Answer:
231.59 years
Step-by-step explanation:
To model this situation we are going to use the exponential decay function:
f(t)= a (1-b)^t
where f(t) is the final amount remaining after t years of decay
a is the final amount
b is the decay rate in decimal form
t is the time in years
For Substance A:
Since we have 300 grams of the substance, a=300. To convert the decay rate to decimal form, we are going to divide the rate by 100%:
r = 0.15/100 = 0.0015. Replacing the values in our function:
f(t) = a (1-b)^t
f(t) = 300 (1-0.0015)^t
f(t) = 300 (0.9985)^t equation (1)
For Substance B:
Since we have 500 grams of the substance, a= 500. To convert the decay rate to decimal form, we are going to divide the rate by 100%:
r=0.37/100= 0.0037. Replacing the values in our function:
f(t) = a (1-b)^t
f(t)= 500 (1-0.0037)^t
f(t)=500(0.9963)^t equation (2)
Since they are trying to determine how many years it will be before the substances have an equal mass M, we can replace f(t) with M in both equations:
M=300(0.9985)^t equation (1)
M=500(0.9963)^t equation (2)
We can conclude that the system of equations that can be used to determine how long it will be before the substances have an equal mass, M, is :
{M=300(0.9985)^t
{M=500(0.9963)^t
Ridgid motions to prove
Answer:
Sequence:
1. [tex]T__{ < 0,-5 > } (ABCDE) = (A'B'C'D'E)[/tex]
. . . . . . . . . . ⭐ please take a ruler and measure the distance from AA', . . . . . . . . BB', CC', DD', and EE', and then write that distance (it should . . . . . . . . be the same for each measurement) in place of 5 in -5. I just . . . . . . . . wrote -5 because it was my best approximation for looking at . . . . . . . . a laptop screen. ⭐
2. [tex]R__{(180,B')} (A'B'C'D'E) = (A''B''C''D''E'')[/tex]
3. [tex]r__{D''E''} (A''B''C''D''E'') = (A'''B'''C'''D'''E''')[/tex]
Step-by-step explanation:
1. [tex]T__{ < 0,-5 > } (ABCDE) = (A'B'C'D'E)[/tex] means that when you move figure ABCDE down by 5 units, it will map onto the image of A'B'C'D'E.
2. [tex]R__{(180,B')} (A'B'C'D'E) = (A''B''C''D''E'')[/tex] means that when you rotate figure A'B'C'D'E' 180 degrees counterclockwise about point B', said figure will map onto the image of A''B''C''D''E''.
3. [tex]r__{D''E''} (A''B''C''D''E'') = (A'''B'''C'''D'''E''')[/tex] means that when you reflect figure A''B''C''D''E'' across segment D''E'', said figure will map onto the image A'''B'''C'''D'''E'''.
How do you solve for x and y values?
Solving for two variables (normally denoted as "x" and "y") requires two sets of equations.
Assuming you have two equations, the best way for solving for both variables is to use the substitution method, which involves solving for one variable as far as possible, then plugging it back in to the other equation. Knowing how to solve a system of equations with two variables is important for several areas, including trying to find the coordinate for points on a graph.
Write out the two equations that have the two variables you want to solve. For this example, we will find the value for "x" and "y" in the two equations "3x + y = 2" and "x + 5y = 20"
Solve for one of the variables in on one of the equations. For this example, let's solve for "y" in the first equation. Subtract 3x from each side to get "y = 2 - 3x"
Plug in the y value found from the first equation in to the second equation in order to find the x value. In the previous example, this means the second equation becomes "x + 5(2- 3x) = 20"
Solve for x. The example equation becomes "x + 10 - 15x = 20," which is then "-14 x + 10 = 20." Subtract 10 from each side, divide by 14 and you have end up with x = -10/14, which simplifies to x = -5/7.
Plug in the x value in to the first equation to find out the y value. y = 2 - 3(-5/7) becomes 2 + 15/7, which is 29/7.
Check your work by plugging in the x and y values in to both of the equations.
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How many points lie on a line?
Need Help With This Question
(The table represents an exponential function) ( what is the multiplicative rate of change of the function) - the question( picture below)
Answer:
A. [tex]\frac{1}{5}[/tex]
Step-by-step explanation:
⭐ What is the multiplicative rate?
