The growth factor for the annual rate of change +100% is 2.
A quantity must vary by a specific percentage each time period in order for growth or decay to be exponential.
With the function displayed to the right, you may represent exponential growth or decay.
A(x) = a( 1 + r)ˣ
Where A is the amount after x time periods, a is the initial amount, x is the number of time periods, and r is the rate of change.
Now, we have the annual rate of change as:
r = + 100% = + 1
From the function A(x) = a( 1 + r)ˣ , the corresponding factor is 1 + r.
So, let B = 1 + r
B = 1 + r
B = 1 + (+1)
B = 2
Now, the value of B is greater than 1 therefore, the corresponding growth factor is 2.
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Scores on an exam follow an approximately normal distribution with a mean of 76. 4 and a standard deviation of 6. 1 points. What is the minimum score you would need to be in the top 2%?.
If scores on an exam follow an approximately normal distribution with a mean of 76.4 and a standard deviation of 6.1 points, then the minimum score you would need to be in the top 2% is equal to 88.929.
A problem of this type in mathematics can be characterized as a normal distribution problem. We can use the z-score to solve it by using the formula;
Z = x - μ / σ
In this formula the standard score is represented by Z, the observed value is represented by x, the mean is represented by μ, and the standard deviation is represented by σ.
The p-value can be used to determine the z-score with the help of a standard table.
As we have to find the minimum score to be in the top 2%, p-value = 0.02
The z-score that is found to correspond with this p-value of 0.02 in the standard table is 2.054
Therefore,
2.054 = x - 76.4 ÷ 6.1
2.054 × 6.1 = x - 76.4
12.529 = x - 76.4
12.529 + 76.4 = x
x = 88.929
Hence 88.929 is calculated to be the lowest score required to be in the top 2%.
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Use the graph to answer the following question.
If ∆ PQR is translated left 2 and down 6, what would be the coordinates of R' ?
The coordinate of the point R' after translation will be (0, - 4).
What is a transformation of a point?A spatial transformation is each mapping of feature space to itself and it maintains some spatial correlation between figures.
If ∆PQR is translated left 2 and down 6. Then the translation rule is given as,
(x', y') → (x - 2, y - 6)
From the graph, the coordinate of point R will be at (2, 2). Then the coordinate of the point R' after translation will be
(x', y') → (2 - 2, 2 - 6)
(x', y') → (0, - 4)
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what is 10,000 less of 84.562 and what is 10,000 more? how would i show my work?
Answer: 10,000 less of 84.562 = −
9915.438 | 10000 more of 84.562 = 10084.562
Step-by-step explanation:
10000 less:
Just subtract 10000 from 84.562.
10000 More:
Just add 10000 to 84.562
The 3rd term of (a-b)4 is
The third term of the expansion is 6a^2b^2
How to determine the third term of the expansion?The binomial term is given as
(a - b)^4
The r-th term of the expansion is calculated using
r-th term = C(n, r - 1) * x^(n - r + 1) * y^(r - 1)
So, we have
3rd term = C(4, 3 - 1) * (a)^(4 - 3 + 1) * (-b)^(3-1)
Evaluate the sum and the difference
3rd term = C(4, 2) * (a)^2 * (-b)^2
Evaluate the exponents
3rd term = C(4, 2) * a^2b^2
Evaluate the combination expression
3rd term = 6 * a^2b^2
Evaluate the product
3rd term = 6a^2b^2
Hence, the third term of the expansion is 6a^2b^2
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Determine whether the statement is true or false. if it is false, rewrite it as a true statement. data at the ordinal level are quantitative only.
According to the given statement;
The statement is False. Data at the ordinal level can be qualitative or quantitative.
What is Ordinal level?Ordinal data is a form of categorical statistical data where the distances between the categories are unknown and the variables have naturally occurring, ordered categories.
Ordinal is the second of four levels of measurement in a hierarchy that also includes nominal , ordinal , interval , and ratio. The degrees of measurement show how well the data were recorded.
In contrast to nominal and ordinal variables, which are categorical, interval and ratio variables are quantitative.
According to the given data,
The statement is False.
Data at the ordinal level can be qualitative or quantitative.
