Answer:
Step-by-step explanation:
The formula for Sn of a geometric series with first term a and common ratio r is:
Sn = a((1-r^n)/(1-r))
In this case, the first term a is $1,000, the common ratio r is 1.02 (since she's depositing 2% more each year), and n is 30 (since we're looking for the amount deposited after 30 years).
Plugging in these values, we get:
Sn = 1000((1-1.02^30)/(1-1.02))
Sn ≈ $87,453
Therefore, the answer is D. $87,453.
Hi! Can someone please help me with this math question? Thanks!
Answer:
Quadratic since it times by 4 every time
Step-by-step explanation:
Graph the system of inequalities. Name the coordinates of the vertices of the feasible region. Find the maximum and minimum of the given function for this region.
Using inequalities, Y(x=0) = -2 and X(y=0) = -2 in region 1.
To pick area 1, draw a line at the intersection of (-2,0) and (0, -2), then choose the right side. such as.
Region 2) To pick the region to the left or upwards in region 2, we must draw a line from (0,2) to (-2,4).
Y(x=0) = 2\sX(y=-2) = -4
Region 3) To pick the region to the right, we must draw a line connecting (-4,0) and (0,4), as I'll demonstrate.
What are inequalities?Inequalities in mathematics describe the relationship between two non-equal numbers. Equal does not necessarily mean unequal. When two values are not equal, we typically use the "not equal symbol ()". However, several inequalities are utilised to compare the numbers, whether it is less than or higher than.
The feasible area is now visible. Let's determine the vertices' coordinates.
Where the blue and green lines intersect is our first vertex.
3x + 2 = x + 4 and y = 3x + 2
3x - x = 4 - 2
y = 3× (1) + 2 = 3 + 2 = 5 when 2x = 2x = 1
(X, Y) = Vertex 1 (1,5)
The intersection of the red and green lines is at vertex #2:
y = -x -2; y = x + 4; y = x + 4 = -x - 2; and y = x + x = -2 - 4
2x = -6, x = -6/2, and y = (-3) + 4 = -3 + 4 = 1 are the results.
(X, Y) = Vertex 2 (-3,1)
The intersection of the red and blue lines is at vertex 3:
y = -x - 2, y = 3x + 2 -x - 2, and y = 2 + 2 -4 x = 4 x = -4 / 4 = -1.
So, y = 3× (-1) + 2 = -3 + 2 = -1
(X, Y) = Vertex 3 (-1, -1)
Let's now modify the graph by including the supplied equation.
The intercept where Y=0 is 0 is given by f(x,y) = -3x + 5y = 0 5y = 3x + 0 y = 3/5 × X + 0
the gradient m = 3/5
A line can be drawn from (0,0) to (-10, -6)
Let's now examine how it would appear in the area where it is practical.
We can see that the function intercepts the blue line or the line of the second section, which is where the largest value is located.
y = 3x + 2 3x + 2 (3/5 - 3) x = 2 -12/5 × x = 2 x = -5/6.
Hence, y = 3x + 2 3/5 × (-5/6) = -1/2.
The maximum is therefore found at (x,y) = (-5/6, -1/2).
The point where the function crosses the red line now marks the minimum.
y = 3/5 × x; y = -x -2
3/5 x = -x - 2\s (3/5 + 1) × x = -2\s8/5 x = - 2\sx = -2× (5/8) = -5/4.
y = 3/5 × (-5/4) = -3/4
The minimum is thus found at (x,y) = (-5/4, -3/4)
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Kristoff needs to fill in the blanks below to factor x2 - 12x + 20. Which of the following is
NOT true about the missing values?
