Final answer:
The average rate of change of the function g(x) = 3(2^x) - 6 over the interval [0,3] is 7. This is found by evaluating g(x) at x = 0 and x = 3 and then dividing the difference by the interval length.
Explanation:
Calculating Average Rate of Change
The average rate of change of a function over an interval is the change in the function's values divided by the change in the independent variable (often x) over that interval. For the function g(x) = 3(2^x) - 6 over the interval [0,3], we first find the values of g(x) at the endpoints of the interval: g(0) and g(3). We then use the formula for average rate of change:
[tex]\[\text{Average Rate of Change} = \frac{g(3) - g(0)}{3 - 0}\][/tex]
Let's compute:
g(0) = 3(2^0) - 6 = 3(1) - 6 = -3g(3) = 3(2^3) - 6 = 3(8) - 6 = 24 - 6 = 18Now we can substitute these values into the formula:
[tex]\[\frac{18 - (-3)}{3 - 0} = \frac{21}{3} = 7\][/tex]
So, the average rate of change of the function g(x) over the interval [0,3] is 7.
Order these numbers from least to greatest
151/20, 7 6/11, 7.32, 7.546
Answer:
76/11 ; 7.32 ; 7.546 ; 151/20
Step-by-step explanation:
Given data:
The numbers are listed as below
151/20 ; 76/11 ; 7.32 ;7.546
The numbers are written in the same format that is in decimal form
7.55 ; 6.90901 ; 7.32 ; 7.546
Arranging the numbers starting with the least number
6.90901 ; 7.32 ; 7.546 ; 7.55
76/11 ; 7.32 ; 7.546 ; 151/20
Please note the value of 151/20 is exactly 7.550 which makes it larger than 7.546.
Which value of the makes \dfrac{8+h}{10}=1
10
8+h
=1start fraction, 8, plus, h, divided by, 10, end fraction, equal, 1 a true statement?
Answer:
h = 2
Step-by-step explanation:
(8+h)/10 = 1
8+h = 1×10
8+h = 10
h = 10-8
h = 2
The value of h that makes the equation [tex]\(\frac{8+h}{10} = 1\)[/tex] true is (h = 2).h=2 is the value that, when substituted into the equation, ensures that the left side of the equation (8+h) is equal to the right side (10 times 1).
To find the value of h that satisfies the
equation: [tex]\(\frac{8+h}{10} = 1\)[/tex],
we can start by understanding the equation. It represents a fraction where the numerator is the sum of 8 and h, and the denominator is 10. The fraction is set equal to 1, which means both sides of the equation should be equal.
To solve for h, we can cross-multiply, which simplifies to
(8 + h = 10)
Now, to isolate h, we need to get it on one side of the equation. Subtracting 8 from both sides yields (h = 2).
So, when h = 2, the equation becomes
[tex]\(\frac{8+2}{10} = 1\)[/tex] , which simplifies to [tex]\(\frac{10}{10} = 1\)[/tex],
making it a true statement.
In essence, h=2 is the value that, when substituted into the equation, ensures that the left side of the equation (8+h) is equal to the right side (10 times 1). This demonstrates the solution's validity and satisfies the equation's condition.
To know more about equation:
https://brainly.com/question/29657983
#SPJ3
points a b and c are collinear point b is between A and C solve for x AB = 3x BC = 2x -2 and AC =18
=====================================
Work Shown:
AB + BC = AC .... see diagram below
(3x)+(2x-2) = 18 ... plug in given expressions
5x-2 = 18
5x-2+2 = 18+2 ... add 2 to both sides
5x = 20
5x/5 = 20/5 ... divide both sides by 5
x = 4
Given points A, B and C are collinear, with B between A and C, and the distances between them expressed in terms of 'x'. We use the fact that AB + BC = AC to form an equation, solve it to find 'x' = 4.
Explanation:To solve for 'x' in this problem, we need to utilize the fact that points A, B, and C are collinear and that point B is between A and C.
Given AB = 3x, BC = 2x - 2, and AC = 18.
When points are collinear and one is between the other two, the sum of the distances between the points equals the total distance. So, we know that AB + BC = AC.
Substitute the known values into this equation to get 3x + 2x - 2 = 18.
