Find the average rate of change of the following function on the given interval. y=5^x on [0,2]
To find the rate of change within this interval, we have
[tex]\begin{gathered} \text{ Rate of change =}\frac{f(2)-f(0)}{2-0} \\ =\frac{25-0}{2-0} \\ =\frac{25}{2} \\ =12.5 \end{gathered}[/tex]Hence, the average rate of change of the function within the interval
[0,2] is 12.5
please help me please help me
Answer:
Only did for Problem 1:
Square is: 4x^2-20x+25
Side is: 2x-5
A^2=4
2AB=-20
B^2=25
Step-by-step explanation:
The Associative Property applies to which operations? Check all that apply. A. divideb -c.xD+
C) x
D)+
Explanation
The assoaciative property states that when three or more are added (or multiplied), the sum (or the ) is the same regardless of the grouping of the multiplicands
[tex]\begin{gathered} a\cdot(b\cdot c)=(a\cdot b)\cdot c \\ a+(b+c)=(a+b)+c=(a+c)+b \end{gathered}[/tex]Associative property can only be used with addition and multiplication and not with subtraction or division
so, the answer is
C) x
D)+
A football field is 1920 inches wide. What is two thirds of a football field?
Answer:
2/3's of a football field is 1280
Step-by-step explanation:
were going to take 1920 and were going to divide that by 3.
1920/3 = 640
After that your going to multiply 640 by 2
640(2) = 1280
So your answer is 1280
21. The table below describes a sample of 15 players in Major League Baseball, chosen from the starting lineups of teams in 2019. The table shows the team, age, position, height, and salary for each player, as well as several statistics from that season. These include the number of games they played (G), their batting average (AVE) (the proportion of their at-bats for which they got a hit), and their home runs (HR).NameTeamAgeHeightGAVEHRSalaryCedric MullinsOrioles25173 cm22.0940$557,500Tim AndersonWhite Sox26185 cm123.33518$1,400,000Christin StewartTigers25183 cm104.23310$556,400Alex GordonRoyals35185 cm150.26613$20,000,000Jonathan SchoopTwins27185 cm121.25623$7,500,000Marcus SemienAthletics29183 cm162.28533$5,900,000Yandy DiazRays28188 cm79.26714$558,400Randal GrichukBlue Jays28188 cm151.23231$5,000,000Josh DonaldsonBraves33185 cm155.25937$23,000,000Joey VottoReds36188 cm142.26115$25,000,000Cody BellingerDodgers24193 cm156.30547$605,000Ryan BraunBrewers35188 cm144.28522$19,000,000Maikel FrancoPhillies27185 cm123.23417$5,200,000Ian KinslerPadres37183 cm87.2179$3,750,000Marcell OzunaCardinals28185 cm130.24129$12,250,000Calculate the Five Number Summary for the number of games played by the players.Min: Q1 : Median: Q3 : Max:
Given:
The number of games played by 15 players are,
22, 123, 104, 150, 121, 162, 79, 151, 155, 142, 156, 144, 123, 87, 130.
The objective is to find five number summary for the number of games.
Explanation:
The five number summary are minimum value, quartile 1, median, quartile 2 and maximum value.
Increasing order:
The increasing order of the given data is,
22, 79, 87, 104, 121, 123, 123, 130, 142, 144, 150, 151, 155, 156, 162.
Minimum and Maximum value:
By considering the increasing order of the data, the minimum value is 22 and the maximum value is 162.
To find median:
The median can be calculated as the middle term of total number of data.
Since, the total number of data is 15, which is odd, then the median can be calculated as,
[tex]\begin{gathered} \text{Median}=\frac{15+1}{2} \\ =\frac{16}{2} \\ =8th\text{ term} \end{gathered}[/tex]Thus, the 8th term of increased order is 130.
To find Q1:
The quartile 1 can be defined as the middle term of the left side of the median.
Since, the left side of the median contains 7 terms, which is odd, then the quartile 1 can be calculated as,
[tex]\begin{gathered} Q1=\frac{7+1}{2} \\ =\frac{8}{2} \\ =4th\text{ term (left)} \end{gathered}[/tex]Thus, the 4th term on left side of median is 104.
