The exponential decay formula is f(x) = abx, where b stands for the decay factor. The decay rate in the exponential decay function is specified as a decimal.
What does the exponential decay formula actually mean?At regular intervals, the sum steadily declines by a specified percentage. This decline in growth is calculated using the exponential decay formula. The general form of f(x) is f(x) = a (1 - r)x. Where, a = The starting point, decay rate = r, x = length of time.
Do we require a calculator for exponential growth and decay?When we need to make rapid calculations in a generic way, the exponential growth and decay calculator comes in handy. However, you should not use it frequently as it may slow down your ability to answer issues through math. To improve your comprehension, you must practice word problems with exponential growth and decay on paper.
The exponential decay formula is f(x) = abx, where b stands for the decay factor. The decay rate in the exponential decay function is specified as a decimal. A percentage is used to represent the degradation rate. Simply decreasing the percent and dividing it by 100 yields the decimal equivalent. The decay factor b = 1-r can therefore be calculated.
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carla’s hair grows 1/2 inch a month 3 months after carla got her last haircut, carla’s hair was 14 inches long. which  equation shows the relationship between the length of Carla’shair and how many months have passed since Carla’s haircut 
The equation that shows the relationship between the length of Carla’shair and how many months have passed since Carla’s haircut will be hair Length - 14 = 1/3(months - 3)
How to calculate the equation?An equation is the statement that illustrates the variables given. In this case, two or more components are taken into consideration to describe the scenario.
In this case, Carla’s hair grows 1/2 inch a month 3 months after carla got her last haircut, carla’s hair was 14 inches long. The equation that illustrates this is Carla’s haircut will be hair Length - 14 = 1/3(months - 3). Therefore, the correct option is D.
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What are 2 examples of geometric sequence?
Two examples of geometric sequence are {2, 6, 18, 54, 162, 486, 1458, ...} and {1, 2, 4, 8, 16, 32, 64, 128, 256, …}.
In mathematics, a geometric sequence or geometric progression refers to a sequence of non-zero numbers where the ratio between consecutive terms is constant. In such a sequence, each term (after the initial term) is determined by multiplying the previous one by a fixed, non-zero number called the common ratio. An example of geometric sequence is {2, 6, 18, 54, 162, 486, 1458, ..} where each term is 3 times the previous term i.e., the common ratio is 3. Another example is {1, 2, 4, 8, 16, 32, 64, 128, 256, .. } where each term is 2 times the previous term i.e., the common ratio is 2.
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Find the dimensions of a rectangle with perimeter 76 m whose area is as large as possible. (If both values are the same number, enter it into both blanks.)
The dimensions of a rectangle are 19m.
Here we have to find the dimensions of a rectangle.
Data given:
Perimeter = 76m
The formula for the perimeter of the rectangle:
perimeter = 2( length + breadth)
So,
76 = 2 ( l+b)
l + b = 38
l = 38 -b
The formula for the area of the rectangle:
Area = length × breadth
A =( 38-b)×b
= 38b - b²
At maximum point:
dA/ dw = 38 - 2b
38 - 2b = 0
b = 19
Therefore the dimension is 19m.
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Determine the measure of the interior angle at vertex E.
The measure of the interior angle at vertex E is; B: 90
What is the sum of interior angles of the Polygon?The formula for the sum of interior angles of an irregular polygon is;
Sum of interior angles = (n − 2) × 180°
where;
'n' is the number of sides of a polygon.
Thus;
Sum of interior angles of an irregular pentagon with 5 sides is;
Sum = (5 - 2) * 180
Sum = 540°
Thus;
3(4x) + 2(3x) = 540
12x + 6x = 540
18x = 540
x = 540/18
x = 30°
Thus, angle at vertex E = 3(30) = 90°
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Mr. Brooks spent one over two of an hour making gingerbread cookies and one over fourths of an hour breaking the cookies. She then spent 45 minutes decorating the cookie. How many total minutes did she spend on her gingerbread cookies
90 minutes
Step-by-step explanation:
1/2 an hour = 30 minutes
1/4 an hour = 15 minutes
45+15=60
60+30=90
Where is the blue point on the number line?
Answer:
-20
Step-by-step explanation:
We see the number line is counting by 5's so let's count down by 5's until we get to the blue dot!
5
0
-5
-10
-15
-20!
We moved down 3 points from -5 on the number line!
Answer:-20
Step-by-step explanation:
57 students choose to attend one of three after school activities: football, tennis or running.
