Answer: 1560
Step-by-step explanation: The average rate of change of a function over an interval is the total change in the value of the function divided by the length of the interval. In this case, the function is f(x) = 10(2)^x and the interval is [3, 5].
To find the average rate of change of the function over the interval, we can first evaluate the function at the two endpoints of the interval, which are x = 3 and x = 5. At x = 3, the function has a value of f(3) = 10(2)^3 = 80. At x = 5, the function has a value of f(5) = 10(2)^5 = 3200.
The total change in the value of the function over the interval is then the difference between the values at the two endpoints, which is f(5) - f(3) = 3200 - 80 = 3120.
The length of the interval is 5 - 3 = 2, since it goes from x = 3 to x = 5. Therefore, the average rate of change of the function over the interval is the total change in the value of the function divided by the length of the interval, which is (3120) / 2 = 1560.
Therefore, the average rate of change of the function f(x) = 10(2)^x on the interval [3, 5] is 1560.
The half-life of a drug in the bloodstream is 14 hours. What fraction of the original drug dose remains in 36 hours? in 72 hours?
What fraction of the original drug dose remains in 36 hours?
(Do not round until the final answer. Then round to the nearest hundredth as needed.)
16.82 % and 2.83% of the original drug dose remain in 36 hours and 72 hours respectively.
What is half-life?
Half-life is a characteristic unit for the exponential decay equation and is constant across the lifespan of an exponentially decaying quantity.
Given, the half-life of a drug(h) = 14 hours
The first condition, time duration (t) = 36 hours
Then, the half-life of the substance can be calculated by:
[tex]A = A_{0} * (1/2)^{\frac{t}{h} }[/tex]
or, [tex]A = A_{0} * (1/2)^{\frac{36}{14} }\\A = A_{0} * (0.1682)\\[/tex]
16.82 % of the original drug dose remains in 36 hours
Hence, 16.82 % of the original drug dose remains in 36 hours
The second condition, time duration (t) = 72 hours
Then, the half-life of the substance can be calculated by:
[tex]A = A_{0} * (1/2)^{\frac{t}{h} }[/tex]
[tex]A = A_{0} * (1/2)^{\frac{72}{14} }\\A = A_{0} * (0.0283)\\[/tex]
2.83 % of the original drug dose remains in 72 hours
Hence, 2.83 % of the original drug dose remains in 72 hours
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Melissa’s mom embroiders 5 flowers on each side of a handkerchief. There is one flower at each corner, how many flowers are embroidered on the handkerchief altogether? If she gets Rs. 6 for embroidering 2 flowers, how much did she get paid for this handkerchief
Answer:
20 flowers at sides and 4 flowers at the corner then
total flowers are 24
cost of 2 flowers is 6 then of one flower will be 3
total cost of the flowers will be 24×3=72
Step-by-step explanation:
a. How many cubes with an edge length of b. What is the volume, in cubic inches, of inch are needed to build a cube with one cube with an edge length of inch? an edge length of 1 inch?
The number of cubes of edge length 1/3 is 27 and the volume of the cube is 1 cubic inches
How to determine the number of cubesFrom the question, we have the following parameters that can be used in our computation:
Edge length of cube 1 = 1/3 inchEdge length of cube 2 = 1 inchThe volume of a cube is the cube of its edge length
This means that the volumes are
Volume = Edge length³
So, we have
Volume of cube 1 = (1/3 inch)³ = 1/27 cubic inches
Volume of cube 2 = (1 inch)³ = 1 cubic inch
The number of cubes is then calculated as
Number of cubes = Volume of cube 2/Volume of cube 1
This gives
Number of cubes = 1/(1/27)
Number of cubes = 27
The volume of the cubesHere, we have
Edge length of cube = 1 inch
The volume of a cube is the cube of its edge length
This means that the volumes are
Volume = Edge length³
So, we have
Volume of cube = (1 inch)³ = 1 cubic inch
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Complete question
a. How many cubes with an edge length of 1/3 inch are needed to build a cube with an edge length of 1 inch?
b. What is the volume, in cubic inches, an edge length of 1 inch?
The width of a rectangle is 4 more than the length. If the perimeter is 36 cm, ind the dimensions (length and width) of the rectangle.
Answer with step-by-step explanation:
Let the width of the rectangle be x.
Given that,
length ⇒ 4
width ⇒ x + 4 ( Because, the rectangle's width is 4 more than the length.)
Perimeter ⇒ 36cm
The formula to find the perimeter of rectangle is:
P = 2 ( l + w )
Now to find the value of x replace P, l & w with 36, 4 & (x + 4) with respectively.