Combine like terms to give 5x -2 = 18. Rearrange this to make 'x' the subject, you get 5x = 20, then x = 4.
So the value of 'x' that satisfies the given conditions is 4.
Learn more about Linear Geometry here:https://brainly.com/question/34413942
#SPJ11
If the probability that a student is on-time to class is 0.1 and the probability he is on-time or marked tardy on the attendance roster is 0.9, what is the probability he will be marked tardy if the events on-time and marked tardy are mutually exclusive? If A and B are independent?
Answer:
.10 %
Step-by-step explanation:
Final answer:
The probability of being marked tardy when events are mutually exclusive is 0.8, and when they are independent, the probability is 0.09.
Explanation:
The probability that a student will be marked tardy if the events on-time and marked tardy are mutually exclusive is 0.9 - 0.1 = 0.8. When events A and B are independent, the probability of both events occurring is the product of their individual probabilities: P(A and B) = P(A) * P(B). In this case, P(on-time) * P(tardy) = 0.1 * 0.9 = 0.09.
A solid figure is
separated into two rectangular prisms.
The volume of Rectangular Prism A is
80 cubic feet. Rectangular Prism B has
a length of 6 feet and a width of 5 feet.
The total volume of the solid figure is
200 cubic feet. What is the height of
Rectangular Prism B? Show your work
and explain your answer.
Thank you!
Answer: 4 feet.
Step-by-step explanation:
Their is one rectangular prison divided into two.
The volume of the first one is
V1= L X H X W=80.
Volume of the second one is
V2= L X H X W
V2= 6 X H X 5
V2 = 30H
Now from the question, the total volume is 200cubic feet which means V1 + V2 = 200, recall that V1=80 and V2=30H, so we say;
80+30H=200, collecting the like term we have, 30H=200-80.
30H=120, divide both side by 30
30H/30=120/30
H= 4feet.
Height is 4feet.
Final answer:
To find the height of Rectangular Prism B, subtract Rectangular Prism A's volume from the total volume to get Prism B's volume (120 cubic feet), then divide by the product of its length and width. The height is 4 feet.
Explanation:
The question is about finding the height of Rectangular Prism B given that the solid figure it's part of (when combined with Rectangular Prism A) has a total volume of 200 cubic feet, and that Rectangular Prism A has a volume of 80 cubic feet. Considering volume calculations for rectangular prisms are done using length × width × height, we can find the height of Prism B by isolating height in the formula. Since Prism B has a length of 6 feet and a width of 5 feet, and we know the combined volume of both prisms, we first subtract the volume of Prism A from the total volume to find the volume of Prism B, which is 120 cubic feet (200 cubic feet - 80 cubic feet).
Volume of Prism B = 120 cubic feet. The formula for volume is then applied as follows:
Volume = Length × Width × Height
120 cubic feet = 6 feet × 5 feet × Height
Height = 120 cubic feet / (6 feet × 5 feet)
Height = 120 cubic feet / 30 square feet
Height = 4 feet.
Therefore, the height of Rectangular Prism B is 4 feet.
3400 dollars is placed in an account with an annual interest rate of 7.5%. How much will be in the account after 17 years, to the nearest cent?
Answer: 11625.8
Step-by-step explanation:
The total amount in the account after 17 years, with an annual interest rate of 7.5%, is approximately $7420.50.
Explanation:To calculate the amount in the account after 17 years, we use the formula for simple interest: Total future amount (with simple interest) = Principal + (Principal × Interest Rate × Time). In this case, the principal is $3400, the interest rate is 7.5%, and the time is 17 years. Plugging in these values, we get:
Total future amount = 3400 + (3400 × 0.075 × 17)
Calculating this, the total future amount in the account will be approximately $7420.50.
Learn more about Simple Interest here:https://brainly.com12/question/22621039
#SPJ12
god dang this is my last question will someone please like just help me on this? I literally made 3 questions and nobody is helping, i just need a complete sentence? my goodness lord please!! i see everyone else not getting ignored, but i'm the only one that is
Kiki has $2.48 in her change purse and $1.69 in her hand. Jordan has $3.05 in his left pocket and $1.09 in his right pocket. Who has more money, and how much more money does that person have? Write your answer in a complete sentence.