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Domain:
Range:
Increasing:
Decreasing:
Positive:
Negative:
The answers are:
Domain: [-7, ∞)
Range: [-3, ∞)
Increasing: [-7, -2] U [4, ∞]
Decreasing: [-2, 4]
Positive: [-5, 2] U [6, ∞)
Negative: [-7, -5] U [2, 6]
How to find the domain and the range of the function?The domain is the set of the possible inputs of the function, by looking at the graph we can see that the graph starts at x = -7 and keeps going to the right, so the domain is:
D: [-7, ∞)
The range is the set of the outputs, in this case, the minimum value is y = -3 and then it keeps going up.
R: [-3, ∞)
Now, the graph increases when it goes upwards, in this case the graph increases in:
[-7, -2] U [4, ∞]
And decreases on:[-2, 4]
And it is negative on the intervals where the function is below the horizontal axis: [-7, -5] U [2, 6]
And it is positive on the intervals: [-5, 2] U [6, ∞)
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Write an equation for the parabola with the vertex (1, 2) and passes through the point (3, 14).
The equation for the parabola with the vertex (1, 2) and passes through the point (3, 14) is y - 2 = 3 · (x - 1)².
How to derive the equation of the parabola whose vertex is known along with another point
Mathematically speaking, parabolas are represented by second order polynomials, whose vertex form is shown below:
y - k = C · (x - h)²
Where:
(h, k) - Coordinates of the vertex.C - Vertex constant.If we know that (h, k) = (1, 2) and (x, y) = (3, 14), then the vertex constant is:
14 - 2 = C · (3 - 1)²
12 = C · 2²
12 = 4 · C
C = 3
Then, the equation for the parabola is y - 2 = 3 · (x - 1)².
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An arrow is modeled on the coordinate plane as shown. What is the area of the arrow? Round your answer to the nearest tenth, if necessary.
y
(0,3)
(0, 1)
O
(4,4)
(4.5,3)
(4.5,1)
(4,0)
(8, 2)
square units:
X
l o o k i t u p o n g a u t h m a t h c o p y u r q e s t i o n t h e r e
Step-by-step explanation: You're welcome
SOMEONE PLEASE HELP 100 points
Answer:
A) No solution
B) No solution
Step-by-step explanation:
[tex]A)[/tex] [tex]\mathrm {If}\:|u|\: < \:a,\:a > 0\:\mathrm{then}\:-a\: < \:u\: < \:a[/tex] (Which in this case leads to no solution because c cannot be less than 0 logically)
[tex]B)[/tex] [tex]\mathrm {If}\:|u|\: < \:a,\:a > 0\:\mathrm{then}\:-a\: < \:u\: < \:a[/tex] (Whether you change the </> sign or not, c cannot be any less than 0 or it will lead to no solution.)
Answer:
All real numbers im pretty sure
Step-by-step explanation:
PRACTICAL APPLICATIONS: DO YOU ADD, SUBTRACT, MULTIPLY, OR DIVIDE
36. ELECTRICAL TRADES: From a roll of no. 12 wire an electrician cut the following lengths:
9, 13, 42, and 12 feet. How many feet of wire did he use?
Using addition, Total length of wire used by the electrician is 76 feet.
What would you say about addition?Through addition, items are combined and counted as a single large group. The process of adding two or more numbers together is known as addition in mathematics. The terms addends and total both refer to the numbers that are added and the result of the operation.
What does addition serve as?One of the four fundamental operations of mathematics is addition, which is typically denoted by the plus sign (+). The other three are subtraction, multiplication, and division. The entire amount or sum of the two whole numbers is obtained by adding them.
We will use simple addition here,
Total length used by electrician is
(9 + 13 + 42 + 12) feet.
= 76 feet
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Which function represents the equation of the line?
Answer:
A linear function is of the form f(x)= mx+b
Which is a graph of Y= -3X +2
Answer:
either the top right or bottom left
Step-by-step explanation:
Hey there!