There are 26 boys.
24 students choose football, of which 15 are girls.
18 students choose tennis.
3 girls choose running.
A student is selected at random.
What is the probability this student chose running?
Give your answer in its simplest form.
The probability that the randomly selected student will chose running can be written as 12/57.
How can the the probability this student chose running be calculated?The concept used is the probability which is the likelyhood of an event to take place.
Total number of students was given as 57
Total number of boys that was given was 26
Total number of girls can be written as 57-26=31`
Number of Girls that chose football can be written as 15
Number of boys that chose football can be wriitten as 9
Number of students that chose Tennis can be written as 18
Now, number of students that chose running will be;
Number of students that chose running = 57 - (24 + 18) = 15
Therefopre, probability that a randomly selected student chose running = 15/57
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Which equation is perpendicular to the line represented by y = 6x +10 and passes through the ordered pair (5, -8)?
1.y+8= -1/6(x - 5)
2.y-5= (1/6x+8)
3.y-(-8)= -6(x - 5)
4.y+8 6(x - 5)
Answer:
option 1
Step-by-step explanation:
the equation of a line in slope- intercept form is
y = mx + c ( m is the slope and c the y- intercept )
y = 6x + 10 ← is in slope- intercept form
with slope m = 6
given a line with slope m then the slope of a line perpendicular to it is
[tex]m_{perpendicular}[/tex] = - [tex]\frac{1}{m}[/tex] = - [tex]\frac{1}{6}[/tex]
the equation of a line in point- slope form is
y - b = m(x - a)
where m is the slope and (a, b ) a point on the line
here m = - [tex]\frac{1}{6}[/tex] and (a, b ) = (5, - 8 ) , then
y - (- 8) = - [tex]\frac{1}{6}[/tex] (x - 5 ) , that is
y + 8 = - [tex]\frac{1}{6}[/tex] (x - 5) ← equation of perpendicular line
8.22. Let S be the set of all polynomials of degree at most 3. An element s(x) of S can then be expressed as
s(x) = ax3 + bx2 + cx + d, where a, b, c, d ? R. A relation R is defined on S by p(x) R q(x) if p(x) and
q(x) have a real root in common. (For example, p = (x ? 1)^2 and q = x^2 ? 1 have the root 1 in common so
that p R q.) Determine which of the properties reflexive, symmetric, and transitive are possessed by R.
R possess Symmetric property.
Let S be the set of all polynomials of degree at most 3.
s(x) = ax³ + bx² + cx + d
we know that polynomial is a mathematical expression of one or more algebraic terms each of which consist of a constant multiplied by one or more variables raised to a non negative power.
The reflexive property states that every element of the set is related to itself.
The symmetric property is defined as if one element in a set is related to the other, then we can say that the second element is also related to the first element.
The transitive property states that if a, b, c are three quantities, and if a is related to b and b is related to c then a and c are related to each other.
So here we observe that R will posses symmetric property.
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the managers of a company are worried about the morale of their employees. in order to determine if a problem in this area exists, they decide to evaluate the attitudes of their employees with a standardized test. they select the fortunato test of job satisfaction which has a known standard deviation of 24 points. they should sample employees if they want to estimate the mean score of the employees within 5 points with 90% confidence.
90% confidence interval is 82.11 < μ < 93.89
"Information available from the question"
The complete question is this:
The managers of a company are worried about the morale of their employees. In order to determine whether a problem in this area exists, they decide to evaluate the attitudes of their employees with a standardized test. They select the Fortunato test of job satisfaction, which has a known standard deviation of 24 points.
Due to financial limitations, the managers decide to take a sample of 45 employees. This yields a mean score of 88 points. What is the 90% confidence interval?
Now, According to the question:
We have :
The confidence level = 0.90
The significance level, [tex]\alpha[/tex] = 0.10
The sample mean, x = 88
The population standard deviation, σ = 24
The sample size, n = 45
Critical value of z using the z - distribution table:
z(critical) = [tex]z_\alpha[/tex] /2
= [tex]z_0_._0_5[/tex]
= ±1.645
90% confidence interval:
μ = x ± z. σ/[tex]\sqrt{n}[/tex]
μ = 88 ± 1.645 x 24 / [tex]\sqrt{45}[/tex]
μ = 88 ± 5.89
82.11 < μ < 93.89
Hence, 90% confidence interval is 82.11 < μ < 93.89
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Write an equation to represent the relationship. Then solve the equation.
