Answer:
volume = 0.5 * b * h * length , where b is the length of the base of the triangle, h is the height of the triangle, and length is prism length.
Step-by-step explanation:
The manager of a pizza restaurant recorded the total number of pizzas delivered after x weeks in this table. Which statement is true?
A. There was an increase of 83.5 pizzas each week from week 4 to week 6.
B. There was an increase of 34.5 pizzas each week from week 4 to week 6.
C. There was an increase of 50 pizzas each week from week 4 to week 6.
D. There was an increase of 28 pizzas each week from week 4 to week 6.
a) There was an increase of 83.5 pizzas each week from week 4 to week 6.
How to find the increase in pizza sales?Increase in no of pizzas from 4 to 5th week = 356 - 278 = 78
78 pizzas sales increased.
Increase in no of pizzas from 5 to 6th week = 445 - 356 = 89
89 pizzas sales increased.
On average = 78 + 89/2
= 167/2
= 83.5
Therefore,
There was an increase of 83.5 pizzas each week from week 4 to week 6.
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Select all the equations that represent a line perpendicular to the line 3x - 2y = 10
All the equations of the family:
y = (-2/3)*x + c
Where c is a real number, are perpendicular to the linear equation 3x - 2y = 10
How we can find the perpendicular equations?A general linear equation is of the form:
y = m*x + b
Where m is the slope and b is the y-intercept.
Now, two linear equations are only perpendicular if the slope of one is equal to the inverse of the opposite of the other line's slope.
So, a line perpendicular to y = m*x + b is of the form:
y = (-1/m)*x + c
In this case, the given line is:
3x - 2y = 10
Writing this in slope-intercept form we get:
-2y = 10 - 3x
y = (10 - 3x)/-2
y = (3/2)*x - 5
So the slope of a perpendicular line will be: (-2/3)
Then any line of the form:
y = (-2/3)*x + c
Is perpendicular to the given line.
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Which of the following functions arecontinuous on the interval 0 < 2 < 2?
Notice that:
[tex]1^2-1=0.[/tex]Therefore:
[tex]f(x)=\frac{x-1}{x^2-1}[/tex]is undefined at x=1.
Now, recall that the natural logarithm is defined over the positive numbers, therefore:
[tex]x^2-1>0[/tex]Then:
[tex]x>1\text{ or }x<-1.[/tex]Therefore the function
[tex]f(x)=ln(x^2-1)[/tex]is not well defined over the interval (0,2).
Finally, notice that:
[tex]p(x)=x^2+1,[/tex]has no real zeros, therefore the function:
[tex]f(x)=\frac{x+1}{x^2+1}[/tex]is well defined over all real numbers, also is continuous over all real numbers, particularly over the interval (0,2).
Answer: First option.
II only.
Please help! Create a scatterplot for the data in the table. Let English scores be X and History Scores be Y.
Part 2: draw line of fit
Part 3: choose two points, find slope, and record slope decimal
A way to pinpoint a point's location on the planet is through the use of a coordinate system. In most coordinate systems, a point's location is determined by two numbers called a coordinate. Each of these values represents the separation between the point and the origin, a fixed point of reference.
Explain about the coordinate system?A two-dimensional number line, such as two perpendicular axes, can be thought of as a coordinate system.
The x-axis stands for the horizontal axis, and the y-axis for the vertical axis.
A coordinate system's origin is its centre (in which the lines intersect). The axes cross if x and y are both 0.
The coordinates of the origin are (0, 0).
for the posed query.
"English score" is one of the independent variables on the x-axis.
The dependent variables "History score" are displayed on the y-axis.
The scattered points are used to plot the graph for the provided table.
Take note of these two points on the graph:
(x₁, y₁) = (60, 65) (60, 65)
(x₂, y₂) = (61, 61) (61, 61)
The slope will then be;
m = (y2 - y1)/(x2 - x1) is the slope.
the values in.
m = (61 - 65)/(61 - 60) (61 - 60)
m = -4
The slope is -4.
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what number is equal to y????????????
solve in the substitution method pleasex - 2y = -5x + 5y = 2
To solve the system of equations:
[tex]\begin{gathered} x-2y=-5 \\ x+5y=2 \end{gathered}[/tex]by the substiturion method we need to solve one of the equations for one of the variables, then we substitute this value in the other equation and solve for the remaining variable. Let's apply this method to the system.
