The limit in question is
[tex]$$\lim_{n\to \infty} \frac{1^3 + 2^3 + 3^3 + \dots + n^3}{n^4}$$[/tex]
This limit can be interpreted as the Riemann sum of a function defined on the interval [0, 16]. To calculate the sum, we need to first find the function that is being approximated. To do this, we can use the fact that the numerator of the limit can be rewritten as a single summation:
[tex]$$\sum_{k=1}^n k^3 = \frac{n^2 (n+1)^2}{4}$$[/tex]
This means that the function we are approximating is [tex]$f(x) = \frac{x^2 (x+1)^2}{4}$[/tex]
Now, to calculate the Riemann sum, we need to divide the interval [0, 16] into $n$ equal subintervals. The width of each subinterval is given by [tex]$\Delta x = \frac{16}{n}$\\The Riemann sum is given by $$\sum_{i=1}^n f\left(x_i\right) \Delta x = \sum_{i=1}^n \frac{\left(x_i\right)^2 \left(x_i+1\right)^2}{4} \cdot \frac{16}{n}$$[/tex]
where [tex]$x_i = \frac{16i}{n}$[/tex]
Plugging this into the limit, we get
[tex]$$\lim_{n\to \infty} \frac{1^3 + 2^3 + 3^3 + \dots + n^3}{n^4}\\ = \lim_{n\to \infty} \frac{\sum_{i=1}^n \frac{\left(x_i\right)^2 \left(x_i+1\right)^2}{4} \cdot \frac{16}{n}}{n^4} = \\frac{16}{4} \lim_{n\to \infty} \frac{\sum_{i=1}^n \frac{\left(x_i\right)^2 \left(x_i+1\right)^2}{n}}{n^3}$$[/tex]
Finally, we can take the limit of the above expression to get
[tex]$$\lim_{n\to \infty} \frac{1^3 + 2^3 + 3^3 + \dots + n^3}{n^4} = \frac{16}{4} \cdot \frac{f(16)}{16^3} = \frac{1}{4}$$[/tex]
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Two communications companies offer calling plans. With Company X, it costs 30c to connect and then 4c for each minute. With Company Y, it costs 15c to connect and then 3c for each minute. Write and simplify an expression that represents how much more Company X charges, in cents, for n minutes.
The expression that represents how much more Company X charges, in cents, for n minutes is 15 + n
How to write and simplify an expression that represents how much more Company X charges?An algebraic expression is a mathematical phrase that can contain numbers, variables, and operations. It can be used to represent a specific value or a range of values e.g. 2x+3.
For Company X:
Since it costs 30c to connect and then 4c for each minute, we can write the expression as:
30 + 4n
For Company Y:
Since it costs 15c to connect and then 3c for each minute, we can write the expression as:
15 + 3n
An expression that represents how much more Company X charges, in cents, for n minutes is:
(30 + 4n) - (15 + 3n) = 30 - 15 + 4n -3n = 15 + n
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You flip a coin 16 times and get heads 7 times. Based on this experiment, what is the probability of flipping a coin and getting heads?
The probability of flipping a coin and getting heads is 7/16
How to determine the probability of flipping a coin and getting heads?from the question, we have the following parameters that can be used in our computation:
Number of flips = 16
Number of heads = 7
The probability is then calculated as
P = Head/Flips
substitute the known values in the above equation, so, we have the following representation
P = 7/16
Hence, the probability is 7/16
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At swimming practice, Coach Warren always sets aside 75% of the total time for laps. At practice yesterday, students spent 45 minutes swimming laps.
Answer: The session was 1 hour long.
75% of an hour is 45 minutes.
let be the linear transformation that first rotates points clockwise through ( radians) and then reflects points through the line . find the standard matrix for .
