Considering an exponential function, it is found that:
a) The half-life of the element is of 39.63 days.
b) The time needed is of 51.82 days.
What is an exponential function?A decaying exponential function is modeled by the equation presented as follows:
[tex]A(t) = A(0)(1 - r)^t[/tex]
In which the variables of the equation are:
A(0) is the initial value.r is the decay rate, as a decimal.In this problem, the parameters are given as follows, from the text:
A(0) = 120, A(11) = 99.
Hence the decay rate r is obtained as follows:
[tex]A(t) = A(0)(1 - r)^t[/tex]
[tex]120 = 99(1 - r)^{11}[/tex]
[tex](1 - r)^{11} = \frac{99}{120}[/tex]
[tex]1 - r = \sqrt[11]{\frac{99}{120}}[/tex]
[tex]1 - r = \left(\frac{99}{120}\right)^{\frac{1}{11}}[/tex]
1 - r = 0.98266367982
Hence the equation is:
[tex]A(t) = A(0)(0.98266367982)^t[/tex]
The half-life is the value of t for which:
A(t) = 0.5A(0).
Hence:
[tex]A(t) = A(0)(0.98266367982)^t[/tex]
[tex]0.5A(0) = A(0)(0.98266367982)^t[/tex]
[tex](0.98266367982)^t = 0.5[/tex]
[tex]\log{(0.98266367982)^t} = \log{0.5}[/tex]
[tex]t\log{(0.98266367982)} = \log{0.5}[/tex]
[tex]t = \frac{\log{0.5}}{\log{(0.98266367982)}}[/tex]
t = 39.63 days.
For item b, the time is obtained as follows:
[tex]A(t) = 99(0.98266367982)^t[/tex]
[tex]40 = 99(0.98266367982)^t[/tex]
[tex](0.98266367982)^t = \frac{40}{99}[/tex]
[tex](0.98266367982)^t = 0.40404040[/tex]
[tex]t = \frac{\log{0.40404040}}{\log{(0.98266367982)}}[/tex]
t = 51.82 days.
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answer this and u a big W if u dont ur a L
Answer:
Part A. (4,5)
Part B. (9,7)
Step-by-step explanation:
Look at the x an y. X is bottom numbers Y is the vertical numbers. Look at A then B and boom you would get what i got.
The map shows a portion of downtown Mapledale. Main Street and 2nd Avenue are parallel. Use the map to answer each question. Question Angle Which angle is an alternate exterior angle to angle 8? Which angle is a same-side interior angle to angle 2? Which angle is a corresponding angle to angle 3?
a. Angle 4 is an alternate exterior angles to angle 8.
b. Angle 3 is same-side interior angle to angle 2.
c. Angle 1 is corresponding angles to angle 3.
What are Corresponding Angles?Corresponding angles are located on the same corner and on the same side of a transversal.
For example, in the given image below, angles 1 and 3 are corresponding angles.
What are Alternate Exterior Angles?Alternate exterior angles are any two exterior angles that lie on two different parallel lines but on alternate sides of the transversal that crosses the two parallel lines.
For example, in the image given, angles 8 and 4 are alternate exterior angles.
What are Same-side Interior Angles?Same-side interior angles are interior angles that are located on the same side of the transversal but on different parallel lines that the transversal cuts across.
For example, angles 2 and 3 are same-side interior angles as seen in the given image.
What are Corresponding Angles?Corresponding angles are located on the same corner and on the same side of a transversal.
For example, in the given image below, angles 1 and 3 are corresponding angles.
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simplify the following
Answer: 12⋅|x3|−512√⋅|3|
PLEASR GIVE BRAINLIEST THANK YOU VERY MUCH!!!
a data analyst creates a scatterplot with a lot of data points. the analyst wants to make some points on the plot more transparent than others. what aesthetic should the analyst use?
Analyzers should use the Alpha aesthetic.
Using the Alpha aesthetic, specific points on a scatterplot are more transparent than others to highlight specific data points.
What is a scatterplot?