First we solve the first equation for x:
[tex]x=2y-5[/tex]now we plug this value in the second equation:
[tex]\begin{gathered} 2y-5+5y=2 \\ 7y=5+2 \\ 7y=7 \\ y=\frac{7}{7} \\ y=1 \end{gathered}[/tex]Hence y=1. Once we have the value of y we substiute it in the equation for x:
[tex]\begin{gathered} x=2(1)-5 \\ x=2-5 \\ x=-3 \end{gathered}[/tex]Therefore the solution of the system is x=-3 and y=1
can someone help me on this
Answer: A, D, E, should be correct because the others are equal
Step-by-step explanation:
A partial payment is made on the date indicated. Use the United States rule to determine the
balance due on the note at the date of maturity. (The Effective Date is the date the note was
written.) Assume the year is not a leap year.
The balance due on the note at the date of maturity is $___ (round to the nearest cent as needed)
The balance due on the note at the date of maturity is $1012.49
Given,
Principal = $2000
Int rate(r) = 5%
Effective date April 1
The partial payment date May 1
Maturity date June 1
partial payment is being made on May 1
Interest from April 1 to May 1 for 30 days and is calculated as:
$2000 x 0.05 x (30/365) = $8.21
Interest Amount deducted from the principal = $2000 - $8.21 = $1991.79
Amount applied to the principal = $1000 - $8.21 = $991.79
Principal due = $2000 - $991.79 =$1008.21
Interest on new principal $1008.215 will be for (61` - 30 ) is 31 days
interest due = $1008.21 x 0.05 x (31/365) = $4.28
Account due on maturity (Total due) is $1012.49
What is the principal amount ?
The principal is the amount of debt originally borrowed that remains unpaid. This amount does not include accrued unpaid interest related to the debt. The term can also refer to a principal participant in a contract or other transaction. Home loan equity is the amount of money originally borrowed by the lender, and it can also refer to the amount of money remaining when the loan is paid off.
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Find x and y . Approximate your answer to one decimal place. I used comma for decimal separation. A random variable X has as a range of values the values 1, 2 and 3 with probabilities P (X = 1) = 0.2, P (X = 2) = x, and P (X = 3) = y. If Var (X) = 0.29, then x = and y =
We have a random discrete variable X, that takes values 1, 2 and 3.
As the probabilities of all the sample space is equal to 1.
So then we can define x in function of y:
[tex]\begin{gathered} P(x=1)+P(x=2)+P(x=3)=1 \\ 0.2+x+y=1 \\ y=1-0.2-x \\ y=0.8-x \end{gathered}[/tex]We can start by calculating the mean of X as:
[tex]\begin{gathered} \mu=\sum ^3_{i\mathop=1}p_i\cdot x_i \\ \mu=0.2\cdot1+x\cdot2+y\cdot3 \\ \mu=0.2+2x+3(0.8-x) \\ \mu=0.2+2x+2.4-3x \\ \mu=2.6-x \end{gathered}[/tex]We can write the variance of X as:
[tex]\begin{gathered} \sigma^2=\sum ^3_{i\mathop=1}p_i\cdot(x_i-\mu)^2 \\ \sigma^2=0.2\cdot(1-(2.6-x))^2+x\cdot(2-(2.6-x))^2+(0.8-x)\cdot(3-(2.6-x))^2 \\ \sigma^2=0.2\cdot(x-1.6)^2+x\cdot(x-0.6)^2+(0.8-x)\cdot(x+0.4)^2 \\ \sigma^2=0.2\cdot(x^2-3.2x+2.56)+x\cdot(x^2-1.2x+0.36)+(0.8-x)(x^2+0.8x+0.16) \\ \sigma^2=0.2x^2-0.64x+0.512+x^3-1.2x^2+0.36x+0.8x^2+0.64x+0.128-x^3-0.8x^2-0.16x \\ \sigma^2=(1-1)x^3+(0.2-1.2+0.8-0.8)x^2+(-0.64+0.36+0.64-0.16)x+(0.512+0.128) \\ \sigma^2=-x^2+0.2x+0.64 \end{gathered}[/tex]As the variance, σ², is equal to 0.29, then we can find the possible values for x as:
[tex]\begin{gathered} \sigma^2=0.29 \\ -x^2+0.2x+0.64=0.29 \\ -x^2+0.2x+0.64-0.29=0 \\ -x^2+0.2x+0.35=0 \\ x^2-0.2x-0.35=0 \end{gathered}[/tex]We can find the roots of this equation as:
[tex]\begin{gathered} x=\frac{-(-0.2)\pm\sqrt[]{(-0.2)^2-4\cdot1\cdot(-0.35)}}{2\cdot1} \\ x=\frac{0.2\pm\sqrt[]{0.04+1.4}}{2} \\ x=\frac{0.2\pm\sqrt[]{1.44}}{2} \\ x=\frac{0.2\pm1.2}{2} \\ x_1=\frac{0.2-1.2}{2}=-\frac{1}{2}=-0.5 \\ x_2=\frac{0.2+1.2}{2}=\frac{1.4}{2}=0.7 \end{gathered}[/tex]The value of x = -0.5, as it is a probability, has to have a value of between 0 and 1, is not valid.