The formula for the standard matrix for the linear transformation is as follows: beginbmatrix cosfracpi2 & -sinfracpi2 & 0 sinfracpi2 & & cosfracpi2 & 0 & & -1 endbmatrix
The following linear transformation rotates the points by[tex]$fracpi$[/tex]radians in the direction of rotation before reflecting the points through the line. We begin by examining the rotational component of the transformation to determine the standard matrix. A matrix beginbmatrix cosfracpi2 & -sinfracpi2 & 0 sinfracpi2 & cosfracpi2 & 0 0 & 0 & 1 endbmatrixan be used to describe the rotation by radians. We can use the matrix beginbmatrix 1 & 0 & 0 0 & -1 & 0 0 & 0 & 1 endbmatrixfor the reflection component. We obtain the final standard matrix for the linear transformation by multiplying these two matrices. $$beginbmatrix cosfracpi2 & -sinfracpi2 & 0 sinfracpi2 & cosfracpi2 & 0 0.
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The complete question is
let be the linear transformation that first rotates points clockwise through ( radians) and then reflects points through the line . find the standard matrix for the standard matrix of the transformation can be found by first computing the matrix of the rotation and then the matrix of the reflection.
Suppose that y varies directly with x, and y=4 when x=20. (a) Write a direct variation equation that relates x and y. Equation: (b) Find y when x = 9. y =
Answer:
Step-by-step explanation:
y = kx
a. Because x and y vary directly, the equation is in the form y = kx.
FOR YOUR UNDERSTANDING WAY
The ratio of y to x would be 4/20 = 1/5. So the equation would be y=1/5x
A bakery makes small batches of bread daily. Each day the bakery records the amount of flour used and the number of loaves of bread made. All loaves…
The linear equation of the line would be y = 7/5x. The number of loaves of bread from 85 pounds of flour would be 7/5(85) = 119 loaves.
What is linear equation and its slope?Each term in a linear equation has an exponent of 1, and when this algebraic equation is graphed, it always produces a straight line. It is called a "linear equation" for this reason.
Slope calculation:
This line's slope would be the proportional constant.
This point (35, 49) is extremely near to the lines that would result in the linear constant 49/35 = 7/5 , the line's equation is y = (7/5)x .
Using 85 pounds of flour, Calculate the loaves of bread that may be made (7/5) * 85 = 119 loaves.
Therefore, the equation is y = (7/5)x that is used to forecast the number of loaves that could be created from 85 pounds of flour, and the result was 119 loaves.
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The complete question is:
A bakery makes small batches of bread daily. Each day, the bakery records the amount of flour used the number of loaves of bread made. All loaves are approximately the same size. The table and graph show the bakery’s data for five days.
write an equation that can be used to model the number of loaves of breast, y that can be made from x pounds flour
Use an equation to predict the number of loaves that can be made from 85 pounds of flour show your work or explain your answer
How do you use the definition of continuity and the properties of limits to show that the function h(t)=(2t-3t²)/(1+t³) is continuous at the given number a=1?
The function h(t) = (2t - 3t²)/(1 + t³) is continuous at x = 1, as the limit exists and is equals to the numeric value of the function.
What is the continuity concept?A function f(x) is continuous at x = a if it is defined at x = a, and the lateral limits are equal to the numeric value of the function, that is:
[tex]\lim_{x \rightarrow a^-} f(x) = \lim_{x \rightarrow a^+} f(x) = f(a)[/tex]
The function is defined as follows:
h(t) = (2t - 3t²)/(1 + t³)
At t = 1, the first step is trying to obtain the limit as the numeric value, hence:
h(1) = (2 - 3)/(1 + 1) = -1/2.
As the limit does not result in an undetermined result, the limit exists, is equals to the numeric value of the function, the function is continuous at x = 1.
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Solve the following system of equations for z and for y: System of Equations: Value of z Value of y y = 9+ 3z y = 51 - 3z
The value of y and z in the equation are 31 and 7 respectively.
How to solve system of equation?System of equation can be solved using different method such as elimination method, substitution method and graphical method.
Therefore, let's solve the system of equation using substitution method as follows:
y = 9 + 3z
y = 51 - 3z
Let's substitute the value of y in equation(ii)
51 - 3z = 9 + 3z
51 - 9 = 3z + 3z
42 = 6z
divide both sides of the equation by 6
z = 42 / 6
z = 7
Therefore, let's find the value of y using equation(i)
y = 9 + 3z
y = 9 + 3(7)
y = 9 + 21
y = 31
Therefore,
y = 31 and z = 7
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Graph a right triangle with the two points forming the hypotenuse. Using the sides, find the distance between the two points in simplest radical form. (3, 2) and (-5, -7)
The distance between the two points in simplest radical form (3, 2) and (-5, -7) is [tex]\sqrt{40}[/tex]
Find the distance?We must determine the hypotenuse's length in order to answer the question because the hypotenuse's endpoints have been provided.