In order to find out which graph the equation is representing, we must first know what each part is and means
-3x: This is the slope of the line, meaning how much it moves by
Slope is always rise over run: -3/1
This means, it moves down 3 and to the right 1
2: This is the y-intercept of the line
The y-intercept of the line shows where the line intersects the y-axis
In this case, it is 2
With this information, we can tell that it is either the top right or bottom left
(*The image is a little blurry and unclear. All I know is that it is either top right or bottom left*)
~Sorry for the inconvenience~
r(x)=-x-7 when x=-2,0, and 5
The output values of x = -2, 0, and 5 in the given function are -5, -7 and -12 respectively.
What are the output values when x = -2, 0, and 5?Given the data in the question;
r(x) = -x - 7r(-2) = ?r(0) = ?r(5) = ?When x = -2. replace all the occurrence of x with -2 in the function and simplify to determine the output value.
r(x) = -x - 7
r(-2) = -(-2) - 7
r(-2) = 2 - 7
r(-2) = -5
When x = 0. replace all the occurrence of x with 0 in the function and simplify to determine the output value.
r(x) = -x - 7
r(0) = -(0) - 7
r(0) = 0 - 7
r(0) = -7
When x = 5. replace all the occurrence of x with 5 in the function and simplify to determine the output value.
r(x) = -x - 7
r(5) = -(5) - 7
r(5) = -5 - 7
r(5) = -12
Therefore the output values of x = -2, 0, and 5 in the given function are -5, -7 and -12 respectively.
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46. Minimum weekly salary is $185. Rate
commission is 6.5%. Weekly sales are
of
$3,790.
well, we know the commission is 6.5% from all sales, and when the sales are $3790, well, what's 6.5% of that?
[tex]\begin{array}{|c|ll} \cline{1-1} \textit{a\% of b}\\ \cline{1-1} \\ \left( \cfrac{a}{100} \right)\cdot b \\\\ \cline{1-1} \end{array}~\hspace{5em}\stackrel{\textit{6.5\% of 3790}}{\left( \cfrac{6.5}{100} \right)3790}\implies 246.35[/tex]
n + 30 + 2n - 10 + 70 =180
Answer:
n=30
Step-by-step explanation:
n+30+2n-10+70=180
We move all terms to the left:
n+30+2n-10+70-(180)=0
We add all the numbers together, and all the variables
3n-90=0
We move all terms containing n to the left, all other terms to the right
3n=90
n=90/3
n=30
A garden center is recording the heights of its available trees. Which of the following displays could be used to represent the data, and why?
A. Bar chart, because tree height is numerical
B. Box plot, because tree height is numerical
C. Histogram, because tree height is categorical
D. Stem-and-leaf-plot, because tree height is categorical
When the garden is recording the heights of its available trees. the display that can be used to represent the data by a Bar chart, because tree height is numerical. The correct option is A.
What is a bar chart?
A bar chart or bar graph uses rectangular bars with heights or lengths proportional to the values they represent to show categorical data. A bar plot could be either vertical or horizontal. A vertical bar graph is sometimes known as a column chart.
A bar chart is used to show the distribution of data points or to compare metrics across different subgroups of your data. We may see how different groups compare to one another and which groupings are most common or prevalent using a bar graph.
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Answer:
Step-by-step explanation:
i think its A., bart chart
7) Estimate the following roots to the nearest integer without using a calculator.
V18,
Estimation of [tex]\sqrt{18}[/tex] to nearest integer is 4.
Integer For every two same numbers multiplied inside the square root, one number can be taken out of the square root.
For every three same numbers multiplied inside the cube root, one number can be taken out of the cube root. The same procedure can be followed for fourth root and more.
Perfect squares are numbers that are the products of integers by themselves. In other words, when an integer is multiplied by itself, the resulting product is termed as a perfect square of the given number. For example, 36 is a perfect square because it is the product of 6 by itself.
[tex]\sqrt{18}[/tex] is not a perfect square.
nearest to 18 , 16 and 25 are the perfect squares
So, [tex]\sqrt{18}[/tex] lies in between [tex]\sqrt{16}[/tex] and [tex]\sqrt{25}[/tex] .
[tex]\sqrt{18}[/tex] lies in between 4 and 5.
Nearest integer is 4.
So , estimation of [tex]\sqrt{18}[/tex] to nearest integer is 4.