Six times a number plus 4 is the same as the number minus 11.
Answer:
-3
Step-by-step explanation:
6x + 4 = x - 11
6x - x = -11 - 4
5x = -15
5/5 x = -15/5
x = -3
help meeeeeeeeeeeeee pleaseeeeeeeeeeeeeeeeeeeeeeeeee
Answer: 3
Step-by-step explanation:
A young boy is growing at a rate of 3.5 cm per month. He is currently 90 cm
Answer:
it's 25.7
Step-by-step explanation:
you just divide the 90 by 3.5
Carol purchased 4 gallons of milk. Which is the BEST estimate of the liters of milk she purchased? (1 liter = 0.264 gallons) Responses
Answer: the best estimate could be 20 liters
Step-by-step explanation: it is 20 liters because 1 liter is = 264 gallons so we round up the number and then use regular estimate methods.
Answer:
15 liters
Step-by-step explanation:
4 gal / .264 gal / liter = 15.15 liters = ~ 15 liters
40 minus 8 divided by -4 + 6 x -7
Answer: 40 minus 8 divided by -4 + 6 x -7 = 0
Step-by-step explanation: i literally just used a calculator -_-
The volume of a packing box is 5 - X cubic feet. The width of X feet and the length is X -2 feet. The height is given by the expression 5-X/ X(X -2). Which of these values of X make the expression undefined.
The values of x that make the expression undefined are 0 and 2
How to determine the undefined height value of xFrom the question, we have the following parameters that can be used in our computation:
Volume = 5 - x
Width = x - 2
Height = 5 - x/x(x -2)
Introduce brackets to the height expression to differentiate between the numerator and the denominator
So, we have
Height = (5 - x)/x(x -2)
The question implies that we calculate the domain
Set the denominator to 0
This gives
x(x - 2) = 0
So, we have
x = 0 or x - 2 = 0
Solve for x
x = 0 or x = 2
This means that the undefined height value of x are 0 and 2
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PLEASE HURRY WILL GIVE BRAINLIEST
Answer:
1.d
2.a
3.e
4.g
5.f
6.c
7.b
Step-by-step explanation:
did it already
I need help pls I’m stuck?
Answer:
-33/35
Step-by-step explanation:
turn mixed fraction into an improper fraction
-2 1/5 = -11/5
times both fractions
Reconsider the data from Medicine and Science in Sports and Exercise described in Exercise 8-32. The sample size was seven and the sample mean and sample standard devi ation were 315 watts and 16 watts, respectively. (a) Is there evidence that leg strength exceeds 300 watts at significance level 0.05? Find the P-value.
Using the t-distribution, it is found that the 95% confidence interval for the mean peak power after training is (301.2, 328.8).
We have the standard deviation for the sample, thus, the t-distribution is used.
The sample mean is 315.
The sample standard deviation is s = 16.
The sample size is n = 7.
The interval is:
mean ± t s/√n
To build the interval, we need to find the critical value, which looking at the t-table for a 95% confidence interval with 8 - 1 = 7 df is t = 2.4469.
Then, replacing the values:
315 - 2.4469 16/√8 = 301.2
315 + 2.4469 16/√8 = 328.8
The 95% confidence interval for the mean peak power after training is (301.2, 328.8).
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I need help with this please help me
Answer: 45
Step-by-step explanation:
find the absolute maximum and absolute minimum values of f on the given interval. f(x) = xe−x2/32, [−3, 8]
The absolute maxima and minima of the function f(x) = xe^-(x²/32) along an interval [-3, 8] are (4, 4/e^1/2) ≅ (4, 2.43) and (-3, -3/e^9/32) ≅ (-3, -2.26) respectively
Absolute Maxima and Minima over an IntervalAn absolute maximum point is a point where the function obtains its greatest possible value. Similarly, an absolute minimum point is a point where the function obtains its least possible value.
Absolute minimum and maximum values of the function in the entire domain are the highest and lowest value of the function wherever it is defined. A function can have both maximum and minimum values, either one of them or neither of them. For example, a straight line extends up to infinity in both directions so it neither has a maximum value nor minimum value.
In this question given,
f(x) = xe^-(x²/32) along an interval [-3, 8]
The absolute maxima = (x, f(x)) = (4, 4/e^1/2) ≅ (4, 2.43)
The absolute minima = (x, f(x)) = (-3, -3/e^9/32) ≅ (-3, -2.26)
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Jangles Co. earned $1.80 per share. Assuming a closing price of $40, the PE ratio is: (Round to the nearest whole number.)