To find Q3:
The quartile 3 can be defined as the middle term of the right side of the median.
Since, the right side of the median contains 7 terms, which is odd, then the quartile 3 can be calculated as,
[tex]\begin{gathered} Q3=\frac{7+1}{2} \\ =\frac{8}{2} \\ =4th\text{ term (right)} \end{gathered}[/tex]Thus, the 4th term on right side of median is 151.
Hence, the five number summary are,
Min: 22
Q1: 104
Median: 130
Q3: 151
Max: 162.
Stella rewrites -2 1/2 plus 3.7 using commutative Property of addition. Which expression did she write?
The rule for the commutative property of addition is:
a + b = b + a
Stella writes:
[tex]-2\frac{1}{2}\text{ plus 3.7}[/tex]This can be expressed mathematically as:
[tex]-2\frac{1}{2}+3.7[/tex]Which according to the property of commutativity can also be written as:
[tex]\begin{gathered} 3.7\text{ + (-2}\frac{1}{2}) \\ 3.7\text{ - 2}\frac{1}{2} \end{gathered}[/tex]The expression Stella wrote based on the commutative property of addition is therefore:
[tex]\begin{gathered} -2\frac{1}{2}+\text{ 3.7 or} \\ 3.7\text{ - 2.5 (Note that 2}\frac{1}{2}=2.5) \end{gathered}[/tex]Members of a band estimated that 200
people were at their show last night. Their manager told them that 227
people had actually been at the show. What was the band's percent error?
Answer:
13.5%
Step-by-step explanation:
Using the percent error formula,
[tex]\frac{227-200}{200}=13.5\%[/tex]
Determine the restriction of x using inequality. Show your work.
The sides of a triangle rule states that the sum of the lenghts of the sides of a triangle has to be greater than the lenght of a third side.
4x+2 +8 >18
x>2
4x+2+18>8
x>-3 (reject)
Answer: x>2
One evening, Hazel and her brother each needed to use the family computer for part of their homework. They worked on their homework for 3 hours, and agreed to share the computer equally for that time.
How long did each person use the computer?
Write your answer as a proper fraction or mixed number.
Each person used the computer for [tex]\frac{3}{2}[/tex] hours.
Define fraction.A fraction is a number that is a component of a whole. By breaking a whole into a number of parts, it is evaluated. For instance, the symbol for half of a complete number or item is 12. 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. A fractional equation is one in which one or more of its terms have the unknown as their denominator.
Given Data
They worked on their homework for 3 hours, and agreed to share the computer equally for that time.
They share computer equally, so
[tex]\frac{time}{2}[/tex]
Fraction - [tex]\frac{3}{2}[/tex]
Each person used the computer for [tex]\frac{3}{2}[/tex] hours.
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2. BANKING Brayden deposited $2700 into a savings account that has an annual
simple interest rate of 0.3%. Find the amount in the savings account after each
number of years.
se notes
a. 2 year
b. 3 years
s
c. 6 years
Answer:
a) $2716.20
b) $2724.30
c) $2748.60
Step-by-step explanation:
You want the account balance after 2, 3, and 6 years if $2700 is deposited into an account earning 0.3% simple interest.
BalanceThe value of an investment P earning simple interest at rate r for t years is given by ...
A = P(1 +rt)
For the given savings deposit, the balance will be ...
A = 2700(1 +0.003t) . . . . . for t = 2, 3, 6
Another way to write this is ...
A = 2700 + 8.10t
The balances are ...
2 years: $2716.203 years: $2724.306 years: $2748.60<95141404393>
I need help with this question. The graph below is option a. I have options to choose from
In this type of exercise ≥ values mean values that are inside the 'area' that the function is determining.
So the correct answer can only be now A or C because B and D are 'outside' areas.