Answer:
kiki has $4.17 and jordan has $4.14 kiki has 0.03 more than jordan
Step-by-step explanation:
If you add up the numbers for kiki you get $4.17 and if you do the same for jordan with the numbers they gave you for him you get $4.14 then you just minus 4.17 and 4.14 and thats how you get 0.03.
Answer:
Kiki has $0.03 more than Jordan, meaning Kiki has more money.
Step-by-step explanation: It's simple! Add 2.48 + 1.69 = 4.17 (This is Kiki's total amount) And then add 3.05 + 1.09 = 4.14 (This is Jordan's total amount)
As we can see, Kiki has more money. To find the difference we simply do 4.17 - 4.14 = 0.03 (:
Solve R=M + B, for B.
Answer:
B = R - M
Step-by-step explanation:
1. R = M + B Subtract M
2. R - M = B
Please help! Give the answer and how you got it
The distance between the points C(-3,1) and D(5,6) is 10.3 units.
Step-by-step explanation:
Let us consider CD is a line segment.
The point C is (-3,1) and D is (5,6).
The Cartesian formula for line is used to find the length between the CD.
Distance between two points = [tex]\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex].
The points are (-3,1) and (5,6).
=[tex]\sqrt{(6-(-3))^2+(6-1)^2}[/tex].
=[tex]\sqrt{(6+3)^2+(6-1)^2}[/tex]
=[tex]\sqrt{9^2+5^2}[/tex].
=[tex]\sqrt{81+25}[/tex].
=[tex]\sqrt{106}[/tex].
=10.295 ≈ 10.3.
Distance between two points 10.3 units.
The solid shown has a volume of 9 units3. Determine the surface area of the solid.
A) 29 units2
B) 36 units2
C) 38 units2
D) 41 units2
Answer:
C) 38 units2
Step-by-step explanation:
we know that
The surface area of the composite figure is equal to the area of all its square faces
Each face area is one square unit
so
[tex]SA=2(9)+2(4)+2(6)=38\ units^2[/tex]
Which statement is best supported by the dot plot? Choose ONE and explain your
answer.
I. The range of the number of miles Amanda skated in August is less than the range
of the number of miles she skated in July.
II. The distribution of data is approximately symmetrical in both sets of data.
III.The mode of the number of miles Amanda skated in July is equal to the mode of
the number of miles skated in August.
Answer:
The first statement.
Step-by-step explanation:
Because when you look at the July graph you can see that the highest number of miles is 15 and the lowest number of miles is 1 so the range is 15 - 1 = 14.
When you look at the August graph you can see that the highest number of miles is 13 and the lowest number of miles is 5 so the range is 13 - 5 = 8
So the range of the July month is greater than the range of the August month
A 1.5-meter snake lives in the ceiling of a college’s Chemistry Building. One day, she decides to go outside, and slithers through a pipe at the speed of 15 centimeters per second. In 90 seconds, she slithers all the way through the pipe and her whole body is outside. How long, in meters, is the pipe? Note: 1 meter = 100 centimeters
Answer:
13.5
Step-by-step explanation:
Answer:
[tex]The~answer~for~this~question~is:135,000[/tex]
Step-by-step explanation:
[tex]15[/tex] × [tex]90=1350[/tex]
[tex]and,[/tex]
[tex]1350[/tex] × [tex]100=135,000[/tex]
[tex]It's~that~simple![/tex]
how many times more is 21.25 than 1.7 answers?
Answer:
19.55
Step-by-step explanation:
21.25
- 1.7
_____
19.55
In Science Class, Sara needed 8 test tubes for 3 different experiments. The first experiment required 2 test tubes and the other two experiments required the same number of test tubes. How many test tubes were need for each of the other two experiments l?
Answer:
[tex]Each\ of\ other\ two\ experiments\ required\ 3\ test\ tubes.[/tex]
Step-by-step explanation:
[tex]Let\ each\ of\ other\ experiment\ requires\ x\ test\ tube\\\\Total\ number\ of\ test\ tubes\ needed=8\\\\Test\ tubes\ used\ in\ the\ experiments=sum\ of\ number\ of\ test\ tubes\ in\ each\ experiment\\\\Test\ tubes\ used\ in\ the\ experiments=2+x+x\\\\2+x+x=8\\\\2+2x=8\\\\Subtract\ 2\ from\ both\ sides\\\\2+2x-2=8-2\\\\2x=6\\\\divide\ both\ sides\ by\ 2.\\\\x=3[/tex]
[tex]Each\ of\ other\ two\ experiments\ required\ 3\ test\ tubes.[/tex]
846 is tens or not why?