The multiplicative rate is the number each consecutive y-value gets multiplied by.The multiplicative rate can only be found in exponential functions.To find the multiplicative rate of this exponential function, we need to make an equation to see what each y-value gets multiplied by to get the next y-value.
I am picking the y-values 2 and 2/5, but you can choose any two consecutive y-values.
Equation (let x= the multiplicative rate of change):
[tex]2x = \frac{2}{5}[/tex]
Solve for x:
[tex]\frac{2x}{2} = \frac{2}{5}(2)[/tex]
[tex]x = \frac{2}{10}[/tex]
Simplify:
[tex]x = \frac{1}{5}[/tex]
∴ The multiplicative rate of change of the function is 1/5.
If d/dx (g(x)) = 0
then d/dx (g(x)sin(x)) = ?
Answer:
Step-by-step explanation:
If the derivative of g(x) with respect to x (denoted d/dx g(x)) is equal to 0, then the derivative of the product g(x)sin(x) with respect to x can be found using the product rule for derivatives.
The product rule states that if f(x) and g(x) are two functions, then the derivative of the product f(x)g(x) with respect to x is given by:
d/dx (f(x)g(x)) = f(x) * d/dx g(x) + g(x) * d/dx f(x)
In our case, f(x) is g(x) and g(x) is sin(x). Substituting these values into the equation above, we get:
d/dx (g(x)sin(x)) = g(x) * d/dx sin(x) + sin(x) * d/dx g(x)
Since the derivative of sin(x) with respect to x is cos(x) and the derivative of g(x) with respect to x is 0, we can simplify this expression to:
d/dx (g(x)sin(x)) = 0 * cos(x) + sin(x) * 0
Which simplifies to:
d/dx (g(x)sin(x)) = 0
Therefore, if the derivative of g(x) with respect to x is equal to 0, then the derivative of the product g(x)sin(x) with respect to x is also equal to 0.
dr. yung tests a new anti-malaria drug in an asian population and concludes that he cannot reject the null hypothesis, and must conclude he does not have sufficient evidence to conclude that the drug works. in reality, the drug does work. dr. yung has committed a error. group of answer choices logical type i (false positive) type ii (false negative) statistical
Dr. Yung has committed a type l ( false positive) error.
What is a type I error?Rejecting a null hypothesis that is actually true in the population results in a type I error (false-positive); failing to reject a null hypothesis that is actually false in the population results in a type II error (false-negative).
A type I error occurs when a null hypothesis that is actually true is mistakenly rejected during statistical hypothesis testing (also known as a "false positive" finding or conclusion; example: "an innocent person is convicted"),
Therefore, the error is a type 1 error.
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Write the number 1. 8 in the form , using integers, to show that it is a rational number.
The number 1. 8 in the form a / b, using integers, to show that it is a rational number is 9 / 5 .
Note that the number 1.8 consists of two parts 1 and 0.8.
The decimal 0.8 can be written as the fraction is 8 / 10
Add these two numbers :
= 1 + 8 / 10
multiply and divide by 10
= 10 / 10 + 8 / 10
= 10 + 8 / 10
= 18 / 10
simplify the number
= 2 * 3 * 3 / 2 * 5
= 1 * 3 * 3 / 1 * 5
= 9 / 5
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I really need help on this page, could anyone help me?
F=9/5C+32 is the required equation and Greg statement is true
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
Given that Greg is expressing temperature in farenheit and Josh expressing it in the celsius.
C=5/9(F-32)
We need to rewrite the formula so that Josh can quicly convert the temperature that Greg describes F.
F=9/5C+32
The temperature where John leaves has 77 F.
Let us convert to celsius.
C=5/9(77-32)
C=5/9(45)
C=5(5)
C=25 degrees.
25 degress< 30 degrees.
Hence, F=9/5C+32 is the required equation and Greg statement is true.
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What are binomials give five examples?
"A binomial is an algebraic expression which has exactly two terms." The examples of binomials are x² + 3, x + y, x³ + 2x, 9 + 7y, xy² + xy, etc.
A polynomial is of various types like monomial, binomial, trinomial, etc.
Monomial contains only single term.
Trinomial contains exactly three terms. All the three are dissimilar.
A binomial is said to have only positive exponents and no negative exponents.