Multiple Choice
7
22
72
20
The PE ratio will be equal to $22. The correct option is B.
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 Jangles Co. earned $1.80 per share. Assuming a closing price of $40. The PE ratio will be calculated as,
Earning per share = $1.80
The price of the share = $40
PE ratio = Price of the share ÷ Earning per share
PE ratio = $40/$1.8-
PE ratio = $22.
Therefore, the PE ratio will be equal to $22. The correct option is B.
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If the function f(x)= 2x – 3 and g(x) = 3/2x + 1 then which of the following is a true statement?
f(0) > g(0)
f(8) = g(8)
f(2) = g(2)
g(4) < f(4)
If the function f(x)= 2x – 3 and g(x) = 3/2x + 1 then g(4) < f(4) is a true statement?
What is a function?A function is a relationship or expression involving one or more variables. It has a set of input and outputs. Each input has only one output. The function is the description of how the inputs relate to the output.
A function can also be said to be a relation between a set of inputs and a set of permissible outputs with the property that each input is related to exactly one output. Let A & B be any two non-empty sets; mapping from A to B will be a function only when every element in set A has one end, only one image in set B.
Functions are generally represented as f(x).
Let , f(x) = [tex]x^{3\\}[/tex].
It is said as f of x is equal to x cube.
Functions can also be represented by g(), t(),… etc.
For g(4) < f(4);
g(4) = 3/2(4) + 1
g(4) = 3/9
f(4) = 2(4) - 3
f(4) = 8 - 3
f(4) = 5
Therefore; g(4) < f(4)
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A library is holding a special five-day event honoring successful local writers. One writer will be invited to be a guest speaker for each night from Monday through Friday, and no writer will be asked to participate twice. The writers have each written books in only one of four different genres—science fiction, mystery, historical fiction, and non-fiction. A, J, and X are all science fiction writers. B and Y are both mystery writers. C and Z are both historical fiction writers. L is a non-fiction writer. The following conditions apply without exception:
At least one writer from each genre will be invited to speak on at least one night.
No two authors from the same genre will be invited to speak on the following night.
If C is invited to speak, then X is invited to speak on the following night.
If Y is invited to speak, then neither C nor A are invited to speak.
If X and J are both invited to speak, then neither will speak on either the first or last night.
If L and B are both invited to speak, then neither will speak on either the first or last night.
If L is invited to speak on Friday, then on what days MUST a science fiction writer be invited? Possible Answers:Monday and Wednesday
Monday and Tuesday
Tuesday and Thursday
Only Wednesday
Monday and Thursday
As per the concept of probability, If L is invited to speak on Friday, then the science fiction writer be invited on Monday and Wednesday
Probability:
In statistics, probability refers the possible and favorable outcome of the particular event.
Given,
Here we need to find if L is invited to speak on Friday, then on what days MUST a science fiction writer be invited.
Here we know that the writers of the same genre may not speak on consecutive nights.
And here we have the only five slots to fill, two of the three science fiction writers must speak on Monday and Friday
So, If both X and J are invited, then at least one will be forced to speak on Monday or Friday, which is not allowed.
Then, modification of the rules is actually just a bit of a red herring, since all of the answer choices except for the one regarding science fiction writers is true regardless.
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Solve the proportion. What is n?
Answer:
n=20
Step-by-step explanation:
(9^x-4)(9^3x+2)=9^10
Answer: x=3
Step-by-step explanation:
[tex]\displaystyle\\(9^{x-4})(9^{3x+2})=9^{10}\\\\9^{x-4+3x+2}=9^{10}\\\\9^{4x-2}=9^{10}\\\\4x-2=10\\\\4x-2+2=10+2\\\\4x=12[/tex]
Divide both parts of the equation by 4:
[tex]x=3[/tex]
A farmer uses a lot of fertilizer to grow his crops. The farmer's manager thinks fertilizer products from distributor A contain more of the nitrogen that his plants need than distributor B's fertilizer does. He takes two independent samples of four batches of fertilizer from each distributor and measures the amount of nitrogen in each batch. Fertilizer from distributor A contained 23 pounds per batch and fertilizer from distributor B contained 18 pounds per batch. Suppose the population standard deviation for distributor A and distributor B is four pounds per batch and five pounds per batch, respectively. Assume the distribution of nitrogen in fertilizer is normally distributed. Let μ1 and μ2 represent the average amount of nitrogen per batch for fertilizer's A and B, respectively. Which of the following is the approptiate conclusion at the 5% significance level?a. Reject H 0; we can conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor Bb. Reject H 0; we cannot conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B.c.Fail to reject H 0; we can conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor Bd. Fail to reject H 0; we cannot conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B
The appropriate conclusion at the 5% significance level is b. Reject H0; we cannot conclude that the mean amount of fertilizer per batch for distributor A is greater than the amount of fertilizer per batch for distributor B.