We must determine the hypotenuse's length in order to answer the question because the hypotenuse's endpoints have been provided.
The formula, Distance =, determines the distance between the two positions (x1, y1) (x2, y2).
The formula, Distance =, determines the distance between the two positions (x1, y1) (x2, y2).
Distance = [tex]\sqrt{(x2 - x1)(y2 - y1)}[/tex]
Distance between the two positions (3, 2) and (--5, --7) equals
Distance =root of ( -5 - 3,-7 - 2)
root of (-8 * -5) = [tex]\sqrt{40}[/tex].
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Can anyone help me? It's hard for me to solve this problem
*Debt payments of $2,100 and $1,950 are due in six months and nine months, respectively. What single payment is required to settle both debts in one month? Assume a simple interest rate of 6.30% p.a. and use one month from now as the focal date.
The required single payment is required to settle both debts in one month is $4071.26.
What is Simple interest?Simple interest is the amount of interest charged on a specific pripal amount at a specific interest rate. Compound interest, on the other hand, is the interest that is computed using both the principal and the interest that has accumulated over the preceding period.
According to question:We have,
Interest of 12 month = 6.30%
For one month = 6.30/12
= 0.525% per month
Total debt = $2,100 + $1,950
Total debt = $4050
Interest of one month = 0.525% of $4050
= $21.26
Net debt = $4050 + $21.26.
Thus, required single payment is required to settle both debts in one month is $4071.26.
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Erin is going to sew a jacket and a skirt.She needs 2 3/4 yards of material for the jacket and 1 1/2 yards of material for the skirt. All together how many yards of material does Erin need.
All together the number of yards of material Erin will need to sew jacket and skirt is 4 1/4 yards
How to find the number of yards Erin will requireFrom the question the following can be gotten
She needs 2 3/4 yards of material for the jacket and 1 1/2 yards of material for the skirt.
The total number of yards she will require is calculated using the addition operation
The total number of yards
Addition of fractions
= 2 3/4 + 1 1/2
= 17 / 4
= 4 1/4
The total number of yard required is 4 1/4
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What is the area of this
polygon?
Enter your answer in the box.
units
The polygon's 39 unit squared surface area.
How is a polygon calculated?A polygon with "n" sides has a total of 180 degrees in its inner angles (n-2) n-sided polygons have [n(n-3)]/2 diagonals as their number of sides. For a regular polygon with n sides, the interior angle measure is [(n-2)180°]/n. A regular polygon with n sides has exterior angles that are 360°/n in length.
Using the equation Area = (number of sides x length of one side x apothem)/2, one may determine the area of a regular polygon.
To create the polygonal shape shown in the attachment, sketch it.
It is therefore possible to separate the polygon into a rectangle and a triangle.
The polygon's 39 unit squared surface area.
The complete question is,
What size polygon does this one have? Put your response in the provided box. points M, V, E, D, and R are located within a 5-sided polygon of unit 2 on a coordinate plane. Points M is at (negative 5, 2), V is at (negative 2, 3), E is at (3, 3), D is at (3, negative 3), and R is at (negative 5, 2). (negative 2, negative 3).
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A 150-pound person uses 6.6 calories per minute when walking at a speed of 4 mph. How long must a person walk at this speed to use at least 160 calories?
A person must walk for at least
(Round up to the nearest minute.)
minutes in order to use at least 160 calories
If a 150-pound person uses 6.6 calories per minute when walking at a speed of 4 mph. The time a person walk at this speed to use at least 160 calories is: 24minutes.
How to find the time?Calories that was used = 6.6 calories per minute
Total calories = 160 calories
So,
Let x represent the minutes to walk
6.6x=160
Divide both side by 6.6x
x=160/6.6
x= 24.24 minutes
x = 24 minutes ( Approximately)
Therefore we can conclude that the time a person walk at this speed to use at least 160 calories is: 24minutes.
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Find the value of X.
X=?