In x³ + 2x, x³ and 2x are two different terms. The variable is only x. The exponent of x³ is 1, the exponent of x is 1. The coefficient of x³ is 1, the coefficient of x is 2.
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what distance has a cheats gone if it travels 25 m/s in 3 seconds
Answer:
75 m
Step-by-step explanation:
three seconds of 25 m/s and 3 x 25 = 75
Use the quadratic formula to solve x^2+3x-28=0
The solutions to the quadratic equation x² + 3x - 28 = 0 are 4 and -7.
What are the solutions to the quadratic equation?The quadratic formula is expressed as;
x = (-b±√(b² - 4ac)) / (2a)
Given the equation;
x² + 3x - 28 = 0
a = 1b = 3c = -28Substitute the values of a, b, and c into the formula and solve for x.
x = (-b±√(b² - 4ac)) / (2a)
x = ( -3 ±√( 3² - ( 4 × 1 × -28) )) / (2×1)
x = ( -3 ±√( 9 - ( -112) )) / (2)
x = ( -3 ±√( 9 + 112 )) / (2)
x = ( -3 ±√( 121 )) / 2
x = ( -3 ± 11 ) / 2
x = ( -3 - 11 ) / 2, x = ( -3 + 11 ) / 2
x = -14/2, x = 8/2
x = -7, x = 4.
Therefore, -7 and 4 are the solutions to the equation.
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I need help on this please someone answer me!
So basically for the first one do 14.0%x 4.6
What are the 3 lengths of a right triangle?
5 dogs had long hair out of the 8 dogs at the park. What percent of the dogs had long hair? Round your answer to the nearest whole percent.
Answer:
62.5%
Step-by-step explanation:
5/8 × 100
should give you 62.6%
Calculate the approximate degree measure of the angle, given the following expression: cos(y°) = -0.10 Round your answer to the nearest tenth.
Answer:
y ≈ 95.7°
Step-by-step explanation:
To solve for the angle a trigonometric function is being used on, we have to use the inverse of the trigonometric function.
Inverse of tan(y°) = 4.12:
[tex]tan^{-1}(-0.10) = y[/tex]
Next, I used a scientific calculator to find the angle measure of y. I recommend using the Desmos Scientific Calculator.
[tex]95.7 = y[/tex]
8. The speed of an object can be found by taking the distance it travels and dividing it by the
time it takes to travel that distance. An object travels 100 feet in 2.5 seconds Let the speed, be
measured in fleet per second. Write an equation to represent the relationship between the three
quantities (speed, distance, and time).
Speed of object = 40 feet per second
What is speed and its formula?Speed is calculated as follows: speed = distance * time. Knowing the units for distance and time is necessary to calculate the units for speed. The units will be in metres per second (m/s) in this example since the distance is measured in metres (m) and the time is measured in seconds (s).Speed is what it means. the speed at which an object's location changes in any direction. The distance travelled in relation to the time it took to travel that distance is how speed is defined. Since speed simply has a direction and no magnitude, it is a scalar number.Based on the distance travelled in a certain amount of time. These automobiles can travel at speeds of more than 150 kilometres per hour (km/h). Meters per second (m/s) is the fundamental unit of speed in the metric system.Given data :
Distance cover by object = 100 feetTime taken by object = 2.5 secondsEquation represent speed is s = d/t
Assume;
Speed = S
Time taken = T
Distance cover = D
So,
Speed = Distance / Time
S = D / T
Speed of object = 100 / 2.5
Speed of object = 40 feet per second
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Which is a discontinuous process?
The function of the graph which is not connected with each other is known as a discontinuous function. A function f(x) is said to have a discontinuity of the first kind at x = a, if the left-hand limit of f(x) and right-hand limit of f(x) both exist but are not equal.
The function is an expression or law that defines a relationship between one variable and the independent variable and another variable the dependent variable
The independent variable is the variable being controlled in the problem, and the dependent variable is the variable that changes because of this control
Some examples of a discontinuous function
f(x) = 1 / (x - 2)
f(x) = tan x
f(x) = x2 - 1
For x < 1 and f(x) = x3 - 5 for 1 < x < 2
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A relationship between one variable, the independent variable, and another variable, the dependent variable, is defined by an expression or law known as the function.