P = 2 ( l + w )
36 = 2 ( 4 + x + 4 )
36 = 2 ( x + 8 )
Solve the brackets.
36 = 2x + 16
Substract 16 from both sides.
36 - 16 = 2x
20 = 2x
Divide both sides by 2.
10 = x
And now let us find the exact dimensions of the rectangle.
Length = 4 cm
Width = x + 4 = 10 + 4 = 14 cm
Which of the following items is shaped MOST LIKE the Moon?
O An egg
O Asphere
O A cone
O A circle
Answer:
An egg
Step-by-step explanation:
Hope this helps you
simplify the expression -3(x + 9) by either combining like terms of distributive property
Answer:
-3x+-27
-3 multiplied by x=-3x
-3x9=-27
Two ocean beaches are being affected by erosion. The table shows the width, in feet, of each beach at high tide measured where 1995 is represented by year 0.
Year number Western Beach width (in feet) Dunes Beach width (in feet)
0 100 20
5 90 45
10 80 70
11 78 75
12 76 80
15 70 95
Describe the patterns shown by the erosion data measurements shown for each of the beaches in the table.
Between which years will the beaches have approximately the same width?
Assuming these rates remain constant, what can you do to get a better approximation of when the two beaches will have the same width?
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A bowling alley charges a flat fee to rent shoes. There is an additional fee for each game played. The function y = 4x + 3.5 represents the cost y of bowling x games. Interpret the parameters of the function.
What represents the price per game?
What represents the shoe rental charge?
Answer: the price per game is 4 per game and the shoe rental is the additional fee to bowl
Step-by-step explanation:
If A is the center of dilation how can we find which point is the dilation of b?
Answer:
C is point of the dilation with a scale factor to 2
D is the point of the dilation with a scale factor of 1/3
Step-by-step explanation:
C is twice as far from A as B.
D is 1/3 the distance from A when compared to B
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Answer:
Step-by-step explanation:
Crumbs Cookies was interested in seeing if there was an association between cookie flavor and whether or not there was frosting. Given are the results of the last week's orders. Frosting No Frosting Total Sugar Cookie 56 Chocolate Chip 70 136 Red Velvet 50 Total 180 400 Which category has the greatest joint frequency? Sugar cookies Cookies with no frosting Chocolate chip cookies with frosting Sugar cookies with no frosting
The category which has the greatest joint frequency is sugar cookies with a frequency of frosting and no frosting as 56 and 120 and a joint frequency of 176
Which category has the highest joint frequency?Frosting No frosting Total
sugar cookies 56 120 176
Chocolate cookie 66 70 136
Red velvet 38 50 88
Total 160 240 400
Chocolate cookies with frosting = Total chocolate cookies - chocolate cookies with no frosting
= 136 - 70
= 66
Red velvet cookies with frosting = Total cookies with frosting - (Chocolate cookies with frosting + sugar cookies with frosting)
= 160 - (56 + 66)
= 160 - 122
= 38
Total red velvet cookies = Red velvet cookies with frosting + Red velvet cookies with no frosting
= 50 + 38
= 88
Total cookies with no frosting = Total cookies - Total cookies with frosting
= 400 - 160
= 240
Total sugar cookies with no frosting = Total cookies with no frosting - (chocolate cookies with no frosting + Red velvet cookies with no frosting)
= 240 - (70 + 50)
= 240 - 120
= 120
Total sugar cookies = Total sugar cookies with no frosting + Total sugar cookies with frosting
= 120 + 56
= 176
In conclusion, the highest joint frequency is sugar cookies.
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The radius of a circular play ground is 77 m. Calculate the distance covered by a runner in 5 complete rounds around the ground.
Answer:
Step-by-step explanation:
77*5=385
A diver starts out at 342 feet below the surface (or -342 feet). She then swims upward 224 feet. Use a signed number to represent the diver's current depth.
Answer:
-118 feet
Step-by-step explanation:
[tex]-342+224=-118[/tex]
The table shows a proportional relationship. x 15 9 21 y 5 3 7 Describe what the graph of the proportional relationship would look like. A line passes through the point (0, 0) and continues through the point (15, 5). A line passes through the point (0, 0) and continues through the point (7, 21). A line passes through the point (0, 0) and continues through the point (5, 15). A line passes through the point (0, 0) and continues through the point (3, 9).
The option that describes the graph of the proportional relationship is the option;
A line passes through the point (0, 0) and continues through the point (15, 5).What is a proportional relationship?
A proportional relationship is one in which one variable in the relationship is a constant multiple of the other variable.