In the letter A we can choose a point to validate the function. Let's choose the point (6,-4):
[tex]y\ge x^2-7x+10[/tex][tex]-4\ge6^2-7\times6+10[/tex][tex]-4\ge36-42+10[/tex][tex]-4\ge4\text{ !!!}[/tex]Look that this result is impossible. -4 is not greater than 4. This invalidate letter A! Therefore the correct answer will be the letter C.
Choose the equation that satisfies the data in the table. in pic
Question:
Solution:
Note that if we evaluate x = -1, 0, and x=1 in the last equation we get:
y = 3(-1)+ 3 = -3+3 = 0
y = 3(0)+3 = 3
y = 3(1)+3 = 6
So that, we can conclude that the correct solution is
D. y =3x + 3
what are the x and y-intercepts of the line described by the equation? 3x - 9y = 10.8A) x-intercept = 1.2 y-intercept = 3.6B) x-intercept = -3.6 y-intercept = 1.2C) x-intercept = 1.2y-intercept -3.6D) x-intercept = 3.6 y-intercept = -1.2
we have the equation
3x - 9y = 10.8
Remember that
x-intercept ----> value of x when the value of y is zero
so
For y=0
substitute
3x-9(0)=10.8
3x=10.8
x=3.6
y-intercept -----> is the value of y when the value of x is zero
For x=0
3(0)-9y=10.8
-9y=10.8
y=-1.2
therefore
the answer is option DD Suppose you are asked to write an equation of the form y = mx + b to
represent a linear function. What is your strategy for each situation?
1. You are given a description of the function in words.
2. You are given two or more (x, y) values or a table of (x, y) values.
3. You are given a graph showing points with coordinates.
HELP PLS this is my homework for tomorrow
What are the different strategies used to write an equation of the slope-intercept form y = mx + b to represent a linear function?
1. When given a description of the function in words.
The y intercept can be represented by b The slope can be represented by m The point through which the line passes is given by (x, y).So, the equation in the slope-intercept form of a linear function is given by y = mx + b.2. When given two or more (x, y) values or a table of (x, y) values.
The two or more (x, y) values are the coordinates which should be used to find slope m using the formula [tex]m =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex].Substituting the values of m and (x, y) in the equation y =mx+ b , find y intercept b.Substitute the values of m and y intercept b in the equation.So, the equation in the slope-intercept form of a linear function is given by y = mx + b.3. When given a graph showing points with coordinates.
In a graph with coordinates (x, y) given ,find slope m using the formula [tex]m =\frac{y_{2}-y_{1}}{x_{2}-x_{1}}[/tex]. Substitute the values of slope m and coordinates (x, y) in the linear equation y =mx+ b so as to find y intercept b. Substitute the values of m and y intercept b in the equation .So, the equation in the slope-intercept form of a linear function is given by y = mx + b.To learn more about slope-intercept form, refer:
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Find the value of 5y - 6 given that -4y - 7= 9. Simplify your answer as much as possible.
Given that:
[tex]-4y-7=9[/tex]We are told to find 5y - 6
Solving for y
[tex]-4y-7=9[/tex]Add 7 to both sides
[tex]\begin{gathered} -4y-7+7=9+7 \\ -4y+0=16 \\ -4y=16 \end{gathered}[/tex]Divide both sides by -4
[tex]\begin{gathered} \frac{-4y}{-4}=\frac{16}{-4} \\ y=-4 \end{gathered}[/tex]Let us now solve for 5y - 6 by substituting y = -4
[tex]\begin{gathered} 5y-6 \\ 5(-4)-6 \\ -20-6=-26 \\ \therefore5y-6=-26 \end{gathered}[/tex]Hence,
[tex]5y-6=-26[/tex]An organism is losing half of its weight each day. The function y=(0.5)^x represents the percent (in decimal form) of the original weight of the organism. where x is the number of days since the organism began to lose weight A. Describe the domain and range of the function. Then graph the function.B. Find and interpret the y interceptC. What percent (in decimal form) of the original weight does the organism weigh on the 5th day?
the domain of this function is:
[tex]x\in\lbrack0,\infty)[/tex]because we count the days.
