The percentage rate of change per minute is approximately 0.98%
The mass of the sample decreases by 59% every hour, so we can write the following differential equation:
dm/dt = -0.59m
Rate of change of the mass (dm/dt) is equal to the mass (m) multiplied by the constant -0.59.
We can solve this differential equation using separation of variables:
dm/m = -0.59 dt
Integrating both sides, we get:
ln|m| = -0.59t + C
where C is the constant of integration.
To find C, we can use the initial condition that the mass of the sample is 530 grams at t=0:
ln|530| = C
C = ln(530)
So the solution to the differential equation is:
ln|m| = -0.59t + ln(530)
[tex]m(t) = 530 e^(^-^0^.^5^9^t^)[/tex]
This function represents the mass of the sample after t hours, where the rate of change per minute is given by the constant
k = -0.59/60 = -0.00983 (rounded to 5 decimal places).
To find the percentage rate of change per minute, we can multiply k by 100 to convert it to a percentage:
-0.00983 × 100 = -0.983%
Therefore, the percentage rate of change per minute is approximately 0.98%
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the length and width of a rectangular piece of paper were measured as 60cm and 12cm respectively, determine the relative error in the calculation of it's area.
Answer:
Step-by-step explanation:
actual area : 60 x 12 = 720
1/2 = 0.5
60 + 0.5 = 60.5 12 + 0.5 = 12.5 -max area = 60.5 x 12.5 = 756.25
60 - 0.5 = 59.5 12 - 0.5 = 11.5 -min area = 59.5 x 11.5 = 684.25
absolute error : 1/2(756.25-684.25) = 36
relative error : 36/720 = 0.05
... your welcome
3. Arthur's mother is a mechanical engineer. She is designing
rectangular carts formoving finished goods from a factory's
manufacturing floor to the loading dock, where the goods are placed
on trucks.
She made a drawing showing where the carts must turn from a
hallway 48 inches wide to pass through a doorway 36 inches wide.
The drawing shows the longest cart that will pass through the
doorway.
to manufacturing floor 30 in.
G
E.
to loading dock
B
D
a) What kind of triangles are AABC and ACFD?
cart
36 in.
48 in.
b) In the drawing, one sixth of an inch represents 1 foot. What is the
scale factor of the drawing? Explain.
a) is Right angle Triangles both of them
b) The scale factor is 1:2.
How to solveGiven AFD = 90 degrees, So CFD = 90 degrees.
So it a Right Angle Triangle.
Again ABC = 90 degrees, It's also a Right Angle Triangle.
Here see both the Triangle are opposite to each other so according to the theorem sum of all three angles of a triangle is 180 degrees
so if any angle is 90 deg then the other two sum is also 90 deg.
Given the scale Factor, 1/6 inch = 1 foot,
So it is a Reducing Scale so let 'x' be in inches
So the Scale Factor = 1:2
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bao mom is picking him up from the ice rink she is at home which is located at the origin (0,0) how many total units is the ice rink away from the origin explain
The total units of length for the ice rink away from the origin is 14.42 units.
How to determine the distance between the coordinates for each points?In Mathematics and Geometry, the distance between two (2) end points that are on a coordinate plane can be calculated by using the following mathematical equation:
Distance = √[(x₂ - x₁)² + (y₂ - y₁)²]
Where:
x and y represent the data points (coordinates) on a cartesian coordinate.
Note: Ice rink is located at point (12, 8).
By substituting the given end points into the distance formula, we have the following;
Distance = √[(12 - 0)² + (8 - 0)²]
Distance = √[(12)² + (8)²]
Distance = √[144 + 64]
Distance = √208
Distance = 14.42 units.
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Missing information:
The question is incomplete and the complete question is shown in the attached picture.
The two-way frequency table shows the results of a survey of students.
Right-handed
Left-handed
Total
In music program Not in music program Total
43
394
437
15
33
48
58
427
475
How many left-handed students are in the music program?
OA. 15
OB. 48
OC. 43
OD. 58
The left-handed students in the music program are option A 15 students.
What is two-way frequency table?A table that shows the frequencies of two category variables is known as a two-way frequency table. It is a method for succinctly and clearly organising and displaying data for two variables. One variable is represented by the table's rows, while the other variable is represented by the table's columns. The frequency of each combination of categories is displayed in the table's cells. To examine the relationship between the two variables and to spot patterns and trends in the data, a two-way frequency table can be employed. To summarise and analyse data, it is frequently used in statistics, the social sciences, and other disciplines.
From the given table the number of students that are in music program and left handed is given by the intersection of the row and column of the two.