The required value of x is 3
What is trapezium?A convex quadrilateral having exactly one set of opposite sides that are parallel to one another is called a trapezium. When drawn on a piece of paper, the trapezium is a two-dimensional shape that resembles a table. A quadrilateral is a polygon in Euclidean geometry that has four sides and four vertices.
According to question:Using the mid-segment theorem of trapezium.
The line segment that joins the midpoints of a trapezoid's two non-parallel sides is known as its mid segment. The average length of the bases makes up a trapezoid mid segment, which is parallel to the trapezoid's set of parallel lines.
[(3x + 1) + 15]/2 = 12.5
(3x + 1) + 15 = 25
3x + 1 = 10
3x = 9
x = 3
Thus, required value of x is 3.
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There are 13 purple flowers. There are nine pink flowers. How many more purple flowers are there?
Answer:4
Step-by-step explanation:
13-9=4
if you are subtracting 9 add more than the number. for example, 17-9=8
8 is one more than the number 7 in 17.
Suppose we know that set A has n subsets, S1, S2,..., Sa If set B consists of the elements of A and one more ele- ment so |B| = |A| + 1 show that B must have 2n subsets.
B must have 2n subsets since it has two corresponding subsets for each subset of A series (S1, S2,..., Sa), one of which contains the extra element and the other of which does not.
Set B's size is |B| = |A| + 1 since it includes all of the components of set A plus an additional element. There must be two equivalent subsets in set B for each subset of A (S1, S2,..., Sa), one of which must contain the extra element and the other of which must not. This extra element must be present in at least one subset. B must therefore have a total of 2n subsets. For instance, if set A has the three subsets S1, S2, and S3, then set B will have the same three subsets plus S1 plus the extra element, S2 plus the extra element, and S3 plus the extra element, for a total of six subsets.
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PLS HELP ALG 1 DUE TMR
Answer:
y=x^3 - 10x + 16
Step-by-step explanation:
A balloon was originally filled to a volume of
4
,
400
4,4004, comma, 400 cubic centimeters. Air inside the balloon leaks out over time.
If a balloon was originally filled to a volume of 4,400 cubic centimeters. The inequality expression of the volume of the balloon is: V < 4400.
How to find the inequality expression?Volume = 4,400 cubic centimeters
Since the air inside the balloon leaks out over time which implies that the air inside the balloon will reduce.
So the expression is:
V < 4400
Where:
V = Volume
< = less than
Therefore the inequality expression is V < 4400.
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The complete question is:
A balloon was originally filled to a volume of 4,400 cubic centimeters. Air inside the balloon leaks out over time.
Write an inequality that describes V, the volume of the balloon in cubic centimeters as air leaks out.
Enter your inequality without a thousands separator.
Attend to Precision Denise needs 4 pounds of soil
to fill a flowerpot. She has a bag with 2 1/3 pounds of soil
and a box with 1 3/4 pounds of soil. Does Denise have enough
soil to fill the flowerpot? Explain.
Yes, she does have the enough soil as she needs 4 pounds of soil.She have [tex]7 \frac{5}{12}[/tex] pound of soil.
What is Fraction?
An element of a whole is a fraction. The number is represented mathematically as a quotient, where the numerator and denominator are split. Both are integers in a simple fraction. A fraction appears in the numerator or denominator of a complex fraction. The numerator of a proper fraction is less than the denominator.
What is BODMAS?
The abbreviation BODMAS was created to aid kids in remembering the right order to carry out mathematical operations when solving problems. B-Brackets, O-Orders (powers/indices or roots), D-Division, M-Multiplication, A-Addition, and S-Subtraction are all abbreviated as Bodmas.
Given that;
She has
⇒ [tex]2\frac{1}{3} + 1\frac{3}{4}[/tex]
⇒ 17/3 + 7/4
⇒ [tex]\frac{17*4 + 7 *3}{12}[/tex]
⇒ 68 + 21 /12
⇒ 89/12
⇒ [tex]7 \frac{5}{12}[/tex]
So, She has [tex]7 \frac{5}{12}[/tex] pound of soil and she need 4 pounds only.
Hence, Denise have enough soil to fill the flower plot.
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NO LINKS!!