The range is
[tex]y\in(0,1_{}\rbrack[/tex]because the maximum value of the percentage of wait is 100% = 1
the y- intercept in this case is when the organism has not lose any weight. So the percentage of weight is 100% (1 in decimal form)
after 5 days we get
[tex]0.5^5=0.03125[/tex]Tickets to the museum cost 7.50 and there is a 15% discount
the cost of the ticket is 7.50
discount is 15 %
so the value of the discount is,
[tex]\begin{gathered} =7.50\times\frac{15}{100} \\ =1.125 \end{gathered}[/tex]so the price of the ticket is 7.50 - 1.125 = 6.375
Actual cost is 6.375
In the coordinate plane, the point X (4, -2) is translated to the point X'(-1, 3). Under the same translation, the points Y (1, -4) and Z (2, 0) aretranslated to Y' and Z', respectively. What are the coordinates of Y' and Z'?
As given by the question
There are given that the point X (4, -2) is translated to the point X' (-1, 3).
Now,
A given point A (X, Y) when translated by the rule (h, k) maps to A' (x+h, y+k).
Then,
[tex]undefined[/tex]In Exercises 1 and 2, graph ACDE and its image after a reflection in the given line.1. C(3, 4), D(2, -1), E(0, -5); y-axis 2. C(1,6), D(12, 2), E(7,-8); x = 8
graph CDE and its image reflection in the given line
C (3,4)
D (2,-1)
E (0,-5)
reflection line: y-axis
If we locate these three points on a graph, we will obtain the following:
now, the reflection points in the y-axis are calculated by multiplying x * -1 ,
for example: the new location for point C is C' = (3*-1 , 4) , therefore, C ' = (-3,4), following the same logic,
D(2,-1) -> D' (-2,-1)
E(0,-5) -> E' (0,-5)
notice that E does not change its location, since it is located on the y-axis, so it doesn't have a relfection.
Now, the graph with the points reflected is the following:
Perform the indicated operation by removing the parentheses and combining like terms.(-2x2 + 5) + (6x2 + 7)
Given the expression:
[tex]\mleft(-2x^2+5\mright)+(6x^2+7)[/tex]Removing the parentheses and combining like terms.
[tex]\begin{gathered} =-2x^2+5+6x^2+7 \\ =-2x^2+6x^2+5+7 \\ \\ =4x^2+12 \end{gathered}[/tex]so, the answer will be:
[tex]4x^2+12[/tex]Answer 733
Step-by-step explanation:
g(x)=4f(x)=×^2-5find (g+f)(n)
g(x)=4
f(x)=×^2-5
(g+f)(n)
Add both equations and replace x by n
(g+f) (n) = n^2-5+4 = n^2-1
Select all of the stories that can be represented by the equation.If none of the stories can be represented, select "None of the above".(a) 40x-20= 620
The correct answers are the first and fourth options
Here, we want to select all stories that goes in line with the equation
a) This can be represented
By multiplying x which is the cost of one training hour by the number of hours which is 40;and subtracting the one-time discount, we can get the or equate to the total paid
b) This cannot be represented
In this case, 20 multiplied by x would give the total amount to be paid after which we can deduct the discount
c) This cannot be represented
It multiplies the charge x by the 20 training hours would give 20x; less the discount of $40 would give 620
d) This can be represented
This narrative is similar to what we have at the first option since the total cost would be 40x and less the discount of $20 would give the after discount payment amount
If you roll a standard six-sided die, what is the probability that you get a 1 or 5? Give your answer as a simplified fraction.