Thus, he left-handed students in the music program are 15.
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Please answer if you know this one with the steps thank you.
Answer: 36600 = E
Step-by-step explanation:
Given:
T=.2 (E - 10600)
T=5200
Find: E
Solution:
>substitute into thequation. You know T=5200
5200 = .2(E-10600) > Divide both sides by .2
26000 = E- 10600 > add 10600 to both sides
36600 = E
Find the surface area of the composite solid to the nearest hundredth.
3 ft.
4 ft
2 ft
The surface area is about
square feet.
snip, that's wrong nvm (not sure how to delete)
I need help pleaseee
The matrix formed by performing the row operation 4R₂ + R₃ — R₃ will result to R₁ = [-4 0 1 5], R₂ = [-6 5 -1 8], and R₃= [-33 24 -9 32]
What is a matrix row operationRow operations are a set of operations that can be performed on the rows of a matrix in order to transform it into a row equivalent matrix, which has the same solution set as the original matrix.
performing the row operation 4R₂ + R₃ — R₃, we have;
4(-6) + (-9) = -33 {row 3 column 1}
4(5) + 4 = 24 {row 3 column 2}
4(-1) + (-5) = -9 {row 3 column 3}
4(8) + 0 = 32 {row 3 column 4}
Therefore, the matrix formed by performing the row operation 4R₂ + R₃ — R₃ will give a new one with R₁ = [-4 0 1 5], R₂ = [-6 5 -1 8], and R₃= [-33 24 -9 32]
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Work out the value of fg^2 when:
f = -5 and g = -4
PLEASE HELP WILL MARK BRAINLY What is the area of a regular pentagon with a side of 5 ? Round the answer to the nearest tenth. TYPE THE NUMBER ONLY
prove that:
(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1)
The given identity (P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1) is proven below
How to prove the given identityGiven the following equation
(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)=-4(2p² + 1)/(p²-4) (p² - 1)
We start by simplifying the left-hand side of the equation:
(P+1/P-1 + P+1/P+1)-(P-1/P+2 + P+1/P-2)= [(P²+1)/(P(P-1))] + [(P²+1)/(P(P+1))] - [(P²-1)/((P+2)P)] - [(P²+1)/((P-2)P)]
Next, we have the following steps to simplify the expression
= [(P³ + P² + P + 1)/(P(P²-1))] - [(P³ - 3P)/(P(P²-4))]
= [(P³ + P² + P + 1)(P²-4) - (P³ - 3P)(P²-1)]/[(P(P²-1))(P(P²-4))]
= [(P⁵ - 3P³ + P³ - 3P² + P² - 4P + P² - 4P - 4 + P³ - 3P)/(P⁴ - 5P² + 4)]
= [P⁵ - 2P³ - 6P² - 8P - 4]/[(P²-4)(P²-1)]
= -4(2p² + 1)/(p²-4) (p² - 1)
Hence, the given identity is proven.
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In this figure, ∠1 and ∠2 are located on a line.
Let m∠1=x° and m∠2=(4/5 x)°.
What is the value of x?
Answer:
x = 100
Step-by-step explanation:
1 and 2 are a linear pair and sum to 180° , that is
x + [tex]\frac{4}{5}[/tex] x = 180 ( multiply through by 5 to clear the fraction )
5x + 4x = 900
9x = 900 ( divide both sides by 9 )
x = 100
50 Points! Multiple choice algebra question. Photo attached. Thank you!
The result of the logarithm function is equal to 9. (Correct choice: D)
How to determine the missing component in a logarithm
The statement shows an incomplete logarithm, whose result must be found by understing relationships between trascendent functions. Logarithm functions and exponential functions are related in the following way:
aᵇ = n ↔ ㏒ₐ n = b
Where:
a - Baseb - Exponentn - ResultIf we know that (base) a = 3 and (exponent) b = 2, then the value of the result (n) is now defined:
n = 9
3² = 9
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write two different equations with variables and draw a diagram to solve the situation. For cleaning the attic Kristin was given $18. now she has $50. how much money did she have before
Once again, we get the same answer: Kristin had $32 before receiving the $18 for cleaning the attic. we solve this by forming equation and solving it
what is equation ?
An equation is a mathematical statement that shows that two expressions are equal. It usually consists of variables, constants, and mathematical operations such as addition, subtraction, multiplication, and division. Equations are used to solve problems in various fields, including mathematics, physics, engineering
In the given question,
Let's use "x" to represent the amount of money Kristin had before receiving the $18 for cleaning the attic. We can set up the following equation:
x + 18 = 50
This equation represents the total amount of money Kristin has now, which is $50, after receiving the $18 for cleaning the attic. To solve for "x", we can subtract 18 from both sides of the equation:
x + 18 - 18 = 50 - 18
x = 32
Therefore, Kristin had $32 before receiving the $18 for cleaning the attic.