The number 846 does have a component in the tens place, which is the digit 4, representing 40 when viewed in terms of place value. Understanding the concept of place value, including the tens place, is fundamental in mathematics for efficient calculation and comprehension of numbers.
Explanation:The question seems to be asking whether the number 846 can be classified in terms of its placement in the tens place value or not. To understand this, let's break down the number 846 in terms of place value. The number 846 is comprised of three digits, each representing a different place value in the base-10 numbering system. Starting from the right, the first digit (6) represents the ones place, the second digit (4) represents the tens place, and the third digit (8) represents the hundreds place.
Therefore, yes, 846 does have a component in the tens place, which is the digit 4. This means that the number 846 has 4 tens or 40 when breaking it down by place value. Understanding place value is crucial in mathematics as it helps in doing calculations, understanding the value of numbers, and in various operations such as addition, subtraction, multiplication, and division. The tens place specifically is important when dealing with numbers ranging from 10 to 99 and beyond, as it helps in grouping numbers in units of ten, simplifying calculations, and enhancing comprehension of numbers' sizes.
the function f(x)=5x+12 models the amount of money in dollars, makes when cutting loans for x hours. How many dollars will alex for 3 hours of loan-cutting work?
Answer:
$27
Step-by-step explanation:
f(x) = 5x + 12
= 5(3) + 12
= 15 + 12
= 27
Alex will earn $27 for 3 hours of lawn-cutting work, as calculated using the function f(x) = 5x + 12.
Explanation:The function f(x) = 5x + 12 models the amount of money, in dollars, Alex makes when cutting lawns for x hours. To calculate the amount Alex will make for 3 hours of lawn-cutting work, we simply substitute x with 3 in the equation:
f(3) = 5(3) + 12
For instance, events G and H (taking a math class and taking a science class, respectively) from Example 3.9 were shown to be independent by verifying that P(G AND H) = P(G) * P(H). Similarly, events A and B from 'Try It Σ' 3.8, learning Spanish and German, were tested for independence by checking if P(A AND B) = P(A) * P(B).
Thus, f(3) = 15 + 12 which equals $27. Therefore, for 3 hours of work, Alex will earn $27.
one third plus one half
Answer:5/6
Step-by-step explanation:
So 1/3 + 1/2 turn them to equivalent denominators so 1/3 = 2/6
1/2 equals 3/6 . 3/6+2/6 is 5/6
Drag each equation to the correct location on the table.
Match the inequalities with the value of a for which they hold true.
4 + 3a + 8 < 16
5a − 4a + 6 < 8
2a + 3 < 9 − 3a
14 + 5a < 12a + 1
2a + 3 > 10 − 3a
3a − 2a + 1 > 2
Answer:
a=1
-2a + 3 < 9 − 3a
5a − 4a + 6 < 8
2a + 3 > 10 − 3a
a=2
-4 + 3a + 8 < 16
14 + 5a < 12a + 1
3a − 2a + 1 > 2
Step-by-step explanation:
i did the test
Answer:
a=1
-2a + 3 < 9 − 3a
5a − 4a + 6 < 8
2a + 3 > 10 − 3a
a=2
-4 + 3a + 8 < 16
14 + 5a < 12a + 1
3a − 2a + 1 > 2
Step-by-step explanation:
i just did the test
Find the value of 49/50 divided by 7/6
The ratio of men to women working for a company is 5 to 3. If there are 63 women working for the company, what is the total number of employees?
Answer:
168 employees
Step-by-step explanation:
5:3
63 / 3 = 21
5*21=105
105+63=168
find ordered pair solution x= -5 (7, -5) (-5, 0) (-5, 6)
Answer:
The correct answer is either (-5,0) or (-5,6)
Step-by-step explanation:
An ordered pair is described as (x,y)
Since x=-5, the last two work just fine, but we don't have a y-coordinate value, so I'm not sure on the details of that
Determine the quadrant(s) in which (x,y) is located so that the condition is satisfied. (Select all that apply.)
xy < 0
Quadrant I
Quadrant II
Quadrant III
Quadrant IV
The quadrants II and IV in which (x,y) are located so that the condition xy < 0 is satisfied.