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Suppose the function f(x)=0.15 x represents the number of U.S. dollars equivalent to x Chinese yuan and the function g(y)=14.07 y represents the number of Mexican pesos equivalent to y U.S. dollars.
a. Write a composite function that represents the number of Mexican pesos equivalent to x Chinese yuan.
A composite function that represents the number of Mexican pesos equivalent to x Chinese yuan. h(x) = ( [tex]\frac{x}{14.07}[/tex] )/ 0.15
What is the composite function that represents the number of Mexican pesos equivalent to x Chinese yuan ?x yuan to y dollars = f(x)
f(x) = 0.15 x
y dollars to x yuan
y= 0.15 x
x = y / 0.15
y dollars to x pesos =g(y)
g(y) =14.07 y
x pesos to y dollars
x = 14.07 y
y = x / 14.07
Substituting the result of second into first,
pesos → dollars → yuan
Lets call this function, h(x) = converts x pesos into y yuan.
h(x) = ( [tex]\frac{x}{14.07}[/tex] )/ 0.15
= 0.474 x
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Using the division properties, how can the expression 2/5÷(−5/5) be simplified? Drag and drop your answers into the boxes to complete the statement.
The required solution of the given expression is -2/5 as a simplified form.
What is expression?
An expression is a set of terms combined using the operations +, – , x or ÷. An expression is a number, a variable, or a combination of numbers and variables and operation symbols. An expression is in simplest form when no terms can be combined
Given:
The given expression is
2/5÷(−5/5)
According to given question we have
The expression is
2/5÷(−5/5)
=2/5÷(-1)
=2*(-1)/5
=-2/5
Therefore, the required solution of the given expression is -2/5 as a simplified form.
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5. square EFGH
Ay
O
H(1,-3)
G(3,-1)
X
F(5,-3)
E(3,-5)
The area of the square is found as -8 unit².
What exactly is the distance formula?We get a list of distance formulas in coordinate geometry that can be used to find the distance between two points, the distance between such a point and a line, this same distances between two parallel lines, the distances between two parallel planes, and so on.The distance between two points, for example, is the length of a line segment linking them.Distance between two coordinates (x₁, y₁) and (x₂, y₂) are-
d = √[(x₁ - x₂)² + (y₁ - y₂)²]
Consider two given coordinates;
(x₁, y₁) = H(1,-3) and
(x₂, y₂) = G(3,-1)
Put the values in the given distance formula;
d = √[(1 - 3)² + (-3 + 1)²]
d = √[(-2)² + (-2)²]
On solving,
d = 2√2 unit
Thus, one side of the square is found as 2√2 unit.
The area of the square is given as;
Area = side²
Area = (2√2)²
Area = 8 unit²
Therefore, the area of the square given by the coordinates if found to be 8 unit².
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The complete question is-
The coordinates of square are given, find the area of the square-
H(1,-3)
G(3,-1)
F(5,-3)
E(3,-5)
reverse mean higher GCSE questions.
Pete has seven Shetland ponies. They have a mean height of 116cm.
Pete buys an eighth pony. The height of this pony is 128cm.
Find the mean height of all eight ponies.
Answer:
dat it
116cm times 7=812
128cm times 8=1024
1024-812=212cm
If a polygon has 5 sides, then it is a pentagon.
Write the inverse of the conditional statement and determine whether it is true or false.
If a polygon does not have 5 sides, then it is not a pentagon.; FALSE
If a polygon is a pentagon, then it has 5 sides.: TRUE
If a polygon is a pentagon, then it has 5 sides; FALSE
If a polygon does not have 5 sides, then it is not a pentagon.: TRUE
Answer:
Step-by-step explanation:
If a polygon does not have 5 sides, then it is not a pentagon.: TRUE
Round this number to the
nearest hundredth.
1.2983
Answer: 1.3
Step-by-step explanation:
Answer:
1.3
Step-by-step explanation:
9 is the hundredth and we round up with 8 so we’d round up 1 and we get 1.3
Evaluate the determinant of each matrix.
[4 -1 8 2]
For the matrix:
[tex]\left[\begin{array}{ccc}4&-1\\8&2\\\end{array}\right][/tex]
The determinant is equal to 16.