Then, the only valid value for x is x = 0.7.
We then can calculate y as:
[tex]y=0.8-x=0.8-0.7=0.1[/tex]Answer: x = 0.7 and y = 0.1
help mee pleasee!!
thank you <3
The function for the cost C(x) of printing the newsletter is :
C(x) = 75 + 0.25x
In this question, we have been given the cost of producing a newsletter is an initial charge of $75 for formatting and editing plus $0.25 for printing each copy.
We need to express the cost C(x) of printing the newsletter as a function of x i.e., the number of copies printed.
Here $75 is the fixed cost.
And the cost of printing 'x' copies would be 0.25x
So, we get a function C(x) = 75 + 0.25x
Therefore, the function for the cost C(x) of printing the newsletter is :
C(x) = 75 + 0.25x
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i really just Need the answer fast,no explnation is needed
Notice that the graph of the parabolla passes through the points (-2,0) and (0,0), which are x-intercepts since the cross the x-axis
I need assistance in intermediate algebra… Graph the solution to the inequality.Right the solution to the inequality both insert builder notation and interval notation
Answer:
Interval notation:
[tex]\lbrack-5,8)[/tex]Set-builder notation:
[tex]\lbrace x|-5≤x<8\rbrace[/tex]Plot of the solution:
Step-by-step explanation:
First, let's put the solution of the inequality into simpler words. We're looking for values of x that are between 5 and 8, including 5 and excluding 8.
This way, the interval notation for the solution is:
[tex]\lbrack-5,8)[/tex]As a set, we would read the solution as: "The set of all x's, such that x is greater or equal than -5 and less than 8 than 0". In set builder notation, this is:
[tex]\lbrace x|-5≤x<8\rbrace[/tex]The plot of the inequality would be:
Where the full end represents a square bracket and the empty end represents a parentheses.
One side of a rectangle is 7 feet shorter than twice and other side find the length of the shorter side if we also know that the perimeter of the rectangle is 100 feet.
The perimeter of a rectangle is 2(l+b).
The length and breadth of a rectangle are 31 ft and 19 ft respectively.
How to find the length and breadth of a rectangle?Let the other side of a rectangle = b
And the one side of a rectangle = l = 2b - 7 ft
The perimeter of a rectangle = 2(l+b) = 100 ft.
2(2b - 7+ b) = 100
2(3b - 7) = 100
3b - 7 = 50
3b = 57
b = 57/3ft
b = 19ft
l = 2b - 7
l = 2*19 - 7
l = 38 - 7
l = 31
l = 31ft
Therefore, length = 31 ft. and breadth = 19ft.
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Solve 2 + by = 32 3x + 4 for y y.
2 + (1/6) y = 3x + 4
Take the 2 from left to right side: (1/6)y = 3x + 4 - 2 = 3x + 2
y/6 = 3x + 2
Take the 6 dividing on the left to the righ side multiplying:
y = 6 (3x + 2) = 18x + 12
Answer:
y = 18x + 12
Determine whether the graphs of the given equations are parallel, perpendicular, or neither. y=x+9 y = -x + 2
Answer: Perpendicular
Step-by-step explanation:
Given are two equations as
We have to find whether these two are parallel or perpendicular or neither
For this first we have to find the slope of these two lines
I line slope = 1
II line slope =-1
Since slopes are not equal, the lines are not parallel.
Let us check product of these slopes. IF product =-1 the lines are perpendicular
We find that product =
Hence two lines are perpendicular
Find volume and weight
The volume of the steel after the hole is cut is 32inches³.
The total weight of the drawing is 960 oz
What is the volume and weight?The volume of the shape that is being drawn is the difference in the volume of the rectangle and the volume of the hole. Th volume of an object is the amount of space that is in the object.