How to calculate test statistic?[tex]\bar{x_1}[/tex] = pounds per batch distributor A = 23
[tex]\bar{x_2}[/tex] = pounds per batch distributor B = 18
[tex]\sigma_{1}[/tex] = standard deviation distributor A = 4
[tex]\sigma_{2}[/tex] = standard deviation distributor B = 5
n = sample size = 4
α = significance level = 5% = 0.05
Test statistic is using z test to find the z value from two population, after that we can search p-value and then comparing the p-value with significance level.
If p-value is lower than significance level, the null hypothesis (H0) is accepted. But, if p-value is higher than significance level, the H0 is rejected.
Calculate test statistic by this formula,
Z = [tex]\frac{\bar{x_1}-\bar{x_2}}{\sqrt{\frac{\sigma^2_1 + \sigma^2_2}{n}}}[/tex]
= [tex]\frac{23-18}{\sqrt{\frac{4^2 + 5^2}{4}}}[/tex]
= [tex]\frac{5}{\sqrt{\frac{16 + 25}{4}}}[/tex]
= 1.56
Using z table for 1.56, we get 0.9406. Since is right tailed test. So, p value is
p-value = 1 - 0.9406
= 0.0594
Then, p-value is 0.0594 is higher than significance level 0.05. So, H0 is rejected.
Thus, the conclusion is reject H0, we cannot conclude the mean amount of fertilizer per batch distributor A is greater than distributor B.
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A fence is to be built to enclose a rectangular area of 260 square feet. The fence along three sides is to be made of material that costs 3 dollars per foot, and the material for the fourth side costs 15 dollars per foot. Find the dimensions of the enclosure that is most economical to construct.
The dimensions of the enclosure that is most economical to construct will be 3 feet and 86.67 feet.
What are the maxima and minima of a function?For the maximum value of the function if f''(x) < 0 and for the minimum value of the function if f''(x) > 0.
The maximum and minimum value of the function is at f'(x) = 0.
A wall is to be worked to encase a rectangular area of 260 square feet. The wall along three sides is to be made of material that costs 3 bucks for every foot, and the material for the fourth side costs 15 bucks for each foot.
LW = 260
L = 260 / W
Then the minimum cost is given as,
y = 3L + 3W + 3L + 15W
y = 18W + 6L
y = 18W + 6(260 / W)
y = 18W + 1560 / W
Differentiate with respect to W and put it zero, then we have
y' = 0
18 - 1560/W² = 0
W² = 1560 / 18
W = 86.67 feet
Then the length is given as,
L = 260 / 86.67
L = 3 feet
The dimensions of the enclosure that is most economical to construct will be 3 feet and 86.67 feet.
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____________ is a test of a single population and is to determine if there is an association between two characteristics of that population. A) The chi-square test for independence B) Pearson product moment test C) The chi-square test for homogeneity D) Goodness-of-fit test E) Welch’s t test
The option a "The chi-square test for independence" is correct.
In the given question we have to find, a test of a single population and is to determine if there is an association between two characteristics of that population.
The given options are
A) The chi-square test for independence
B) Pearson product moment test
C) The chi-square test for homogeneity
D) Goodness-of-fit test
E) Welch’s t test
As we know that;
When a categorical variable has more than two levels, a chi-square test can be performed. A one proportion z test may be performed if there are precisely two categories. There must be no overlap between those category variable's levels. To put it another way, every situation must fall into exactly one group.
So, the chi-square test for independence is correct answer.
Option (B) and (E) are two-sample tests.
(C) involves two attributes.
(D) Doesn't check association.
Hence all these are incorrect.
So the option a "The chi-square test for independence" is correct.
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What is 150% of 32?
Answer: 48
Step-by-step explanation:
[tex]\displaystyle\\\frac{32(150\%)}{100\%} =\\\\\frac{4800}{100}= \\\\48[/tex]
Answer:
48
Step-by-step explanation:
150% = 150/100 = 1.5
Then:
32 * 1.5 = 48
