
A is correct
Step-by-step explanation:
Given: [tex]6ab+3ay-2bx-xy[/tex]
We need to factor the given expression.
First we make two group
[tex]\Rightarrow (6ab+3ay)+(-2bx-xy)[/tex]
Factor each group
[tex]\Rightarrow 3a(2b+y)-x(2b+y)[/tex]
[tex]\Rightarrow (3a-x)(2b+y)[/tex]
So, we get two factor (3a-x) and (2b+y)
Hence, The factors of given expression is (3a-x)(2b+y)
Simplify the following expression: 2x − 6y + 3x2 + 7y − 14x. 3x2 + 12x + y 3x2 − 12x − y 3x2 − 12x + y 3x2 − 12x − 13y
The required simplified solution of the given expression 2x − 6y + 3x² + 7y − 14x is 3x² -12x + y.
Given that,
To simplified solution of the given expression 2x − 6y + 3x² + 7y − 14x.
The process in mathematics to operate and interpret the function to make the function or expression simple or more understandable is called simplifying and the process is called simplification.
What is arithmetic?In mathematics, it deals with numbers of operations according to the statements. There are four major arithmetic operators, addition, subtraction, multiplication, and division,
= 2x − 6y + 3x² + 7y − 14x.
= 3x² + 2x -14x + 7y -6y
= 3x² -12x + y
Thus, the required simplified solution of the given expression 2x − 6y + 3x² + 7y − 14x is 3x² -12x + y.
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Erika and Rita have added a 1-mile walk to their daily exercise schedule. The table lists the time each of them took to walk the 1-mile distance over the past five days. Erika’s Time (in minutes) Rita’s Time (in minutes) 20 21.25 21.5 24.75 22.75 23 23.25 23 20.25 20.75 On average, it takes Erika about minute(s) per mile less than Rita.
What is the area of the polygon shown below?
2. If you have budgeted 12% of your monthly income for groceries, how much can you spend on groceries if you earn $950 bi-weekly?
bi weekly means you get paid every 2 weeks ( 2 times a month)
950*2 = 1900 per month for pay
1900*0.12 = 228 a month for food
Answer:
if you earn $950 bi-weekly, you earn 2 x 950 = $1900 per month. If you have budgeted 12% of your monthly income for groceries you need to find 12% of $1900: (1900 / 100) x 12 = 228. Answer: you can spend $228 a month on groceries.
How to simplify the expression 60/(-4)
how to write place value 35 thousand,26hundredand 16 tens and 12 ones
can someone help with this
Solve the equation by completing the square. Round to the nearest hundredth if necessary? X^2+3x=24
The height of a ball thrown directly up with a velocity of 10 feet per second from a initial height of of 100 feet is given by the equation h(t) = -16tsquared + 10t + 100, where t is the time in seconds and h is the ball’s height, measured in feet. When will the ball hit the ground? Round your answer to the nearest tenth.
Answer:
The ball will hit at 2.83 seconds.
Step-by-step explanation:
It is given that,
Velocity with which a ball is thrown up is, v = 10 ft/s
Initial height, h = 100 ft
The equation for the height of an object as a function of t is given by :
[tex]h(t)=-16t^2+10t+100[/tex]...............(1)
Where
t is the time in seconds
h is the ball's height measured in feet
We have to find the time when the ball hits the ground. It can be calculated by solving the quadratic equation of equation (1). On solving we get the value of t as :
t = 2.832 seconds
So, at 2.83 seconds the ball will hit the ground. Hence, this is the required solution.
11 POINTS GUYS PLZ
Answer 12 and 14
12) 10.77 + 2.09 + 0.75 = 13.61
13.61 x 1.07 = $14.56
total amount = $14.56
14) C shows the possible combinations
Solve the equation for the letter L: A=LW
L = AW
L equals W over A
L = A − W
none of the above
Find the value of X in the problem below. Geometry
(3x+10) +14x = 180
17x +10 = 180
17x=170
x = 170/17 = 10
x = 10
c+1/c-2 = 4/7 please show how you got the answer
Let set A = {odd numbers between 0 and 100} and set B = {numbers between 50 and 150 that are evenly divisible by 5}. What is A ∩ B? (2 points)
Answer ALL if u cant see all the answers it don't matter all u need is the question
In italy about 74 of every 100 people use celular telephones. Write the fraction of celular phone users in italy. Then write it as a decimal.
If the family has three pets, what is the theoretical probability that they have three dogs or three cats?
The probability helps us to know the chances of an event occurring. The theoretical probability that they have three dogs or three cats is 0.25.
What is Probability?The probability helps us to know the chances of an event occurring.
[tex]\rm{Probability=\dfrac{Desired\ Outcomes}{Total\ Number\ of\ outcomes\ possible}[/tex]
As it is given that the pet can either be a dog or a cat, therefore,
The probability that all the three pets are dogs is:
[tex]\rm P(X= 3\ dogs) = \dfrac{1}{2}\times \dfrac{1}{2}\times \dfrac{1}{2} = \dfrac{1}{8}[/tex]
The probability that all the three pets are cats is:
[tex]\rm P(X= 3\ Cats) = \dfrac{1}{2}\times \dfrac{1}{2}\times \dfrac{1}{2} = \dfrac{1}{8}[/tex]
Now, we need to calculate the probability that all three pets are either dogs or cats, therefore, the probability can be written as,
[tex]\rm P(3\ Dogs\ or\ 3\ Cats) = P(X = 3\ dogs) + P(X = 3\ cats)[/tex]
[tex]= \dfrac{1}{8}+\dfrac{1}{8}\\\\=\dfrac{2}{8}\\\\ = \dfrac{1}{4} = 0.25[/tex]
Hence, the theoretical probability that they have three dogs or three cats is 0.25.
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When the factors of a trinomial are (x - p) and (x - q) then the constant term of the trinomial is:
A. The quotient of -p and -q
B. The product of -p and -q
C. The difference of -p and -q
D. The sum of -p and -q
The constant term will be the product of -p and -q.
What is a trinomial?A trinomial is an algebraic expression that has three non-zero terms and has more than one variable in the expression.
Given that the factors of a trinomial are (x - p) and (x - q) we need to determine the constant term of the trinomial:
We know that a trinomial in its factors form can be written as,
x² + (α+β)x + αβ, where α and β are factors.
So, here the constant term of the trinomial will be (-p) × (-q) = pq.
Hence the constant term will be the product of -p and -q.
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0.75 = log x raise each side of the equation as power
o graph the equation 2x + 5y = 10, Zeplyn draws a line through the points (5, 0) and (0, 2). What is the slope of the line represented by 2x + 5y = 10?
a.-5/2
b.-2/5
c.2/5
d.5/2
we have
[tex] 2x + 5y = 10 [/tex]
we know that
the formula to calculate the slope is equal to
[tex] m=\frac{(y2-y1)}{(x2-x1)} [/tex]
Let
[tex] A( 5,0)\\B( 0,2) [/tex]
Step [tex] 1 [/tex]
Find the slope AB
[tex] mAB=\frac{(2-0)}{(0-5)} \\ \\ mAB=-\frac{2}{5} [/tex]
therefore
the answer is the option B
[tex] -\frac{2}{5} [/tex]
the graph in the attached figure
on every 3rd day Ivan goes to the gym. On every fifth day Gavin goes to the gym. What day will Ivan and Gavin will see each other.