The factor that both trinomials have in common is; C: (x + 2)
How to factor polynomials?In mathematics, a polynomial is defined an expression that consists of variables that are also referred to as indeterminates and coefficients, that involves only the operations of addition, subtraction, multiplication, and non-negative integer exponentiation of variables. An example of a polynomial of a single indeterminate x is x² - 7x - 18
The trinomial of james is;
x² - 7x - 18
Factorizing this gives;
x² + 2x - 9x - 18
= x(x + 2) - 9(x + 2)
= (x + 2)(x - 9)
The trinomial of Kaitlin is;
x² + 14x + 24
Factorizing this gives;
x² + 12x + 2x + 24
= x(x + 12) + 2(x + 12)
= (x + 2)(x + 12)
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Use the diagram of the cylinder to answer the question. Use 3.14 for π and round to the nearest tenth. SHOW PROOF PLEASE
803.84 square inches is the surface area of a cylinder with an 8-inch radius and 8-inch height.
What is the surface area of a solid?Any solid shape has a surface area equal to the total of the areas of its faces. For instance, to calculate the surface area of a cuboid, we add the areas of all the rectangles that make it up.
According to the given information:The formula for the surface area of a cylinder is given by:
Surface Area = 2πr² + 2πrh
where r is the radius and h is the height of the cylinder, and π (pi) is a mathematical constant approximately equal to 3.14.
Substituting the given values, we get:
Surface Area = 2 × 3.14 × 8² + 2 × 3.14 × 8 × 8
= 401.92 + 401.92
= 803.84 square inches
the surface area of the cylinder with radius 8 inches and height 8 inches is 803.84 square inches.
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What is the distance from Point A to BC?
The least distance by Pythagorean theorem is equal to √5. (Correct choice: B)
How to determine the least distance of a point to a line
In this problem we find the representation of a point and a line on Cartesian plane. There is a least distance between the point and the line when the line segment between them is perpendicular to the line. The line segment AC fulfill these features. Given the location of points A and C, we can determine the distance by means of Pythagorean theorem:
d = √[(Δx)² + (Δy)²]
Where:
d - DistanceΔx - Change in variable x.Δy - Change in variable y.If we know that A(x, y) = (1, 3) and C(x, y) = (3, 2), then the least distance between the point and the line:
d = √[(3 - 1)² + (2 - 3)²]
d = √[2² + (- 1)²]
d = √5
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If the given sample variance is 17.56, what is the standard deviation?
According to the preceding statement, then standard deviation becomes 4.19 if the sample variance is given as 17.56.
How to interpret a standard deviation?A measurement of a data set's departure from the mean is referred to as "standard deviation" (or ""). Whereas a large variance shows that the numbers are more spread, a lower number suggests that its data are clustered around the mean. The standard deviation is a measure of how volatile your collected data is generally. It displays the standard deviation for every score with respect to the mean.
We must consider the square root of both the sample covariance matrix to determine the standard deviation.
= √17.56
≈ 4.19
Hence, their standard deviation is around 4.19
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pls show work i’m struggling
The distance between points A and B is 6 units.
What is the distance between two points ( p,q) and (x,y)?The shortest distance (length of the straight line segment's length connecting both given points) between points ( p,q) and (x,y) is:
[tex]D = √[(x-p)² + (y-q)²] D = \sqrt{(x-p)^2 + (y-q)^2} \: \rm units.[/tex]
We are given that;
The points= (-1.4) and B (5.-2)
Now,
To find the distance between points A (-1.4) and B (5.-2), we can use the distance formula:
d = [tex]\sqrt((x2 - x1)^2 + (y2 - y1)^2)[/tex]
where (x1, y1) and (x2, y2) are the coordinates of points A and B, respectively.
Substituting the values we have:
[tex]\sqrt{(5 - (-1))^2 + (-2 - (-4))^2}[/tex]
d = [tex]\sqrt{(5 + 1)^2 + (-2 + 2)^2}[/tex])
d = [tex]\sqrt{(6^2 + 0^2)}[/tex]
d = [tex]\sqrt{36}[/tex]
d = 6
Therefore, by the distance formula answer will be 6 units.
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Problem is down below Please find the answer.