A scatter plot is a set of points plotted along a horizontal and vertical axis. In statistics (also known as variables), scatter plots are crucial to demonstrating whether a correlation exists between observational quantities or phenomena.
A scatter plot plots data points on a horizontal and vertical axis to demonstrate one variable's influence on another. Each row in the data table is represented by a marker whose position is determined by the values of the columns on the X and Y axes.
Using a scatter plot, this line indicates the prevailing direction of a phenomenon. In a scatter plot, a trend line can be used to highlight the direction and speed of price changes.
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help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
help meeeeeeeeeeee pleaseeeeeeeeeee rn rnnnnnnnnn!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!!
The function has a maximum value of 30 at x = 3.
Given Function:
f(x) = -3+18x+3
here a = -3 , b = 18 , c = 3
a is negative so it has maximum value
x = -b/2a
= -18/2*(-3)
= -18/-6
= 18/6
= 3
f(x) = -3* + 18*3 + 3
= -3*9+54+3
= -27+54+3
= 27+3
= 30
Therefore the function has a maximum value of 30 at x = 3.
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Which statements are true about the ordered pair (5, -6) and the sys
[x+y=−1
3x - y = 21
Select each correct answer.
Select 3 correct answer(s)
The ordered pair (5, -6) is a solution to the first e
because it makes the first equation true.
The ordered pair (5, -6) is a solution to the secon
equation because it makes the second equation
The ordered pair (5, −6) is a solution to the first and second equations because it makes both equations true.
What are linear equations?In mathematics, a linear equation is one that may be written in the form where the variables are alphabets, and the coefficients are frequently real integers. An algebraic equation with simply a constant and a first-order (linear) term, such as y=mx+b, where m is the slope and b is the y-intercept, is known as a linear equation. The variables in the previous sentence, y and x, are referred to as a "linear equation with two variables" at times.
The given system of equations is
x + y = -1 ......(1)
3x - y = 21 ......(2)
Rewrite equation (1)
y = - x - 1 ......(3)
Put equation (4) in equation (3)
3x -(-x -1) = 21
3x + x + 1 = 21
4x = 20
x = 20/4
x = 5
Put x= 5 in equation (3)
y = - 5 - 1
y = - 6
So, both the options are correct, (5, -6) is the solution of both equations.
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help me please please please triangle 111111
Answer:
144 cm²
Step-by-step explanation:
1.) Find the area of all of the faces
10*4=40 (Top Face)
4*8=32 (Bottom Face)
6*8*0.5=24 (One Triangle)
6*8*.5=24 (Other Triangle)
6*4=24 (Back Face)
2.) Add them all together to get the surface area
40+32+24+24+24= 144
***Don't forget the cm². Some teachers are really annoying about this
true or false? finding a random sample with a mean this low in a population with mean 7 and standard deviation 2 is very unlikely.
It is false that " finding a random sample with a mean this low in a population with mean 7 and standard deviation 2 is very unlikely".
What is standard deviation?The term "standard deviation" (or "") refers to a measurement of the data's dispersion from the mean. A low standard deviation indicates that the data are grouped around the mean, whereas a high standard deviation shows that the data are more dispersed. The average degree of variability in your data set is represented by the standard deviation. It reveals the average deviation of each score from the mean. The standard deviation gauges how widely the data deviates from the mean. When comparing data sets that may have the same mean but a different range, it is helpful. The mean of the two numbers 15, 15, 15, 14, 16 and 2, 7, 14, 22, 30 for instance, is the same. The second, however, is obviously more dispersed.
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Chelsea has final exams in calculus, physics, and history.
She has up to 25 hours to study for exams. She plans to
study history for 2 hours. She needs to spend at least 7
hours studying for calculus, but over 14 is too much.
She hopes to spend between 8 and 12 hours on physics.
Write and graph a system of inequalities to represent
the situation.