What is the quadrant?A quadrant is defined as an area contained by the x and y axes, which there are four quadrants in a graph.
For Quadrant I : the value of x and y both are positive ( +,+ )
For Quadrant II : the value of x is negative and y is positive ( -,+ )
For Quadrant III : the value of x is negative and y is negative ( -, - )
For Quadrant IV : the value of x is positive and y is negative ( +, - )
To determine the quadrant(s) in which (x,y) is located so that the condition is satisfied.
⇒ xy < 0
When the value of x is negative and y is positive in Quadrant II
So that the condition xy < 0 is satisfied
When the value of x is positive and y is negative in Quadrant IV
So that the condition xy < 0 is satisfied
Hence, the quadrants II and IV in which (x,y) are located so that the condition xy < 0 is satisfied.
Learn more about the quadrant of the graph here:
brainly.com/question/7196312
#SPJ2
Math,,,,,,,,,?????????
the picture isn't clear, but my guess is.... c?
Help me please. 10 pts.
3.)
Variables:
New tablet cost (575),
Money already saved, (56),
Money saved per week(14w)
Write an Equation:
The amount of weekly money you need to earn must cover the leftover cost needed to buy the tablet, therefore:
money_needed - money_you_have = money_earned_per_week
575 - 56 = 14w
Solving:
575 - 56 = 14w
519 = 14w
37.071428 = w
37 weeks needed
You solve the other two on your own.
14/y=112/72,what is y someone pls help
Answer:
9
Step-by-step explanation:
14/y=112/72
simplify 112/72 into 14/9
14/y=14/9
y=9
Can you please help me
area of the rectangle = 8 * 18 = 144ft
area of circle = pi*r^2 = pi * ((18-12)/2)^2 = pi * (3)^2 = approx. 28.27ft
total = 144 + 28.27 = 172.27ft
Hans runs 3 miles in 25 minutes. At the same rate, how many miles would he run in 20 minutes?
Answer:
2.4 miles
Step-by-step explanation:
If Hans ran 3 miles in 25 minutes, that would mean he ran 0.6 miles every five minutes. So, 0.6*4=2.4, as 4/5*25=20.
F(x) { X_1 if x≤-2
{ 2x-1 if -2 < x ≤4
{ 3x +8 if x>
Graph the piecewise function
Step-by-step explanation:
go to desmos.com and type the following on separate lines:
y=x+1{x≤-2}
y=2x-1{-2<x≤4}
y=3x+8{x>4}
What does 15+d>10 equal
Hey there!
15 + d > 10
OR YOU COULD SAY
d + 15 > 10
SUBTRACT 15 to BOTH SIDES
d + 15 - 15 > 10 - 15
CANCEL out: 15 - 15 because that gives you 0
KEEP: 10 - 15 because that helps compare with your d-value
10 - 15 = -5
Therefore, d > -5
Answer: d > -5
Good luck on your assignment and enjoy your day!
~Amphitrite1040:)
3.4.13
E Question Help
Scott invested a total of $5900 at two separate banks. One bank pays simple interest of 12% per year while the other pays simple interest at a rate of 6% per year. If
Scott earned $540.00 in interest during a single year, how much did he have on deposit in each bank?
Scott had $ 2,800 on deposit at the bank that payed 12% interest.
Answer:
$3100 at 12%$2800 at 6%Step-by-step explanation:
Let x represent the amount on deposit at 12%. Then 5900-x is the amount deposited at 6%, and the total interest earned is ...
12%·x +6%·(5900 -x) = 540
0.06x + 354 = 540 . . . . . . . . eliminate parentheses
0.06x = 186 . . . . . . . . . . . . . . subtract 354
x = 3100 . . . . . . . . . . . . . . . . . divide by 0.06
Scott invested $3100 at 12% and $2800 at 6%.
_____
Quick sanity check
The average interest earned is $540/$5900 ≈ 0.0915 ≈ 9.15%. This is more than the average of 12% and 6%, which is (12+6)/2 = 9 percent. Hence more than half of the money must be deposited at 12%.