[tex](2x-1)^{2} = 25 \iff (2x-1)^{2} = 5^{2}\\[/tex]
[tex]x > 0 \implies 2x - 1 = 5 \iff 2x = 5 + 1 \iff 2x = 6 \implies \bf x = 3\\[/tex]
[tex](3y-1)^{2} = 36 \iff (3y-1)^{2} = 6^{2}\\[/tex]
[tex]y > 0 \implies 3y-1 = 6 \iff 3y = 6 + 1 \iff 3y = 7 \implies \bf y = \dfrac{7}{3}\\[/tex]
⇒
[tex]\dfrac{3x - y}{x+y} \cdot \dfrac{1}{7} = \dfrac{3(3) - \frac{7}{3} }{7(3+\frac{7}{3} )} = \dfrac{9 - \frac{7}{3} }{7(\frac{16}{3})} = \dfrac{\frac{27-7}{3} }{7(\frac{16}{3})}=\\[/tex]
[tex]= \dfrac{\frac{20}{3} }{\frac{112}{3}} = \dfrac{20}{3} : \dfrac{112}{3} = \dfrac{20}{3} \cdot \dfrac{3}{112} = \dfrac{20}{112} = \bf \dfrac{5}{28}\\[/tex]
Mr. and Mrs. Smith took their children on a trip to the Grand Canyon. When they left home, Mrs. Smith noted the odometer read 5,478.18 miles. When they arrived at the Grand Canyon, she noted that the odometer read 6,010.63. How far had the family-driven?
Mr Smith looks their children 1 times 1
the graph y=x^2 and x=y^2, show the similarities and differences
One key difference between the two graphs is that [tex]$y=x^2$[/tex] is a function, meaning that for each x value there is only one y value. On the other hand,[tex]$x=y^2$[/tex]is not a function.
How to find similarities and differences between graphs?The graph of[tex]$y=x^2$[/tex] is a parabola that opens upwards, centered at the origin (0,0). The graph of [tex]$x=y^2$[/tex] is also a parabola, but it opens to the right, also centered at (0,0). Both graphs intersect at the origin, where x=y=0.
Another important similarity between the two graphs is that they are both symmetric with respect to the y=x line,
which is the line of symmetry for both graphs. This means that if we reflect one of the graphs across the line y=x, we get the other graph.
One key difference between the two graphs is that [tex]$y=x^2$[/tex] is a function, meaning that for each x value there is only one y value.
On the other hand,[tex]$x=y^2$[/tex]is not a function, because for some y values there are two corresponding x values (one positive and one negative). This means that the graph of [tex]$x=y^2$[/tex] fails the vertical line test.
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Integers of 7° F below 0
The integer number that represents a temperature of 7 ºF below zero is given as follows:
-7 ºF.
What are integer numbers?Integer number are numbers that can have either positive or negative signal, but are whole numbers, meaning that they have no decimal part.
For temperatures, we have that:
Temperatures above 0ºF are positive.Temperatures below 0ºF are negative.Hence the integer number that represents a temperature of 7 ºF below zero is given as follows:
-7 ºF.
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15
The circle graph shows the percentages of a family budget used for different monthly expenses.
Family Budget
Utilities
20%
Gasoline
10%
Clothes
15%
Mortgage
30%
Groceries
25%
Which statement is supported by the data in the graph? 7.6G
A The amount of money budgeted for gasoline and clothes combined is greater than the amount budgeted for groceries.
B The amount of money budgeted for utilities and gasoline combined is less than the amount budgeted for the mortgage.
The amount of money budgeted for the mortgage is half of the amount budgeted for clothes.
The amount of money budgeted for groceries and clothes combined is twice the amount budgeted for utilities.
the number of square units for the area because Area=LW so A=10x10 which is 100 and perimeter is P=2L=2W so that would be P=2(10)+2(10) which is 40, therefore, the area is greater
The number of square units for the area of the square is greater than the number of units for the perimeter.
How can the area and perimeter of a square be calculated?The area of a square is calculated using the formula below:
Area of square = (length of side)²
The length of the side of the square = 10 units
Ares of the square = 10 * 10
Area of the square = 100 units
The perimeter of a square = 4 * length of the side
Perimeter of a square = 4 * 10
The perimeter of a square = 40
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Complete question:
One side of a square is 10 units. Which is greater the number of square units for the area of the square or the number of units for the perimeter?