The table of values can be presented as follows;
x; 15 9 21
y; 5 3 7
The domain of the function is therefore; 15, 9, 21
The range of the function is therefore; 5, 3, 7
The coordinates of points on the graph of the function is therefore;
(15, 5), (9, 3), (21, 7)
The relationship between the xi and y-values of the function is therefore;
5/15 = 3/9 = 7/21 = 1/3
The constant of proportionality in the relationship is 1/3
The relationship is therefore a proportional relationship.
The characteristics of the graph of a proportional relationship includes;
The graph passes through the origin, (0, 0).
The correct option that therefore describes the graph is the option;
A line passes through the point (0, 0), and continues through the point (15, 5)
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pls hp me with this question
Answer:30 1/8
Step-by-step explanation:
A 12 ft ladder reaches 9 ft up a wall.
What is the angle formed between the
ladder and the ground?
Answer:
Step-by-step explanation:
1. Julia used square tiles to make
a design. She laid the tiles in a
square, 8 tiles wide by 8 tiles
long. Each tile has an area of 1
square inch. What is the area of
Julia's tile design?
Solomon invested money in his bank account. He had a principal, P,
of $100 in his account at the beginning of the period, which
increased at a rate, r, of 0.15 per year. At the end of the period, he
had interest, I, of $135 in his account. Use the simple interest
formula 1 Prt, to solve for the time, t, in months that it took to
earn this amount. (1 point)
h
O 9 months
O 108 months
O 233 months
900 months
The total time required in months is 108 months.
What is simple interest?
Simple interest is defined as the amount of interest paid on a specific principal, an amount at a specific interest rate. It is given by
I = Prt
where, I = simple interest, P = Principal, r = rate of interest, t = time taken
Given, P = $100
I = $135
r = 0.15
t = ?
So, simple interest is given by:
I = Prt
or, 135 = 100*0.15*t
or, 135 = 15*t
or, t = (135/15) = 9 years = 9*12 = 108 months
Hence, the total time required in months is 108 months.
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Answer: 108
Step-by-step explanation:
just took test
what is the value of x?
Options: 4, 3, 5, 2
Answer: X = 3
Step-by-step explanation:
3x + 6 = 15
6x - 3 = 15
5 times 3 = 15
John read the first 114 pages of a novella, this was 3 pages less than 1/3
Answer:
351 pages
Step-by-step explanation:
In order to figure this out, we need to know what 114 plus 3 is.
114 + 3 = 117
Now that we have 117, we know that this is equal to 1/3 of the book.
In order to find out the total pages in this book, we need to multiply 117 by 3.
117 × 3 = 351
There are 351 pages in Johns book.
Does the graph below represent a function
A. Yes
B. No
C. Sometimes
D. Not enough information
Answer:
Step-by-step explanation:
Yes, it is a function.
The reason for this is because it passes what is called the Vertical Line Test, notice how if you draw a completely straight line down, it will only make contact with the graph one time. It is hard to tell, but even though it looks like the graph stops at x=±3, the graph is actually approaching the values ever so slightly, therefore maintaining the conditions for the vertical line test.
The answer is A. Yes.
CAN SOMEONE HELP WITH THIS QUESTION?✨
The new equation of graph will be-
y = 5ˣ - 4y = 5ˣ⁻⁵y = 5⁻ˣExplain the term translation?Each point in such a figure is moved the same distances in same direction using a kind of transformation known as translation.A reflection is the shape's mirror image. A line, called the line of reflection, will allow an image to reflect through it. Each point in an image is thought to reflect other figure when they are all equally spaced apart from one another.For the stated conditions.
The equation of the graph is given as-
y = 5ˣ
Part a: f(x) is shifted 4 units downward,
y = 5ˣ - 4, is the new image location.
Part b: f(x) is shifted 5 units left,
, y = 5ˣ⁻⁵, change in the y axis with negative sign.
Part c: f(x) is reflected about the y axis.
y = 5⁻ˣ, x coordinates will change, keeping the y axis same.
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5/6 over -2/3 minus 1.25 over 1/4 write your answer in simplest form.....please help
Answer: -1.5625
Step-by-step explanation:
5/6/-2/3 - 1.25/1/4 = -25/16 = -1 9/16 = -1.5625
Each lap of the pool is 1/10 of a mile. You need to swim 25 laps. How many miles did you swim?