45. Express 3log₅x + log₅y - 2log₅w as a single logarithm
46. Find the missing value: log21 -2log7 + log28 = log__
47. Expand ln[(x - 4)(2x+5)²]
Answer:
[tex]\textsf{45.} \quad \log_5\left(\dfrac{x^3y}{w^2}\right)[/tex]
[tex]\textsf{46.} \quad \log 12[/tex]
[tex]\textsf{47.} \quad \ln(x-4)+2\ln(2x+5)[/tex]
Step-by-step explanation:
[tex]\boxed{\begin{minipage}{8cm}\underline{Log laws}\\\\Product law:\quad\:$\log_axy=\log_ax + \log_ay$\\\\Quotient law:\;\;\;$\log_a \left(\dfrac{x}{y}\right)=\log_ax - \log_ay$\\\\Power law:\quad\;\;\;\:$\log_ax^n=n\log_ax$\\\end{minipage}}[/tex]
Question 45[tex]\begin{aligned}3\log_5x + \log_5y - 2\log_5w&=\log_5x^3 + \log_5y - \log_5w^2\\&=\log_5\left(x^3 \cdot y\right)- \log_5w^2\\&=\log_5\left(\dfrac{x^3y}{w^2}\right)\end{aligned}[/tex]
Question 46[tex]\begin{aligned}\log21 - 2 \log7 + \log28 &=\log21 - \log7^2 + \log28\\&=\log21 - \log49 + \log28\\&=\log\left(\dfrac{21}{49}\right) + \log28\\&=\log\left(\dfrac{3}{7} \cdot 28\right)\\&=\log\left(\dfrac{84}{7}\right)\\&=\log12\end{aligned}[/tex]
Question 47[tex]\begin{aligned}\ln \left[(x - 4)(2x+5)^2\right]&=\ln(x-4)+\ln(2x+5)^2\\&=\ln(x-4)+2\ln(2x+5)\\\end{aligned}[/tex]
find the position vector of a point r which divides the line joining two points p and q whose position vectors are externally in the ratio 1 : 2. also, show that p is the mid point of the line segment rq
So, the position vector of a point r is (1-1/3)p + (1/3)q.
The position vector of a point can be found using the following formula:
r = (1-λ)p + λq
where λ is the scalar value that represents the ratio in which the point divides the line segment.
In this case, the ratio of the point dividing the line segment is 1:2. So, λ = 1/3.
Substituting the values of p and q, we get:
r = (1-1/3)p + (1/3)q
To show that point p is the midpoint of the line segment rq, we can use the following property of midpoints:
The position vector of the midpoint of a line segment with endpoints p and q is given by (p+q)/2.
In this case, the position vector of point p is (1-1/3)p + (1/3)q, and the position vector of point q is (2/3)p + (2-2/3)q = (2/3)p + (4/3)q
So, the midpoint of the line segment rq is given by:
((1-1/3)p + (1/3)q + (2/3)p + (4/3)q)/2 = (3/3)p + (5/3)q
which is (p+q)/2, so p is the midpoint of the line segment rq
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which of the statements best describes a bar graph? data are presented with bars that are proportional in height to the measured value. continuous data are presented as dots that are placed at specific x- and y-coordinates. categories of data are presented with sections of a circle that are proportional in size to the measured value. data points are scattered across the graph at specific x- and y-coordinates.
The tatment which describe best a bar graph is data are presented with bars that are proportional in height to the measured value.
Let us know more about a bar graph .
The pictorial representation of grouped data, in the form of vertical or horizontal rectangular bars, where the lengths of the bars are equivalent to the measure of data, are known as bar graphs or bar charts.
The bars drawn are of uniform width, and the variable quantity is represented on one of the axes. Also, the measure of the variable is depicted on the other axes. The heights or the lengths of the bars denote the value of the variable, and these graphs are also used to compare certain quantities. The frequency distribution tables can be easily represented using bar charts which simplify the calculations and understanding of data.
The three major attributes of bar graphs are:
1) The bar graph helps to compare the different sets of data among different groups easily.
2) It shows the relationship using two axes, in which the categories are on one axis and the discrete values are on the other axis.
3) The graph shows the major changes in data over time.The bar graphs can be vertical or horizontal. The primary feature of any bar graph is its length or height. If the length of the bar graph is more, then the values are greater than any given data.