Alternatively, we can also use a diagram to represent the situation. We can draw a rectangle to represent the total amount of money Kristin has now, which is $50. We can then divide the rectangle into two parts: one part representing the $18 she received for cleaning the attic, and the other part representing the amount of money she had before. We can label this unknown amount as "x", and set up the following equation:
x + 18 = 50
This equation is the same as the one we set up earlier. To solve for "x", we can again subtract 18 from both sides of the equation:
x + 18 - 18 = 50 - 18
x = 32
Once again, we get the same answer: Kristin had $32 before receiving the $18 for cleaning the attic.
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Evaluate each expression using the graphs of y=f(x) and y=g(x) shown below.
The composition of functions is solved and the expressions are
a) ( g o f ) ( -1 ) = 1
b) ( g o f ) ( 0 ) = 4
c) ( f o g ) ( -1 ) = -2
d) ( f o g ) ( 4 ) = -1
Given data ,
Let the composition of function be represented as A
Now , the value of A is
a)
( g o f ) ( -1 ) = g ( f ( -1 ) )
On simplifying the function , we get
when x = -1 , f ( -1 ) = 2
g ( 2 ) = 1
So , ( g o f ) ( -1 ) = 1
b)
( g o f ) ( 0 ) = g ( f ( 0 ) )
On simplifying the function , we get
when x = 0 , f ( 0 ) = 0
g ( 0 ) = 4
So , ( g o f ) ( 0 ) = 4
c)
( f o g ) ( -1 ) = f ( g ( -1 ) )
On simplifying the function , we get
when x = -1 , g ( -1 ) = 2
f ( 2 ) = -2
So , ( f o g ) ( -1 ) = -2
d)
( f o g ) ( 4 ) = f ( g ( 4 ) )
On simplifying the function , we get
when x = 4 , g ( 4 ) = 1
f ( 1 ) = -1
So , ( f o g ) ( 4 ) = -1
Hence , the composition of function is solved
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A triangular prism and it’s net are shown below. The top and the bottom of the prism are shaded. All lengths are in centimeters.)
The solution is: the area of the shaded base in square centimeters is:
B= 15 cm²
Here, we have,
The base of the triangular shaped wedge of cheese is a right-triangle.To find the area of a right-triangle you apply the formula for half base by height.
A=1/2*b*h
= base area
= B
In this case, assume the sides of the triangle given are;
a=5 cm and b=6 cm,
thus area will be 1/2*6*5 =15 cm²
Hence, the area of the shaded base in square centimeters is :
B= 15 cm²
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complete question:
Evelyn cut a wedge of cheese into the shape of a triangular prism-like the one shown below. The shaded part represents one of the bases of the prism.
A formula for the volume of a triangular prism is v=Bh . Which equation can be used to find B , the area of the shaded base in square centimeters?
A car pulls the emergency hand brake, accelerating at -4.0 m/s2 for 7.5 seconds to a complete and total stop. What was the initial velocity of the car before the brake was pulled?
The initial velocity of the car before the brake was pulled is 30m/s
What was the initial velocity of the car before the brake was pulled?From the question, we have the following parameters that can be used in our computation:
A car pulls the emergency hand brake, accelerating at -4.0 m/s2 for 7.5 seconds
This means that
Acceleration = -4.0m/s^2
Time = 7.5 seconds
Using the above as a guide, we have the following:
Initial velocity = -Acceleration * Time
substitute the known values in the above equation, so, we have the following representation
Initial velocity = 4 * 7.5
Evaluate
Initial velocity = 30
Hence, the initial velocity is 30
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Express all real numbers greater than 5 in interval notation.
All real numbers greater than 5 can be expressed in interval notation as:
(5, ∞)
How to express all real numbers greater than 5 in interval notation?Interval notation is a way of representing an interval on a number line. Simply, it is a method of writing subsets of the real number line.
All real numbers greater than 5 can be expressed in interval notation as:
(5, ∞)
Where the round bracket "(" means 5 is not included in the interval, and the infinity symbol "∞" means the interval continues indefinitely to the right.
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using the table feature of a graphing utility what would be the intensity of an earthquake with an amplitude of 200,000 micrometers for 0.5 seconds?