The variable being controlled in the problem is the independent variable, and the variable that changes as a result of this control is the dependent variable.
f(x) = 1 / (x - 2)
f(x) = tan x
f(x) = x2 - 1
For x < 1 and f(x) = x3 - 5 for 1 < x < 2
How do you store 3 values in one variable in Python?
My_3_variables = [title, author, date] and then put this list at the first position of your other list : my_list[0] = my_3_variables .
Now, According to the question:
Create a list containing your 3 variables : my_3_variables = [title, author, date] and then put this list at the first position of your other list : my_list[0] = my_3_variables .
How do I store multiple values in one variable Python?
append()
We use the append() method for this. You can use this to append single values to the list – value, list, tuple.
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How do you find the missing value in an isosceles triangle?
Isosceles triangle has three sides, three angles, a base, a height, and an area in which two sides are equal to each other .
the sum of triangle is 180, sum of all the interior angles is equal to 180.
so if you know two angles then apply sum of triangles and find out the value of the third triangle.
isosceles triangle
An isosceles triangle is a type of triangle that has any two sides equal in length. The two angles of an isosceles triangle, opposite to equal sides, are equal in measure.
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Solve for x: 7x-22=3x+18
Answer:
x = 10
Step-by-step explanation:
7x-22=3x+18
4x -22 = 18
4x = 40
x = 10
[tex]\sqrt{x} 4=x-3[/tex]
The simplification of the given expression is x² - x + 3.
What is an expression?The mathematical expression combines numerical variables and operations denoted by addition, subtraction, multiplication, and division signs.
Mathematical symbols can be used to represent numbers (constants), variables, operations, functions, brackets, punctuation, and grouping. They can also denote the logical syntax's operation order and other properties.
Given that the expression is √x⁴ = x - 3. The expression will be simplified as,
√x⁴ = x - 3
Solve the radical term first and simplify the expression further,
x² = x - 3
x² - x + 3 = 0
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is an integer.
Given that the value of lies between between 29 and 39 Write down the value of .
The values of the integers lie between 29 and 39 and is 30,31,32,33,34,35,36,37,38.
What is a number system?A numeral system is a writing system for expressing numbers; that is, a mathematical notation for representing numbers of a given set in a consistent manner using digits or other symbols. In different numeral systems, the same sequence of symbols can represent different numbers.
A zero, a positive natural number, or a negative integer with a minus sign is an integer. The negative numbers are the additive inverses of their positive counterparts.
Given that the integers lie between the numbers 29 and 39. The numbers will be,
29, { 30,31,32,33,34,35,36,37,38 }, 39
Therefore, the values of the integers lie between 29 and 39 and are 30,31,32,33,34,35,36,37,38.
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how do I convert 5 rows of ribbons to inches
You may use the expression to convert the length of 5 rows of ribbons to inches: length = 5w + (5 - 1)s inches, where w is the width of the ribbons and s is the spacing between the rows.
To convert 5 rows of ribbons to inches, you need to know the width of the ribbons and the spacing between the rows.
Let's say the width of the ribbons is w inches, and the spacing between the rows is s inches. In this case, the total length of the ribbons in 5 rows would be 5w + 4s inches, since there are 5 ribbons and 4 spaces between them.
For example, if the width of the ribbons is 0.5 inches and the spacing between the rows is 0.1 inches, the total length of the ribbons in 5 rows would be :5 × 0.5 inches + 4 × 0.1 inches = 2.5 inches + 0.4 inches = 2.9 inches.
In general, to convert the length of n rows of ribbons to inches, you can use the formula: length = nw + (n - 1)s inches, where w is the width of the ribbons and s is the spacing between the rows.
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In a survey of 118 randomly selected gun owners, it was found that 81 of them said they owned a gun primarily for protection.
Find the margin of error and 95% confidence interval for the percentage of all gun owners who would say that they own a gun primarily for protection. Report answers to at least 2 decimal places.
Margin of Error (as a percentage)
The margin of error is 0.086 and its C.I is (0.575 , 0.785).
What is margin of error?