Hamburgers can be purchased from two different popular fast food restaurants. Restaurant A sells 11 burgers for $14.52, and Restaurant B sells 2 burgers for $2.58. Which restaurant offers the best value per hamburger, and what is its amount?
Restaurant A for $1.29
Restaurant B for $1.29
Restaurant A for $1.32
Restaurant B for $1.32
Answer: Restaurant B
Step-by-step explanation:
First, Divide 14.52 by 11 as shown below to get the cost per burger for Restaurant A:
14.52/11 = 1.32
Next, divide 2.58 by 2 for the cost of the burger at Restaurant B:
2.58/2 = 1.28
Now we can see that Restaurant B's burgers are 4 cents cheaper than Restaurant A.
Good Luck!
What is solve for k=
Answer:
k=77
steps:
k/11=7
k=7*11
k=77
Answer:
k = 77Step-by-step explanation:
[tex]\tt \cfrac{k}{11} =7[/tex]
The opposite of division is multiplication, so we need multiply both sides by 11:-
[tex]\tt \cfrac{k}{11}\times 11 =7\times 11[/tex]
[tex]\tt k=7\times 11[/tex]
[tex]\tt k=77[/tex]
______________________
Hope this helps! :)
PLS HELPPP THYANK UUU PLS The data below shows the colors preferred by a group of people. We want to plot this on a pie chart. What will be the central angles of each of these categories?
Red=
blue=
green=
purple=
Answer:
Red 100
Blue 150
Green 50
Purple 60
Step-by-step explanation:
The total number of people surveyed
= 20 + 30 + 10 + 12
= 72
The relative area of each pie in the pie chart will be in the ratio of
number of people who prefer a color ÷ total number of people
The central angles of each pie category = above ratio x 360°
Fraction of people who prefer red = 20/72These angles should add up to 360°
100 + 150 + 50 + 60 = 360
0
T
1
0 10
لسل
5
8
Centimeters
3
2
2
Millimeters
4 5
20 30 40 50
There is a proportional relationship between any length
measured in centimeters (cm) and the same length
measured in millimeters (mm).
Use the ruler to help you complete the table.
Length (mm)
884
25
240
699.1
Length (cm)
What is the constant of proportionality?
ONDE
Submit
Sign out
US
The proportionality constant (mm to cm) is 10 and the complete table is -
9 cm 90 mm
12.5 cm 125 mm
50 cm 500 mm
88.49 cm 884.9 mm
What is proportional relationship?A proportional relationship between two variables {x} and {y} means that if {x} increases, then {y} increases with it proportionally.
Given is a proportional relationship between two scales.
{ 1 } -
We can write the proportionality constant (mm to cm) as -
{k} = (20 - 10)/(2 - 1)
{k} = 10
{ 2 } -
We can write the complete table as -
9 cm 9 x 10 = 90 mm
12.5 cm 12.5 x 10 = 125 mm
50 cm 50 x 10 = 500 mm
88.49 cm 88.49 x 10 = 884.9 mm
Therefore, the proportionality constant (mm to cm) is 10 and the complete table is -
9 cm 90 mm
12.5 cm 125 mm
50 cm 500 mm
88.49 cm 884.9 mm
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Dan has 16 pencils. Quentin gives him
5 more pencils. Choose all the ways you
can use to find how many pencils Dan
has in all.
016 +5
o 16 + 4+
o 16-5
16 + 5
Because Dan has 16 pencils and he gets 5 more
complete the table 8 to 16 __ to 1 __ to 10 __ to 17
The values in the table using the expression (time=2 × no. of pages) will be 0.5, 5 and 8.5.
What exactly are expressions?In mathematics, an expression is a combination of numbers, variables, and operations that can be evaluated to produce a value.
Expressions can be simple or complex, and can involve arithmetic, algebraic, or logical operations. Some examples of expressions include:
5 + 3x - 2y(a + b) / (c - d)In each of these examples, the expression consists of one or more terms that are combined using operations such as addition, subtraction, multiplication, division, or exponentiation.