Answer:5/2 miles or 4 and half mile
Step-by-step explanation:
1/10 times 25
25/10
5/2
Answer:
Step-by-step explanation:
the answer is 2 1/2 miles
Think About the Process You have 30 quarters. You find 20% more quarters in your room. Then you go shopping and spend 50% of the total number of quarters. Write an expression to represent the total number of quarters you take with you shopping. Calculate, in dollars, the amount of money you have left.
Answer: $4.5 left.
Step-by-step explanation:
You have 30 quarters, and find 20% more. To convert percentages to decimals for calculations, simply move the decimal two spaces to the left.
20% is 20. ---> 2.0 ---> .20
30 * 0.2 = 6. Now add 6 (found) to 30 (original) to get the total.
30+6 = 36 total quarters.
You spend 50% of the quarters, 36 * 0.5 = 18.
This means you have 18 quarters left (or you spent 18).
18 quarters, each quarter is worth 0.25 dollars, so multiply the number left by how much each is worth.
18 * 0.25 = $4.5.
$4.50 is the amount left
4. Abby receives a gift card worth $20 to an online retailer that sells digital music and games. Each song
costs $1each, and each game costs $2. She wants to buy at least 15 items with the card. Write a systems
of inequalities and represent the solution on the graph.
Answer:
card worth $20
the link to the graph down in the below
Step-by-step explanation:
Find x when () = 2. Please explain step by step
Answer: Ans is 990. First such a number is 5×0 +2=2, then 5×1 +2=7, like that in all 20 numbers are there from 2 to 97 in A.P.with common difference of 5.
Step-by-step explanation:
Plot four lines to connect the points in adjacent
quadrants. One is done for you.
Line
# 1 y= -2 (x-6)+1
10
# 2?
#3?
#4?
Answer:
[tex]\textsf{Line \#2}: \quad y=x-5[/tex]
[tex]\textsf{Line \#3}: \quad y=\dfrac{1}{4}(x-1)-4[/tex]
[tex]\textsf{Line \#4}: \quad y=-8x-29[/tex]
Step-by-step explanation:
Given points:
(-4, 3)(6, 1)(1, -4)(-3, -5)To find the equations for each of the lines:
Find the slope of the line by substituting two points on the line into the slope formula.Substitute the found slope and one of the points on the line into the point-slope formula and simplify.Line #2Points:
Let (x₁, y₁) = (6, 1)Let (x₂, y₂) = (1, -4)Find the slope:
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-4-1}{1-6}=\dfrac{-5}{-5}=1[/tex]
Substitute the found slope and one of the points into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-1=1(x-6)[/tex]
[tex]\implies y=(x-6)+1[/tex]
[tex]\implies y=x-5[/tex]
Line #3Points:
Let (x₁, y₁) = (1, -4)Let (x₂, y₂) = (-3, -5)Find the slope:
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{-5-(-4)}{-3-1}=\dfrac{-1}{-4}=\dfrac{1}{4}[/tex]
Substitute the found slope and one of the points into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-(-4)=\dfrac{1}{4}(x-1)[/tex]
[tex]\implies y+4=\dfrac{1}{4}(x-1)[/tex]
[tex]\implies y=\dfrac{1}{4}(x-1)-4[/tex]
Line #4Points:
Let (x₁, y₁) = (-3, -5)Let (x₂, y₂) = (-4, 3)Find the slope:
[tex]\implies \textsf{slope}\:(m)=\dfrac{y_2-y_1}{x_2-x_1}=\dfrac{3-(-5)}{-4-(-3)}=\dfrac{8}{-1}=-8[/tex]
Substitute the found slope and one of the points into the point-slope formula:
[tex]\implies y-y_1=m(x-x_1)[/tex]
[tex]\implies y-(-5)=-8(x-(-3))[/tex]
[tex]\implies y+5=-8(x+3)[/tex]
[tex]\implies y=-8(x+3)-5[/tex]
[tex]\implies y=-8x-24-5[/tex]
[tex]\implies y=-8x-29[/tex]
d) please help me with question d)
Given f(x) = 2x and g(x) = f(x − 4) + 5, write the new function rule (equation) for function and
describe
The new function rule is g(x) = 2x -3
What is a function?A technical definition of a function is: a relation from a set of inputs to a set of possible outputs where each input is related to exactly one output.
This means that if the object x is in the set of inputs (called the domain) then a function f will map the object x to exactly one object f(x) in the set of possible outputs (called the codomain).
if f(x) = 2x, then f(x-4) = 2(x-4)
g(x) = f(x-4) + 5
substitute f(x-4) into g(x)
g(x) = 2(x-4) + 5
g(x) = 2x -8 + 5
g(x) = 2x - 3
In conclusion, the function rule g(x) is 2x - 3
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