Answer:
x-variable y-variable Inequalities
calculus physics 7≤x≤14
8≤y≤12
x+y≤23
Step-by-step explanation:
During a bean bag toss, Abby threw the bean bag 2.2 meters. Which of the following values are not equivalent to 2.2
The values are not equivalent to 2.2 include
2.6 - 0.6
1.8 + 2.5
What is an expression?Expression simply refers to the mathematical statements which have at least two terms which are related by an operator and contain either numbers, variables, or both. Addition, subtraction, multiplication, and division are all possible mathematical operations. As an illustration, the expression x + y has the terms x and y with an addition operator between them.
In this case, 2.6 - 0.6 will be:
= 2.6 - 0.6
= 2.0
Also, 1.8 + 2.5 will be:
= 1.8 + 2.5
= 4.3
Therefore, they're not equivalent to 2.2
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Complete question
During a bean bag toss, Abby threw the bean bag 2.2 meters. Which of the following values are not equivalent to 2.2
1.2 + 1.0
2.6 - 0.6
0.9 + 1.3
1.8 + 2.5
Angles RTG and GTU are adjacent angles. If m∠RTG=5.8° and m∠GTU=113.6°, what is m∠RTU in degrees?
If m∠RTG = 5.8° and m∠GTU = 113.6°. Then the measure of the angle ∠RTU will be 119.4°.
What is an angle?The inclination is the separation seen between planes or vectors that meet. Degrees are another way to indicate the slope. For a full rotation, the angle is 360 °.
Adjacent angle - In math, two points are nearby in the event that they have a typical side and a typical vertex.
Angles RTG and GTU are adjacent angles. If m∠RTG = 5.8° and m∠GTU = 113.6°.
∠RTU = ∠RTG + ∠GTU
∠RTU = 5.8° + 113.6°
∠RTU = 119.4°
The measure of the angle ∠RTU will be 119.4°.
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Write an equation for the cubic polynomial function whose graph has zeroes at 2, 3, and 5. Write the polynomial function for the graph. f(x) = (x – 2)(x – 3)(x – 5) Simplify the right side. What is the equation? f(x) = x3 + 31x – 30 f(x) = x3 – 10x2 + 31x – 30 f(x) = x3 – 10x2 + 19x – 30 f(x) = x3 + 19x – 30 graph
The equation which represents a cubic polynomial function with zeroes 2, 3 and 5 is; f(x) = x³ - 10x² + 31x - 30.
What is the equation of the polynomial with zeroes 2, 3 and 5?It follows that if a polynomial function has zeroes, a, b and c; The factors of such polynomial function are; (x - a), (x - b) and (x - c).
Therefore, since the given polynomial function has zeroes, 2, 3 and 5, the polynomial function is;
f(x) = (x - 2) (x - 3) (x - 5)
Therefore, by simplification; we have;
f(x) = (x² - 5x + 6) (x - 5)
f(x) = x³ - 5x² + 6x - 5x² + 25x - 30.
f(x) = x³ - 10x² + 31x - 30.
Therefore, the required cubic polynomial function is; f(x) = x³ - 10x² + 31x - 30.
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What is the direct variation equation for the line passing through the points A(4,−2) and B(10,−5)
The direct variation equation for the line passing through the points A(4,−2) and B(10,−5) as given in the task content is; y = -2x.
What is the direct equation of the points given?It follows from the task content that the direct variation of equation of the two points given be determined.
On this note, since the relation is said to be a direct variation.
It follows that the ratio of inputs to output in both ordered pairs, k is same and can be determined as;
10/-5 = 4/-2 = k = -2.
Therefore, the required direct variation equation is written as;
y = -2x.
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a new car model is available with 5 choices of color, 3 choices of transmission and 4 types of interior. how many different variations of this model car are possible?
In 120 different variations of this model car are possible.
Define multiplication.One of the four fundamental mathematical operations, along with addition, subtraction, and division, is multiplication. Multiply in mathematics refers to the continual addition of sets of identical size. Let's use the ice creams as a multiplication example to help us comprehend. There are two such groupings, and each group has ice cream.
Calculating the sum of two numbers multiplied together is the process of multiplication. Simple tests in addition, subtraction, multiplication, and division will be given. 2. a noncount noun The process or occurrence of something of a certain kind multiplying occurs when their quantity or number increases.