A rectangular prism is a three dimensional object that has 6 faces, 12 edges and 8 vertices.
Volume of a rectangular prism = length x width x height
3.77 x 9.32 x 1 = 35.14 inches³
The shape of the hole would be a cylinder. Thus, the formula for the volume of a cylinder would be used to determine the volume of the hole.
Volume of a cylinder = πr²h
Where:
π = 3.14 r = radius = diameter /2 = 1 h = height3.14 x 1² x 1 = 3.14 inches³
Volume of the steel after the hole is cut = 35.14 inches³ - 3.14 inches³ = 32inches³.
Total weight of the drawing = 32 inches x 30 = 960 oz
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In a newspaper it was reported that yearly robberies in Springfield were up 6% to 265 in 2011 from 2010. How many robberies were there in Springfield in 2010?
The no. of robberies in 2010 was 4416 and in 2011 it grew up 6% (six percent) to 265 that is 4681 robberies.
What is Percentage?The value of the whole is always 100 in a percentage, which is a ratio or fraction. Sam, for instance, would have received a score of 30 out of 100 on his math test if he received a 30%. When expressed as a ratio, it is written as 30:100 and as a fraction, 30/100.
An amount or part that is contained in each hundred is known as a percentage. The symbol "%" designates that it is a fraction with 100 as the denominator.
Lets assume the no. of robberies in 2010 be 100
We have given that by 2011 the robbers were upto 6% that is
106 robberies
the difference here is 106 - 100 = 6
When difference = 6, the robberies = 100
When difference = 1, the robberies = 100/6
When difference = 265 , the robberies = 100/6 × 265
= 4416
So, the no. of robberies in 2010 was 4416 and in 2011 it grew up 6% to 265 that is 4681 robberies.
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Write an equation of the line. Write the answer in slope-intercept form. The line passes through (0,5) and is perpendicular to the line x + 4y = 2.?
The product of the slopes of 2 lines that are perpendicular is equals to negative 1. Therefore,
[tex]\begin{gathered} m_1m_2=-1 \\ \end{gathered}[/tex]x + 4y = 2
4y = 2 - x
y = 1/2 - 1/4 x
[tex]\begin{gathered} m_1(-\frac{1}{4})=-1 \\ \frac{-m_1}{4}=-1 \\ -m_1=-4 \\ m_1=4 \end{gathered}[/tex]Therefore,
[tex]\begin{gathered} 5=4(0)+b \\ b=5 \\ y=4x+5 \end{gathered}[/tex]Polygon Exterior Angle Sum Theorem - The _____ of the ________ angle measures, one at each vortex, of a ________ polygon is_____.
The completed statement is:
Polygon Exterior Angle Sum Theorem - The sum of the exterior angle measures, one at each vortex, of a convex polygon is 360°.
What is a polygon?A polygon is a planar figure characterized by a limited number of straight line segments joined to create a closed polygonal chain in geometry. A polygon is defined as a bounded planar region, a bounding circuit, or both. A polygonal circuit's segments are known as its edges or sides.
Polygon examples include the following:
Concave PolygonsConvex PolygonsHexagon PolygonsIrregular PolygonsPentagon PolygonsQuadrilateral PolygonRegular Polygons.Learn more about Polygon:
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1/2. (.5) 2. Frosty and the kids travel 2 miles through town in 2 hours. What is the unit rate per hour?~ is the question, can you show me how to find a unit rate?
EXPLANATION
Frosty and kids travel ---------------> 2 miles / 2 hours
The unit rate will be:
[tex]\text{unit rate = }\frac{2\text{ miles}}{2\text{ hours}}=\frac{1\text{ mile}}{\text{hour}}=\text{ 1mph}[/tex]Write the decimal as a fraction.0.6 = [?]Simplify your answer completely.
0.6 is a decimal and it can be converted to fraction by moving the dot to the right sides and dividing by the number of zero that existed by the dot movement to the right.
[tex]\begin{gathered} 0.6=\frac{6}{10}=\frac{3}{5} \\ \end{gathered}[/tex](14−3 to the 2nd power +1) to the 2nd power1÷3⋅1/4
answers: 1, 3, 144, 432.