Step 1: Theorem
[tex]\text{Probability of an event = }\frac{N\text{umber of required outcome}}{N\text{umber of sample space}}[/tex]Step 2: Given data
Sample space = { 1, 2, 3, 4, 5, 6}
Number of sample space = 6
Event space = {1, 5}
Number of event space = 2
Step 3: Substitute to find the probability that you get 1 or 5
[tex]\begin{gathered} \text{Probability that you get 1 or 5 = }\frac{2}{6} \\ =\text{ }\frac{1}{3} \end{gathered}[/tex]Answer: 1/3
There are 6 sides. Both of those numbers are two numbers, so it would be 2/6. To simplify it, divide the top and the bottom by the same number. I divided both the numerator and the denominator by 2.
then, your answer would be 1/3
One simple method to predict adult height is to average the parents’ heights in inches and then add 2.5 inches if the child is a boy or subtract 2.5 inches if the child is a girl. This method can be fairly accurate, but can also be as much as 5 inches above or below the child’s eventual height.Use the variable D, which means height of dad and M, which means height of mom1. Write the formula for a boy’s adult height.(5 points) 2. Write the formula for a girl’s adult height.(5 points)
We are given that a boy's height is predicted by adding 2.5 inches to the average of the height of the parents. If "D" is the height of the father and "M" is the height of the mother then the average is determined by adding the two heights together and dividing by 2, like this:
[tex]\frac{D+M}{2}[/tex]Since the height of the boy is determined by adding 2.5 inches to this average, this means that the height of the boy "B" is:
[tex]B=\frac{D+M}{2}+2.5[/tex]The height of a girl "G" is determined by subtracting 2.5 to the average, therefore we have:
[tex]G=\frac{D+M}{2}-2.5[/tex]Which is greater, 2 or 8 ?
Answer:
8
Step-by-step explanation:
Counting up from 1 to 10 you go:
1 2 3 4 5 6 7 8 9 10
As you can see the eight is further to the right meaning it has more value.
(I did this for the points)
8. My proof is the number line (I'm also doing this for points pff) 2<8
What’s the answer to this problem please help me
[tex]f(g(2))=f(2)=3 \\ \\ g(f(1))=g(2)=2 \\ \\ f(f(4))=f(2)=3[/tex]
lassify the number as natural, whole, integer, rational, and/or irrational.
Select all terms that are correct.
Natural Whole Integer Rational Irrational
7√
1. Natural – square root of 7
2. Whole – square root of 7
3. Integer – square root of 7
4. Rational – square root of 7
5. Irrational – square root of 7
wich ones are the right ones
Square root of 7 is classified as an irrational number
What are irrational numbers?Proceeding from definition of rational numbers we say that rational numbers are real numbers that can be expressed as a fraction.
hence such numbers can have areal number in the numerator and a real number in the denominator.
Irrational numbers are the opposite of rational numbers such that when numbers cannot be expressed as fraction such number is said to irrational number.
The number asked in the question √7 is an example of irrational number. Numbers like this there decimal is usually continuous
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Function f is represented by f(x) = 3(x + 4). Find the value of x such that
f(x) = 39
Answer:
x = 9
Step-by-step explanation:
[tex]3(x + 4) = 39[/tex]
[tex]x + 4 = 13[/tex]
[tex]x = 9[/tex]
what is the relation ships for 1 2 3 4 5 and n please help
To find the relationship you:
1. The relation can be the difference between every term in the sequence:
In the first sequence you have between every term a diferencen of:
Where n is the term
Youn can notice that the relationship is the way you get that term and is equal to the previous term plus an odd number (3,5,7,9), as the sequences do not have a constant difference the sequence is a non-regular succession. But as the set of differences (1,3,5,7,9) Follows a regular succesion of (2n-1) you have quadratic sequences that have the next formula:
1. First sequence:
[tex]n^2+10[/tex]2. Second sequence:
[tex]n^2-4[/tex]Find the values of x and y. (90 - 4y)° (50 - 2x)° (х +5y)° (2x+3y)°
1) According to the Vertical angle Theorem
We can state that
50-2x =90-4y
-2x +4y=90
2x -4y = -90
In addition to that, since those three angles make up a straight angle:
2x +3y + x +5y +50 -2x = 180º Combine like terms
x+6y =180º
2) Now, we can set this linear system:
x +6y = 180 x-2 To eliminate x
2x -4y = -90
-2x -12y =-360
2x -4y = -90
----------------
-16y = -450
16y= 450
y = 28.12
y ≅ 28
x + 6(28)=180
x+168=180
x=12