Given,
There are five different ways to choose a car's color.
3 different car transmission selection options are available.
There are four different interior automobile selection options.
There are two different ways to pick a car's engine.
The potential number of car variations is thus:
Multiplying:
5 × 3 × 4× 2
120
In 120 different variations of this model car are possible.
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Given:-16=m-18;Prove:m=10
Answer:
m=2
Step-by-step explanation:
-16=m-18
-16+18=m
2=m
What is the value of 5.53?
The value of 3 in 5.53 is 3 hundredths.
What is place value?It is important to note that place values can be defined as the value that's represented by a digit based on the position that it takes. In mathematics, place value refers to the position or location of a digit in a number.
Each digit has a specific place in a number. The position of each digit will be expanded when we represent the number in general form. Those positions begin with a unit place, also known as one's position.
In this case, we want to know the value of 3 in 5.53. It should be noted that the first 5 is 5 ones, the second 5 is 5 tenths and the 3 is 3 hundredths.
Therefore, it's 3 hundredths.
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Complete question
What is the value of 3 in 5.53?
Find the equation of the linear function represented by the table below in slope-
intercept form.
The equation of the linear function represented by the table would be y = 4x - 1.
What is the slope-intercept form of the line?
When you know the slope of the line to be examined and the point given is also the y-intercept, you can use the slope-intercept formula
y = mx + c.
The y value of the y-intercept point is represented by c in the formula.
By using the given table,
for x = 0 , y = -1
so by using the slope-intercept form of the line, we can write
y = mx + c
-1 = m(0) + c
c = -1 ----------(I)
Then for x = 1, y = 3
again by using the slope-intercept form of the line, we can write
y = mx + c
3 = m(1) + (-1) -----from (I)
3 = m - 1
⇒ m = 3 + 1
⇒ m = 4 -----------(II)
Now by using (I) and (II), we can make a linear function by using the slope-intercept form of the line
y = 4x - 1
Hence, the equation of the linear function represented by the table would be y = 4x - 1.
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Which expression is the factored form of−4.5n+3?
Responses
A. −3(1.5n−1)
B. −1.5(3n+2)
C. −1.5(−3n+2)
D. −3(1.5n+1)
An expression which is factored form of given expression -4.5n+3 is −3(1.5n−1)
The correct answer is an option (A)
In this question we have been given an expression -4.5n + 3
We need to identify an expression which is factored form of given expression.
If we simplify the factored form then it must be a give expression.
consider ,A. −3(1.5n−1)
= -4.5n + 3
consider an expression B. −1.5(3n+2)
= -4.5n - 3
consider C. −1.5(−3n+2)
= 4.5n - 3
consider D. −3(1.5n+1)
= -4.5n - 3
Therefore, an expression which is factored form of given expression -4.5n+3 is −3(1.5n−1)
The correct answer is an option (A)
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An elevator ascends at a rate of 29.6 feet per second. If a building is 1,450 feet tall, about how long would it take for the elevator to travel from the ground floor to the roof?
A. 0.49 minutes
B. 0.82 minutes
C. 4.9 minutes
D. 8.2 minutes
the probability that a single radar station will detect an enemy plane is 0.65. (a) how many such stations are required to be 98% certain that an enemy plane flying over will be detected by at least one station? stations (b) if four stations are in use, what is the expected number of stations that will detect an enemy plane? (round your answer to one decimal place.)
If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.
What is probability?The area of mathematics known as probability deals with numerical representations of the likelihood that an event will occur or that a statement is true.An event's probability is a number between 0 and 1, where, roughly speaking, 0 denotes the event's impossibility and 1 denotes certainty.The likelihood that an event will occur increases with its probability.A straightforward illustration is tossing a fair (impartial) coin.The chance of both outcomes ("heads" and "tails") is equal because the coin is fair, "heads" is more likely than "tails," there are no other conceivable outcomes, and the likelihood of either outcome is half.acc to our question-,
(b) If seven stations are in use, what is the expected number of stations that will detect an enemy plane?The expected number of sucesses of a binomial variable is given by:If seven stations are in use, the expected number of stations that will detect an enemy plane is 4.55.learn more about probability click here:
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An isosceles right triangle has a hypotenuse length that can be modeled with the function . the combined length of the legs can be modeled with the function l(x) = 2x. which function, p(x), can be used to find the perimeter of the triangle?