Using the table feature of a graphing utility the intensity of an earthquake with an amplitude of 200,000 micrometers for 0.5 seconds would be 2.16 x 10¹⁴ joules/second/meter².
How did we get this ?First, note that the intensity of an earthquake with an amplitude of 200,000 micrometers for 0.5 seconds can be calculated using the formula..
I = (1/2)ρv²
Here I Intensity
ρ = density of the medium - this is a constatnt
v = velocity of the S-waves
If we used a graphing tool
a coumun ffor v will be created
a column for the formula for velocity will also be created.
The formula for velocity is
V = A/ T
A = amplitude
T = time or period in seconds
Since A = 200,000 micrometers; and
T = 0.05 secons
v = 200,000 / 0.5
v = 400,000 micrometer/sec
Back o the table, we ahve to add another oclumn for V²
then enter the values for V²
V² = 400,000²
v² = 160,000,000,000 micrometer²/sec²
Nowe we add another column which is
I = 1/2(pv²)
I = 2.16 x 10¹⁴ joules/second/meter².
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Is this correct for problem 15?
The solution to the given inequality is: 10 > x ≤ 12
How to solve Inequality expressions?Inequalities are defined as mathematical expressions that involve the symbols >(greater than), <(less than), ≥(greater than or equal to) and ≤(less than or equal to).
In order for us to 'solve' an inequality, we have to find a range, or ranges, of values that an unknown x can take and still satisfy the inequality.
We are told that the angle (9x + 7)° is greater than 97° and at most 118°
Thus:
9x + 7 > 97
9x > 90
x > 10
Similarly:
9x + 7 ≤ 115
9x ≤ 108
x ≤ 12
Thus, the solution to the inequality is: 10 > x ≤ 12
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Find sin (ñ/4). Round to 3 decimal places.
Answer:To find sin(π/4), we can use the fact that sin(π/4) = sin(45°). We also know that sin(45°) = 1/√2 or approximately 0.707 (rounded to 3 decimal places). Therefore, sin(π/4) is approximately equal to 0.707.
Step-by-step explanation:
Graph the feasible region and find the values of x and y that give the maximum possible value of g=8x+12y subject to the following constraints.
The feasible region on the attached graph of the inequalities created with MS Excel indicates that the maximum value of g = 8·x + 12·y is 100
What is an inequality?The feasible region is the region on the graph of the inequalities that satisfies the specified constraints.
The specified equations obtained from the constraints in slope intercept form are;
y = -0.5·x + 7; The region below the graph is shaded
y = -0.75·x + 9; The region below the graph is shaded
x = 0; The region to the right of the line x = 0 is shaded
y = 0; The region above the line y = 0 is shaded
The point of intersection of the graphs can be found from the equation; -0.5·x + 7 = -0.75·x + 9
Which indicates that at the intersection, x = 8, and y = -0.5×8 + 7 = 3
The corner points are; (0, 0), (0, 7), (8, 3), (12, 0)
The value of the function g for each of the feasible region are therefore;
g(0, 0) = 8 × 0 + 12 × 0 = 0
g(0, 7) = 8 × 0 + 12 × 7 = 84
g(8, 3) = 8 × 8 + 12 × 3 = 100
g(12, 0) = 8 × 12 + 12 × 0 = 96
The maximum possible value of g therefore is 100, which is the value at the point (8, 3)Please find attached the graph of the inequalities showing the feasible region created with MS Excel
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3. Abby has 3 bags of oranges with 14,
23 and 28 oranges in them. Abby
rounds the number of oranges in each
bag to the nearest ten. About how
many oranges does Abby have
altogether?
Answer:
60
Step-by-step explanation:
14 rounds to 10
23 rounds to 20
28 rounds to 30
10+20+30=60
Given (x – 7)2 = 36, select the values of x.
x = 13
x = 1
x = –29
x = 42
Answer: X = 25
Step-by-step explanation: Since 36 divided by 2 equals 18, which would cancel out the two on the left side leaving us with. (x - 7) = 18 we can add 7 to both sides to get. X = 25
Edit: To whoever said my math is incorrect is wrong, I even double checked with multiple sources and people. It must’ve been a different equation or number. Sorry for not being able to help, however the math was correct.
Find the circumference and the area of a circle with radius 4 m.
Use the value 3.14 for , and do not round your answers. Be sure to include the correct units in your answers.