Now,
As given pages = 8 and time= 16 minutes
this can be deduced by expression Time=2 × no. of pages
Then for time= 1,10 and 17 minutes
no. of pages will be 1/2,10/2 and 17/2.
Hence, the table will be:
Pages 8 0.5 5 8.5
Minutes 16 1 10 17
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Complete the equation of the line through (2,1) and (5,-8) in y=Mx+b form
Answer:
y=-3x+7
Step-by-step explanation:
find the slope which is (y1-y2)/(x2-x1). therefore the slope is -3. and then put it in point slope intercept form which is (y-y1)=m(x-x1) = (y-1)=-3(x-2) and simplified the expression is y=-3x+7.
Identify the equation for the graph shown.
A. y = 5x - 2
B. y = 2x - 5
C. y = 2x + 5
D. y = x - 4
E. y = 2x - 6
graph the line with y-intercept 1 and slope 4
Answer:
y = 4x + 1
Step-by-step explanation:
Let's graph it in slope intercept form y = mx + b
m = the slope
b = y-intercept
m = 4
b = 1
So, the equation is y = 4x + 1
ALL
A cube lies inside a cylinder as shown The sides of the cube measure 3.2 inches and the diameter of the cylinder is 4.5 inches. What is the geometric probability of the cube? Use 3.14 for pl and round to the nearest tenth
06
0.16
0.46
0.36
The geometric probability of the cube is 0.64
How to determine the geometric probability of the cube?The complete question is added as an attachment
From the question, we have the following parameters that can be used in our computation:
Cube side length, l = 3.2 inchesDiameter of cylinder, d = 4.5 inchesHeight of cylinder, h = 3.2 inchesNext, we calculate the volumes of the cube and the cylinder using the following formulas
V(Cube) = l³
V(Cylinder) = πr²h
So, we have
V(Cube) = 3.2³ = 32.768
V(Cylinder) = 3.14 * (4.5/2)² * 3.2 = 50.868
The geometric probability of the cube is then calculated as
P = V(Cube)/V(Cylinder)
So, we have
P = 32.768/50.868
Evaluate
P = 0.64
Hence, the probability is 0.64
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Measure of arc ML=76 Degrees and Measure of Angle JLK = 54 Degrees. What is the value of X
The value of x is 54 when measure of arc MLis 76 Degrees and measure of Angle JLK is 54 Degrees.
What is Circle?A circle is a shape consisting of all points in a plane that are at a given distance from a given point, the centre.
Measure of arc ML=76 Degrees and
Measure of Angle JLK = 54 Degrees
We have to find the value of x
O is the centre of the circle.
As we see the figure angle L is corresponding to 54 degrees.
x=54
Hence, the value of x is 54 when measure of arc MLis 76 Degrees and measure of Angle JLK is 54 Degrees.
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The equation Q=2s2+4sh represents the surface area, Q, of a cracker box in the shape of a square prism with a base side length of
In square prism , A cracker box in the shape of a square prism with a base side length of [tex]SA - \frac{2S^{2} }{4S} = h[/tex].
What is square prism?
The bases of a square prism are square, and the other four faces are rectangles. A square prism is a cuboid object in three dimensions.
Angles and sides that are in opposition to one another are congruent. A magnet bar is an illustration of the shape of a square prism.
we know that'
The formula to calculate the surface area of a square prism is
[tex]Q = 2s^{2} + 4sh[/tex]
subtract 2s² both sides
SA - 2s² = 4sh
Divide by 4s both sides
[tex]SA - \frac{2S^{2} }{4S} = h[/tex]
Rewrite
[tex]SA - \frac{2S^{2} }{4S} = h[/tex]
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Find the centroid of the region bounded by the given curves y=2-x^2 , y=x
The centroid of the region is at the point (0, 2/5).