Your results will vary from the actual population value by how many percentage points, as indicated by the margin of error. A 95% confidence interval with a 4% margin of error, for instance, indicates that your statistic will, 95% of the time, be within 4% of the true population figure.n = 117 , x =87
Point estimate for the proportion:
P = x/n
= 81/118
= 0.68644
Confidence = 95%, α = 0.05
From z-table area 0.975 close to z=1.96
Margin of error, E = 1.96 √((0.68*0.55)/130)
= 1.96 * 0.05363
= 0.105
= 0.086
Confidence = P ± E
= 0.68 ± 0.105
=(0.68-0.105 , 0.68+0.105)
= (0.575 , 0.785)
Hence, the margin of error is 0.086 and its C.I is (0.575 , 0.785).
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Can a 7th grader take algebra?
Yes, a 7th grader may be taken algebra. Depending on the school district, and capacity some 7th graders may be able to take algebra as an elective or as part of their regular curriculum.
Algebra is the branch of mathematics that helps in the rendering of problems or situations in the form of mathematical expressions.
It includes variables like x, y, z, and mathematical operations like addition, subtraction, multiplication, and division to form a meaningful mathematical expression.
Some of the branches of mathematics such as trigonometry, calculus, coordinate geometry, involve the use of algebra. One example is in algebra is 2x + 4 = 8.
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True or false math. Make sure you are correct though. Thank you!
Answer:
True
Step-by-step explanation:
Most of the function f(x) has the domain is (- infinity, positive infinity), So I think this is true!
What is the relation between area height and volume?
The relation between area, height and volume is: volume = area * height
In this question we need to find the relation between area height and volume.
the formula for area and volume are based on height:
volume = base area * height
Let v represents the volume, A represents area and h represents the height.
V = A * h
As we know the volume of rectangular prism is:
volume = length * width * height
i.e., V = l * w * h
and the base area is:
area = length * width
i.e., A = l * w
Substitute A = l * w in V = l * w * h
Then we get, V = A * h
Therefore, the relation between area, height and volume is: V = A * h i.e., volume = area * height
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Harry's soccer team is trying to raise $2,520 to travel to a tournament in florida, so they decided to host a pancake breakfast. Each person must pay $15 for the breakfast. How many people need to attend their breakfast in order to raise $2520?.
Harry's soccer team needs 168 people to attend their pancake breakfast in order to raise $2,520.
To find the number of people that need to attend the pancake breakfast, we can set up the following equation:
Number of People x Cost per Person = Total Cost
We know that the total cost is $2,520 and the cost per person is $15, so we can substitute those values into the equation:
Number of People x $15 = $2,520
We can solve for the number of people by dividing both sides of the equation by $15:
Number of People = $2,520 / $15
This gives us the number of people that need to attend the pancake breakfast in order to raise the desired amount of money. In this case, the number of people is 168.
Therefore, Harry's soccer team needs 168 people to attend their pancake breakfast in order to raise $2,520.
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Find the missing measures in the parallelogram given below. Also, state the property used.
Answer:
see explanation
Step-by-step explanation:
AD = BC = 8 ( opposite sides of a parallelogram are congruent )
DC = AB = 15 ( opposite sides of a parallelogram are congruent )
Consecutive angles in a parallelogram are supplementary , sum to 180° , so
∠ A + ∠ D = 180° , that is
∠ A + 68° = 180° ( subtract 68° from both sides )
∠ A = 112°
the opposite angles of a parallelogram are congruent , then
∠ B = ∠ D = 68° , and
∠ C = ∠ A = 112°
How do you describe the relationship of the volume between the volume of a sphere and the volume of a cylinder?
The relationship between the volume of a sphere and the volume of a cylinder is: the volume of a sphere is 2/3 of the volume of a cylinder with same radius, and height equal to the diameter.
In this question we need to describe the relationship of the volume between the volume of a sphere and the volume of a cylinder.
Consider a cylinder with radius r and height h.
we know that the formula for the volume of cylinder is,
V1 = π * r² * h
Consider a sphere with radius r1.
We know that the formula for the volume of sphere is,
V2 = 4/3 * π * r1³
If the sphere and a cylinder have same radii and height of cylinder equal to the diameter then, r1 = r and h = 2r
V2 = 4/3 * π * r³
And V1 = π * r² * (2r)
V1 = 2 * π * r³
V1 = 2 * 3/4 * V2
V1 = 3/2 * V2
volume of cylinder = 3/2 * volume of sphere
Therefore, the volume of a sphere = 2/3 * the volume of a cylinder
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