Bar graph normally show categorical and numeric variables arranged in class intervals. They consist of an axis and a series of labelled horizontal or vertical bars. The bars represent frequencies of distinctive values of a variable or commonly the distinct values themselves. The number of values on the x-axis of a bar graph or the y-axis of a column graph is called the scale.
The types of bar charts are as follows:
Vertical bar chart
Horizontal bar chart
Even though the graph can be plotted using horizontally or vertically, the most usual type of bar graph used is the vertical bar graph. The orientation of the x-axis and y-axis are changed depending on the type of vertical and horizontal bar chart. Apart from the vertical and horizontal bar graph, the two different types of bar charts are:
Grouped Bar Graph
Stacked Bar Graph
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The statment which describe best a bar graph is data are presented with bars that are proportional in height to the measured value.
Let us know more about a bar graph .
The pictorial representation of grouped data, in the form of vertical or horizontal rectangular bars, where the lengths of the bars are equivalent to the measure of data, are known as bar graphs or bar charts.
The bars drawn are of uniform width, and the variable quantity is represented on one of the axes. Also, the measure of the variable is depicted on the other axes. The heights or the lengths of the bars denote the value of the variable, and these graphs are also used to compare certain quantities. The frequency distribution tables can be easily represented using bar charts which simplify the calculations and understanding of data.
The three major attributes of bar graphs are:
1) The bar graph helps to compare the different sets of data among different groups easily.
2) It shows the relationship using two axes, in which the categories are on one axis and the discrete values are on the other axis.
3) The graph shows the major changes in data over time.The bar graphs can be vertical or horizontal. The primary feature of any bar graph is its length or height. If the length of the bar graph is more, then the values are greater than any given data.
Bar graph normally show categorical and numeric variables arranged in class intervals. They consist of an axis and a series of labelled horizontal or vertical bars. The bars represent frequencies of distinctive values of a variable or commonly the distinct values themselves. The number of values on the x-axis of a bar graph or the y-axis of a column graph is called the scale.
The types of bar charts are as follows:
Vertical bar chart
Horizontal bar chart
Even though the graph can be plotted using horizontally or vertically, the most usual type of bar graph used is the vertical bar graph. The orientation of the x-axis and y-axis are changed depending on the type of vertical and horizontal bar chart. Apart from the vertical and horizontal bar graph, the two different types of bar charts are:
Grouped Bar Graph
Stacked Bar Graph
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Integrate the following question
∫x/(x^2+1)^3
The integration of the expression [x / (x² + 1)³] will be - 1 / 4(x² + 1)² + c.
What is integration?Integration is a way of finding the total by adding or summing the components. It's a reversal of differentiation, in which we break down functions into pieces. This approach is used to calculate the total on a large scale.
I = ∫ [x / (x² + 1)³] dx
Let x² + 1 = t, then x dx = dt / 2. Then we have
I = ∫ [1 / 2(t)³] dt
I = (1/2) ∫ [1 /(t)³] dt
I = (1/2) [-1 /2t²] + c
I = - (1/4) (1/(x² + 1)²) + c
I = - 1 / 4(x² + 1)² + c
The integration of the expression [x / (x² + 1)³] will be - 1 / 4(x² + 1)² + c.
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Suzy orders supplies for quick stop gas station and she needs to order additional lids for the disposable soda cups. She knew that the top of the cup had a diameter of 3 inches. Which size lid does she need to purchase from the soda cups?
If Suzy orders supplies for quick stop gas station and she needs to order additional lids for the disposable soda cups. The size that lid need to purchase from the soda cups is 9.42in.
How to find the circumference ?Using this formula to find the size that lid need to purchase from the soda cups
C= πd
Where:
C = circumference = ?
π =constant pi = 3.14
d = diameter = 3
Let plug in the formula
C = 3.14 × 3
C = 9.42 in
Therefore we can conclude that the size that lid need to purchase from the soda cups is 9.42in.
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Please answer this question for me
Answer:
not sure about this ......
The population of a city in 2015 was 36,000. The population is increasing at 15% per year.
Part A:
Write an exponential equation that models the population, P (z), where a represents the number of years since 2015.