How to find the determinant of the given matrix?Remember that for a general 2 by 2 matrix:
[tex]\left[\begin{array}{ccc}a_1&b_1\\a_2&b_2\\\end{array}\right][/tex]
The determinant is given by the simple formula:
D = a₁*b₂ - b₁*a₂
This is the only thing we need to use in this problem, we will use this formula to find the determinant of the given 2 by 2 matrix.
In this case we have the matrix:
[tex]\left[\begin{array}{ccc}4&-1\\8&2\\\end{array}\right][/tex]
Then we can just use the given formula for the determinant, we will get
D = 4*2 - (-1)*8
We just need to solve that expression, we will get:
D = 8 - (-8) = 8 + 8 = 16
We can see that the determinant of the given matrix is equal to 16.
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5⋅f(1)+5⋅g(9)=5, dot, f, left parenthesis, 1, right parenthesis, plus, 5, dot, g, left parenthesis, 9, right parenthesis, equals A coordinate plane. The x- and y-axes both scale by one. There is a graphed function, y equals f of x, which is made up of line segments. A line segment connects negative ten, negative six to negative eight, negative six. A line segment connects negative eight, negative six to negative seven, negative seven. A line segment connects negative seven, negative seven to negative six, negative seven. A line segment connects negative six, negative seven to negative five, negative six. A line segment connects negative fix, negative six to negative three, negative six. A line segment connects negative three, negative six to negative two, negative five. A line segment connects negative two, negative five to negative one, negative seven. A line segment connects negative one, negative seven to zero, negative five. A line segment connects zero, negative five to two, negative five. A line segment connects two, negative five to three, negative three. A line segment connects three, negative three to four, negative three. A line segment connects four, negative three to five, negative two. A line segment connects five, negative two to six, negative three. A line segment connects six, negative three to seven, negative two. A line segment connects seven, negative two to eight, negative two. A line segment connects eight, negative two to ten, negative four. There is another graphed function, y equals g of x, which is also made up line segments. A line segment connects negative ten, one to negative nine, two. A line segment connects negative ten, zero to negative nine, zero. A line segment connects negative nine, zero to negative eight, two. A line segment connects negative eight, two to negative seven, three. A line segment connects negative seven, three to negative six, three. A line segment connects negative six, three to negative five, two. A line segment connects negative five, two to negative four, ze
I don't know I really needed help on this one
GSE Geometry
Unit 3
Check For Understanding!!
Parallel Lines cut by a Transversal
1. Given and m/8 = 119, find the measures of all the
numbered angles in the figure.
m<1=_
m<2=_
m<3=_
m<4 = _
m<5 =_
m<6 =_
m<7=_
The measure of all the angles are :
∠1 = 119°, ∠2 = 61°, ∠3 = 61° , ∠4 = 119° , ∠5 = 119° , ∠6 = 61° and ∠7 = 61°
According to the question we have been given two parallel lines which is cut by a transversal line. There total 8 angles and given is the measure of
∠8 = 119°.
We need to find the measure of all other 7 angles.
Note that when two parallel lines are cut by a transversal then
i) corresponding angles are equal that is
∠1 = ∠5, ∠2 = ∠6, ∠3 = ∠7, and ∠4 = ∠8
ii) alternate interior angles are equal that is
∠3 = ∠6, and ∠4 = ∠5
iii) alternate exterior angles are equal that is
∠1 = ∠8, and ∠2 = ∠7
iv) Consecutive interior angle sum is 180°
∠4 + ∠6 = 180°, and ∠3 + ∠5 = 180°.
So according to the rules given above the measure of all the angles are:
∠1 = 119°, ∠2 = 61°, ∠3 = 61° , ∠4 = 119° , ∠5 = 119° , ∠6 = 61° and ∠7 = 61°
Hence measure of all the angles is given above
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pls pls help whoever gets it right gets a crown
Answer:
m=-1
Step-by-step explanation:
20m+5-2m=-13
18m=-18
m=-1
Answer:
[tex] \sf \: m=−1[/tex]
Step-by-step explanation:
5(4m+1)-2m=-13
Step 1: Simplify both sides of the equation.