The perimeter of the isosceles triangle will be P(x) = x√2 + 2x.
A polygon with three sides is known as a triangle. The angles of a triangle add up to form 180° and the sum of all sides of a triangle is known as the perimeter. In an isosceles triangle, the two sides are equal and their opposite angle too. In an isosceles triangle, the hypotenuse side of the triangle can be written as h(x) = x√2. The combined length comes out to be L(x) = 2x. Using this information the perimeter of the triangle comes out to be,
P(x) = h(x) + L(x).
P(x) = x√2 + 2x
Hence the perimeter of the triangle comes out to be P(x) = x√2 + 2x
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20 percent of all printers of a certain type are submitted for service under waranty. of these, 60 percent can be repaired and 40 percent must be replaced. if a company buys 10 such printers, what is the probability that exactly two will be replaced under warranty.
The probability that exactly two will be replaced under warrant is 0.1937.
Define probability.The possibility of an event occurring is determined by the probability formula. The ratio of positive outcomes to the total number of outcomes serves as the basis for calculating an event's probability. The probabilities are always between 0 and 1. A probability is a number that expresses the possibility or likelihood that a specific event will take place. Probabilities can be stated as proportions with a range of 0 to 1, or as percentages with a range of 0% to 100%.
Given,
W = Warranty
V = Replaced
P(W) = 20/100
P(W) = 0.20
P(U/W) = 0.40
P(W ∩ U)
= P(U/W) × P(W)
= 0.40 × 0.20
0.-08
P( exactly two will be replaced under warranty)
Using binomial distribution:
= P(X = 2)
= 10/2 (0.0.8)² (0.9)⁸
= 0.1937
The probability that exactly two will be replaced under warrant is 0.1937.
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new york city is the most expensive city in the united states for lodging. the mean hotel room rate is $204 per night. assume that the room rates are normally distributed with a standard deviation of $55. answers to 3 decimals. what is the probability of more than $225?
The probability of more than $225 is 0.35197.
Here we need to find the probability of more than $225.
We need to calculate the z-score associated with x = $225
Z(score) = 225 - 204 / 55
= 0.381818
z(score) = 0.38
For z = 0.38 the corresponding probability is P(z < 0.38) = 0.64803.
Here we have to find the values greater than this value:
P(z > 0.38) = 1 - P (z < 0.38)
P( z > 0.38) = 0.35197
So the probability that a hotel room costs 225 or more per night is P (x > 225) = 0.35197 and the percentage is 35.197%.
Therefore the probability is 0.35197.
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if Richard correctly answered 52 questions on an exam that had 65 questions , what percent did he get
The percentage that Richard get is 8%
How to determine the percentage he got?The statement can be interpreted as:
He answered 52 correctly from a total of 65 questions
From the above statement, we have the following parameters
Dividend = 52
Divisor = 65
The percentage is then calculated as
Percentage = Dividend/Divisor x 100%
Substitute the known values in the above equation
So, we have
Percentage = 52/65 x 100%
Evaluate the quotient
Percentage = 0.8x 100%
Evaluate the product
Percentage = 8%
Hence, the percentage is 8%
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Which of The following Best describes the transformation of Y=x^2 so that the resulting equation is as follows?
Y=(x-3)^2+4
By using the concept of translation, it can be inferred that
The graph of the equation is translated 3 units to the left and 4 units down
What is translation?
Translation is a transformation which changes the position of a figure without changing the shape and size of the figure.
The given equation is
[tex]y = (x +3)^2 + 4[/tex]
This means the parabola [tex]y = x^2[/tex] is first translated 3 units to the left and then translated 4 units up.