4m
Circumference:
Area:
Sally is putting her dominions back into their storage tin. She wants to know how many dominoes can fit in the tin. While placing the dominoes in the tin, she counts how many dominos can be stacked on top of each other and she finds that to be 3 dominoes. She counts how many can be set side-by-side and she finds that to be 9 dominoes. Finally she counts how many can be placed end-to-end in the tin and she finds that to be 4 dominoes. Sally knows she can use addition to figure out how many total dominoes fit in the tin. She also knows that 27 dominoes fit in one row in the tin when she stacks up as many as she can in that row. Write an expression using only addition to show how Sally can determine how many dominoes can fit in the tin based on the number of dominoes in each row stacked
The expression that Sally can use to determine how many dominoes can fit in the tin based on the number of dominoes in each row stacked is (Number of rows stacked ÷ 0.75) x (9 x 4)
Sally can use the fact that she can fit 3 dominoes stacked on top of each other, 9 dominoes side-by-side, and 4 dominoes end-to-end in the tin to figure out how many dominoes can fit in the tin. Since she knows that 27 dominoes fit in one row stacked, she can use addition to determine the total number of dominoes that can fit in the tin.
First, she can find the number of dominoes that can fit in one layer of the tin by multiplying the number of dominoes that fit side-by-side and the number that fit end-to-end: 9 x 4 = 36.
Then, she can divide the total number of dominoes that fit in one row (27) by the number of dominoes that can fit in one layer (36): 27 ÷ 36 = 0.75.
This means that each layer of the tin can hold 0.75 rows of dominoes.
To find the total number of dominoes that can fit in the tin, Sally can multiply the number of layers by the number of dominoes in each layer: Number of layers x Number of dominoes in each layer = Total number of dominoes that can fit in the tin.
Therefore, the expression that Sally can use to determine how many dominoes can fit in the tin based on the number of dominoes in each row stacked is:
Total number of dominoes = Number of layers x Number of dominoes in each layer
Total number of dominoes = (Number of rows stacked ÷ 0.75) x (9 x 4)
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Add: -8x8 + (-3x8 + 3)
Enter the correct answer.
What is the base pic attached below
Answer: 2.5
Step-by-step explanation:
the base is always positive, and it says f(x)= 1/2*5^x
1/2*5 is 2.5, so I think the base is 2.5
hope it helped:)
At Wynne College, there are 240 students in Year 12.
The interquartile range of the times taken for these students to travel to college is 32 minutes.
How many of these students have travel times within this interquartile range?
About 120 students have travel times within the quoted interquartile range.
InterquartileThe interquartile range (IQR) represents the range of the middle 50% of a set of data, which is the difference between the third quartile (Q3) and the first quartile (Q1).
Assuming that the travel times are normally distributed and that we have information on the quartiles, we can use the formula:
IQR = Q3 - Q1
To find the number of students whose travel times fall within the interquartile range, we need to know the values of Q1 and Q3.
Since the IQR is 32 minutes:
32 = Q3 - Q1
We also know that the total number of students in Year 12 is 240. Assuming that all students have reported their travel times, we can use the interquartile range to estimate the proportion of students whose travel times fall within this range.
If the interquartile range covers the middle 50% of the data, then each quartile should cover 25% of the data. Therefore, we can estimate that the number of students whose travel times fall within the interquartile range is:
Number of students = 240 x 0.50 = 120
Therefore, we estimate that 120 of the 240 Year 12 students have travel times within the interquartile range of 32 minutes.
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ACTIVITY 2: Simplify the following.
The index forms are simplified to;
1. [tex]5^6^\sqrt{2}[/tex]
2.[tex]3^5\sqrt{3}[/tex]
3. [tex]2^2^\sqrt{25}[/tex]
How to simply the index formsIt is important to note the following about the rules of index forms;
Add the exponents when multiplying index forms of like basesSubtract the exponents when dividing index forms of like basesExponents of unlike bases cannot be add or subtracted.From the information given, we have that;
[tex]5^\sqrt{2}[/tex] × [tex]5^\sqrt{50}[/tex]
Add the exponents, we have;
[tex]5^\sqrt{2} ^+ 5\sqrt{2}[/tex]
Then, we have;
[tex]5^6^\sqrt{2}[/tex]
2. [tex]3\sqrt{12}[/tex] × [tex]3^\sqrt{27}[/tex]
We have;
[tex]3^2^\sqrt{3} + 3\sqrt{3}[/tex]
Add the exponents
[tex]3^5\sqrt{3}[/tex]
3. [tex]2^2^\sqrt{25}[/tex]
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1. Which of the following is a set or not?
(a) A=Set of tall man
(b) B=Set of beautiful women
(c) C=Set of tall students of class 10
(d) D=Set of counting number
(e) E=Set of good students
(f) F=Set of yellow roses