5(4m+1)−2m=−13
(5)(4m)+(5)(1)+−2m=−13(Distribute)
20m+5+−2m=−13
(20m+−2m)+(5)=−13(Combine Like Terms)
18m+5=−13
18m+5=−13
Step 2: Subtract 5 from both sides.
18m+5−5=−13−5
18m=−18
Step 3: Divide both sides by 18.
18m/18 = −18/18
m=−1
Riya is applying mulch to her garden. she applies it at a rate of 250{,}000\text{ cm}^3250,000 cm 3 250, comma, 000, start text, space, c, m, end text, cubed of mulch for every \text{ m}^2 m 2 start text, space, m, end text, squared of garden space.
The area of her garden where Riya is applying Mulch is 0.25m³.
To understand this answer, we will analyze the information in the question statement. So, we know that Riya is applying Mulch to her Garden. The application of Mulch is at the rate of 250 000 cm^3 for every m^2. Now to find the rate for every m^3, we will use the basic conversion formula for converting cm to m:
we know that,
100 cm = 1m
Now we can write this formula as follows,
1 cm = 1 / 100 m
1 cm = 0.01 m
We will use the same relation for the values given to us in the question:
250, 000 cm^3 = 250, 000 x 1 cm x 1cm x 1cm
1 cm^3 = 1 cm x 1cm x 1cm
250, 000 cm^3 = 250, 000 x 0.1 x 0.1 x 0.1
From, 1 cm = 0.01 m
250, 000 cm^3 = 250, 000 x 0.000001
250, 000 cm^3 = 0.25 m^3
Hence Riya is applying at 0.25 m^3 per m^2 (meter square).
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Psychologists use an exponential model of the learning process, f(t)= c(1-e -kt) , where c is the total number of tasks to be learned, k is the rate of learning, t is time, and f(t) is the number of tasks learned.
c. Open-Ended Does this function seem to describe your own learning rate? If not, how could you adapt it to reflect your learning rate?
We will know 8 complete names after 2 days and 20 complete names after 8 days. Whether or not this function represents your learning rate will vary from person to person.
Here, we are given an exponential function: f(t)= c{1- e^(-kt)}
where
f(t) = number of tasks learned.
c = total number of tasks to be learned
k = rate of learning
t = time
Now, when we move to a new school, number of names we need to learn ⇒ c = 25
learning rate for new tasks = 20%
⇒ k = 0.2
and time = 2 days
⇒ t = 2
Substituting these values in the function we get-
f(2) = 25{1- [tex]e^{-0.2 * 2}[/tex]}
= 25{1- [tex]e^{-0.4}[/tex]} [tex]e^{-0.4}[/tex]
= 0.67
Thus, f(2) = 25( 1-0.67 )
f(2) = 25(0.33)
f(2) = 8.25
Thus, we will be able to learn 8 complete names in 2 days.
If t = 8f(8) = 25{1- [tex]e^{-0.2*8}[/tex]}
= 25{1- [tex]e^{-1.6}[/tex]}
= 25(1- 0.20)
= 25(0.80)
= 20
Thus, we will be able to learn 20 complete names in 8 days. Whether of not this function describes your own learning rate will vary from person to person. Some people are fast learners whereas others take their time. A fast learner will have a higher learning rate whereas a slow learner will have a lower learning rate as depicted by k. You can change the value of k to adjust the function as per your learning abilities.
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Your question was incomplete, check for full content below-
Psychologists use an exponential model of the learning process, f(t)= c(1-e -kt) , where c is the total number of tasks to be learned, k is the rate of learning, t is time, and f(t) is the number of tasks learned.
a. Suppose you move to a new school, and you want to learn the names of 25 classmates in your homeroom. If your learning rate for new tasks is 20 % per day, how many complete names will you know after 2 days?
b. After 8 days?
c. Does this function seem to describe your own learning rate? If not, how could you adapt it to reflect your learning rate?
which answer choice correctly represents the quotient of 738/13 you will be reported if wrong
Answer:
Quotient = 60
Remainder = 3
Full calculation: 783 = 13 × 60 + 3
Answer:
Step-by-step explanation:
Remainder = 3
Quotient = 60
Full calculation: 13 × 60 + 3=783