So the first option is correct.
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a group of 350 people includes 187 play the flute, 172 play the clarinet, and 47 both the flute and the clarinet. a person is selected at random. 1. what is the probability that he/she plays the clarinet but not the flute? a. 0.4213 b. 0.3571 c. 0.7812 d. 0.4587 e. 0.2743 2. what is the probability that he/she plays exactly one of these types of instruments? a. 0.7821 b. 0.2457 c. 0.5057 d. 0.7571 e. 0.3645 3. what is the probability that he/she plays at most one of these instruments? a. 0.7514 b. 0.9245 c. 0.5151 d. 0.2486 e. 0.8657
Using probability concepts, we calculated that the likelihood that the person plays the clarinet but not the flute is 0.2743.
What is conditional probability?The possibility of an event or outcome occurring based on the existence of a prior event or outcome is known as conditional probability. It is calculated by dividing the likelihood of the previous event by the likelihood of the subsequent, or contingent, event.
Here,
Finding people who can play the clarinet but not the flute is necessary. There are 172 people who can play the clarinet.
There are 47 people who can play both the clarinet and the flute.
As a result, 172-47=125 represents the number of people who can only play the clarinet and not the flute.
Probability(P),
P=( 125 / 350)
P=0.2743.
Therefore, the probability that a single person chosen at random can play clarinet but not flute is 0.2743.
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Question 5 of 10
Which of the following graphs represents a function that has a positive
leading coefficient? Check all that apply.
A. Graph A
B. Graph B
C. Graph C
D. Graph D
determine if l=these points have a right angle
2,3 6,3 2,7
The points (2, 3) (6, 3), and (2, 7) sides corresponds to length of 4 : 4 : 5 and do not form Pythagorean triple hence they do not form a right angle
How to determine if the points (2, 3) (6, 3), and (2, 7) form a right angleThe distance between the points is calculated and Pythagoras theorem is used to determine if the triple forms a right angle
let the points be
A (2, 3) B (6, 3), and C (2, 7)
using the equation
d = √{(x₁ - x₂)² + (y₁ - y₂)²}
AB = √{(2 - 6)² + (3 - 3)²} = 4
BC = √{(6 - 2)² + (3 - 7)²} = 5
CA = √{(2 - 2)² + (3 - 7)²} = 4
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Find the equation of a line parallel to 6x + y = -8 that passes through the point (7, 7).
The equation of a line parallel to 6x + y = -8 that passes through the point (7, 7) is y = -6x + 49
The equation of the parallel line is given
6x + y = -8
y = -8 -6x
y = -6x - 8
The slope intercept form is
y = mx + b
Where m is the slope of the line
b is the y intercept
Comparing the equation
Slope of the line m = -6
The slope of the all the parallel lines will be equal
Then line is passing through the point (7, 7)
The point slope form is
[tex]y-y_1=m(x-x_1)[/tex]
Substitute the values in the equation
y-7 = -6(x-7)
y - 7 = -6x + 42
y = -6x +42 +7
y = -6x + 49
Hence, the equation of a line parallel to 6x + y = -8 that passes through the point (7, 7) is y = -6x + 49
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suppose i randomly assign one group of angelenos to read a book about the history of the seattle supersonics, and the other to read a book about cheese. i then give them a quiz about basketball history (including recent events such as the los angeles lakers' twelfth championship). what is the independent variable in this experiment?
Using the concepts of probability, we got that book is independent variable in the experiment in which I randomly assign one group of angelenos to read a book about the history of the Seattle supersonics, and the other to read a book about cheese.
The independent variable is the condition that you actually change in an experiment. It is the variable you control. It is known as independent because its value does not depend on the value and is not affected by the state of any other variable in the experiment.
Hence, when i randomly assign one group of Angelenos to read a book about the history of the Seattle supersonics, and the other to read a book about cheese and then give them a quiz about basketball history (including recent events such as the Los Angeles Lakers then the independent variable in this experiment is the book given by me.
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https://brainly.com/question/11234923
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