Part B
based on your equation what was the population in 202 show how you obtained your answer
Answer: I am Not that good In Maths But here you go
Step-by-step explanation:
Part A:
The population of a city in 2015 is 36,000 and it is increasing at 15% per year. We can model this using an exponential equation of the form:
P(z) = P0 * (1 + r)^z
Where:
P(z) is the population after z years
P0 is the initial population in 2015 (36,000)
r is the rate of growth (0.15)
z is the number of years since 2015
So the exponential equation that models the population is:
P(z) = 36,000 * (1 + 0.15)^z
Part B:
To find the population in 2020, we would substitute z = 5 (2020 - 2015) into the equation:
P(5) = 36,000 * (1 + 0.15)^5
P(5) = 36,000 * 1.15^5
Calculating this gives us a population of approximately 63,746 in 2020.
To obtain this answer, we used the exponential equation that models the population, P(z), where a represents the number of years since 2015, with the given information that population in 2015 was 36,000 and it's increasing at 15% per year and substitute the value of 5 for z.
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The equation of y = f(x) and the equation of the new function g(x) under the transformation applied is Y=-3(x-1)² -1 or Y=-3x+6x-4.
What is the quadratic function opens upward or downward?
There is a simple way to identify whether the graph of a quadratic function opens upward or downward: if the leading coefficient is bigger than zero, the parabola expands upward; otherwise, the parabola opens downhill.
Y = -(3x²+2) reflects it about the x-axis. All positive y’s now become negative.
It used to be an upward-opening parabola with y-intercept = 2. Now, it’s a downward opening parabola with y-intercept = -2
Move it to the right by 2 means replace x by x-2
Move it up by 1 means replacing the y-intercept of -2 by -1, just add 1 to the y-intercept
Y=-3(x-1)² -1 or Y=-3x+6x-4
Hence, The equation of y = f(x) and the equation of the new function g(x) under the transformation applied is Y=-3(x-1)² -1 or Y=-3x+6x-4.
To learn more about parabolas opens visit,
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Draw a polygon with the given conditions in a coordinate plane 19. A rectangle with a perimeter of 18units
According to the information, to create a rectangle polygon with a perimeter of 18 units, we must put sides of 3 units and bases of 6 units.
What is a polygon?A polygon is a term that refers to a plane geometric figure composed of a finite sequence of consecutive line segments that enclose a region in a plane. These segments are called sides, and the points at which they intersect are called vertices.
A rectangle is a polygon with four sides and four vertices that is characterized by having two of its sides longer than the other two sides. Therefore, to draw a rectangle with a perimeter of 18 units we must distribute the measurements as follows:
Two sides of 3 unitsTwo bases of 6 unitsLearn more about rectangles in: https://brainly.com/question/29123947
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Graph the following system of inequalities.
4y is less than or equal to x + 12, -4y is less than or equal to 3x +4, 5x -4y is less than or equal to 4.
A graph of the solution to this system of inequalities on a coordinate plane is shown in the image attached below.
How to graph the solution to this system of inequalities?In order to to graph the solution to the given system of inequalities on a coordinate plane, we would translate the word problem into an algebraic equation and then use an online graphing calculator to plot the given system of inequalities;
4y is less than or equal to x + 12 ⇒ 4y ≤ x + 12.-4y is less than or equal to 3x +4 ⇒ -4y ≤ 3x + 45x - 4y is less than or equal to 4 ⇒ 5x - 4y ≤ 4.Based on the graph (see attachment), we can reasonably infer and logically deduce that the solution to the given system of inequalities is the shaded region as shown in the image attached below.
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during one period a bakery rejected 372 items as unfit for sale in the following period the bakery rejected only 323 items a decrease in unfit bakery items what is the percent decrease
Answer:
To calculate the percent decrease in the number of rejected items, we can use the following formula:
Percent decrease = ((initial value - final value) / initial value) x 100
In this case, the initial value is 372 (the number of items rejected in the first period) and the final value is 323 (the number of items rejected in the second period).
So, the percent decrease is:
((372 - 323) / 372) x 100 = 13.1%
Therefore, there is a 13.1% decrease in the number of rejected items from the first period to the second period.