What is the centroid of the region bounded by the curves?To find the centroid of the region bounded by the curves y=2-x² and y=x, we first need to find the limits of integration and the expressions for the x-coordinate and y-coordinate of the centroid.
The curves intersect at (1,1) and (-1,1), so we will integrate over the interval [-1,1].
To find the x-coordinate of the centroid, we need to evaluate the following integral:
x' = (1/A) ∫[a,b] xf(x) dx
where;
A is the area of the region (which we can find by integrating the difference between the two curves).A = ∫[a,b] (f(x) - g(x)) dx
In this case, f(x) = 2 - x² and g(x) = x, so
A = ∫[-1,1] (2 - x² - x) dx
= [2x - (1/3)x³ - (1/2)x²] | from -1 to 1
= (4/3)
Now we can evaluate the x-coordinate of the centroid:
x' = (1/A)∫[-1,1] x*(2-x²-x) dx
= (1/(4/3))∫[-1,1] (2x - x³ - x²) dx
= (3/4) [(x²/2) - (1/4)x⁴ - (1/3)x³] | from -1 to 1
= 0
So the x-coordinate of the centroid is 0.
To find the y-coordinate of the centroid, we need to evaluate the following integral:
y' = (1/A) ∫[a,b] (1/2) [f(x)² - g(x)²] dx
y' = (1/(4/3)) ∫[-1,1] (1/2)[(2-x²)² - x²] dx
= (3/4)[(8/15)x⁵ - (2/3)x³ + (1/2)x] | from -1 to 1
= (2/5)
So the y-coordinate of the centroid is 2/5.
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find the image coordinates of a triangle with the coordinates M(0,4), N(4,2), and P(2,-2), dilated by a scale facotr of three
The image triangle has vertices after the dilation by a scale factor of 3 are M'(0,12), N'(12,6), and P'(6,-6).
How to determine image coordinates of the triangleTo find the image coordinates of a triangle after dilation, we need to multiply the coordinates of each point by the scale factor.
In this case, the scale factor is 3.
So the image coordinates of the triangle with vertices M(0,4), N(4,2), and P(2,-2) after dilation by a scale factor of 3 are:
M' = (3 * 0, 3 * 4) = (0, 12)
N' = (3 * 4, 3 * 2) = (12, 6)
P' = (3 * 2, 3 * (-2)) = (6, -6)
Hence, the image triangle has vertices M'(0,12), N'(12,6), and P'(6,-6).
In summary, the image coordinates of the triangle after dilation by a scale factor of 3 are M'(0,12), N'(12,6), and P'(6,-6).
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1.1. Thembile is a second hand dealer. She bought the sewing machine for R5700 and later sold it for R8850. 1.1.1. How much profit/loss was made? Profit selling price - cost price
The profit made from Thembile selling the second hand sewing machine if the cost price is R5700 and the selling price is R8850 is R3150.
How much profit/loss was made?Profit/loss refers to the difference between the cost price and selling price of an item. When the difference is positive; it is profit. When the difference is negative; it is loss.
Cost profit = R5700
Selling price = R8850
Profit = Selling price - Cost price
= R8850 - R5700
= R3150
Ultimately, Thembile made a profit of R3150 on the second hand sewing machine.
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what is Net profit?
Answer:
Net profit is the amount of money that a company has earned after deducting all of its expenses, taxes, and other costs from its total revenue. It is the final result of a company's income statement, which shows the revenue, expenses, gains, and losses incurred during a specific period of time, typically a year. Net profit is often used as a key measure of a company's financial performance and is a crucial metric for investors and stakeholders in evaluating the success of a business.
Step-by-step explanation:
9. A number multiplied -32 is 256. What is the number?
Answer:
See below.
Step-by-step explanation:
We are asked for a unknown number.
To find our number, we should use the Inverse Operation.
What is the Inverse Operation?The Inverse Operation is the opposite operation.
For example: If we Multiplied, then we should use the Inverse Operation which is Dividing.
Let's divide 256 by -32 to identify our missing number.
Divide:
[tex]\frac{256}{-32} = -8[/tex]
Our missing number is -8.