The solution to the expression (14−3 to the 2nd power +1) to the 2nd power1÷3⋅1/4 is 3
How to evaluate the expression?The expression is given as
(14−3 to the 2nd power +1) to the 2nd power1÷3⋅1/4
Rewrite the expression properly
So, we have
(14 - 3² + 1)² ÷ 3 * 1/4
Evaluate the exponent
So, we have
(14 - 9 + 1)² ÷ 3 * 1/4
Evaluate the sum and the difference
So, we have
6² ÷ 3 * 1/4
Evaluate the exponent of 6
So, we have
36 ÷ 3 * 1/4
This gives
36 x 1/3 x 1/4
Evaluate
3
Hence, the value of the expression is 3
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A triangle with vertices (−1, 1), (2,−1), and (3, 0) is translated using the rule (x,y)→(x+2, y−6). What are the coordinates of the image?
The coordinates are (1, -5),(4, -7) and (5, -6)
What is Translation?
In mathematics, a translation is the up, down, left, or right movement of a shape. Because the translated shapes appear to be exactly the same size as the original ones, they are consistent with one another. Just one or more directions have been altered. There is no change in the shape because it is simply being moved from one location to another.
Given,
(−1, 1), (2,−1), and (3, 0)
The translation rule:
(x,y)→(x+2, y−6)
In the case (-1, 1):
(x, y)→(-1+2, 1−6)
(x, y)→(1, -5)
In case (2, -1):
(x,y)→(2+2, -1−6)
(x,y)→(4, -7)
In case (3,0):
(x,y)→(3+2, 0−6)
(x,y)→(5, −6)
Hence, The coordinates are (1, -5),(4, -7) and (5, -6)
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Look at image!! Math question. Urgent. Pls answer
Convert 32cups into Gallon: 2gallon
There are 1200 persons in the throng that is 4 feet deep along ONE side of the roadway for a 300-yard stretch of a parade route.
Describe conversion.An amount that is multiplied or divided between one set of units and another is known as a conversion factor. If a conversion is necessary, it must be carried out with the right conversion factor to produce a value that is identical. For instance, 12 inches equals one foot when converting between inches and feet.
7)
Since, We know that
1 gallon = 16cups
Now, we have to convert 32cups into gallon
So,
1gallon = 16cups
32cups = 32/16gallon
32cups = 2gallon
Hence, 32cups = 2 gallon
8)
Since, 16people fit in 6 feet by 8feet
Then, how many people will be fit in the area of 300yard
1yard = 3feet
300yard = 3 x 300feet
300yard = 900feet
Let C be the size of a crowd that is 4 feet deep on ONE side of the street along a 300yards section of a parade route.
16/48 = C/900 x 4
1/3 = C / 3600
C = 3600 / 3
C = 1200people
Hence, the size of the crowd that is 4 feet deep on ONE side of the street along a 300yard section of a parade route is 1200 people
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URGENT!! ILL GIVE
BRAINLIEST! AND 100 POINTS
Jimmy ran 20 meters west
from home and then turned
north to jog 25 meters. Jimmy
ran 45 meters, but could have
arrived at the same point by in
a straight line. How many
meters could he have using a
line distance?
A. 3.5 meters
B7 meters
C. 32 meters
D. 45 meters
Jimmy would've jogged 32.02m if he ran through a straight line by Pythagorean theorem.
What is Pythagorean theorem?
The Pythagorean Theorem states that the squares on the hypotenuse of a right triangle, which is the side that faces the right angle, are equal when added together.This is written as a2 + b2 = c2 in the usual algebraic notation.We can proceed to use this to find the distance from point a to point b assuming he ran through a straight line.
Mathematically, the theorem can be expressed as
x² = y² + z²
Let's substitute the values into the equation and solve
x² = 20² + 25²
x = 32.02m
Jimmy would've jogged 32.02m if he ran through a straight line.
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Is 21 over the square root of 4 a rational or irrational?
The algebraic expression ''21 over the square root of 4'' is a Rational number.
What is square root of a number?
The square root of a number is a value that multiplied by itself gives the same number.
Given that;
The algebraic expression is;
⇒ ''21 over the square root of 4''.
Now,
Since, The algebraic expression is;
⇒ ''21 over the square root of 4''.
It can be written as;
⇒ 21 / √4
⇒ 21 / 2
Since, The number 21 / 2 is of the form p / q where, 2 ≠ 0.
Hence, The number 21 / 2 is a Rational number.
Therefore,
The algebraic expression ''21 over the square root of 4'' is a Rational number.
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Start with 16÷8. Rewrite as an equivalent multiplication expression using the multiplicative inverse of 8.
Using the multiplicative inverse of 8, we will find the equivalent expression:
16*(1/8)
How to rewrite the quotient?
Here we have a quotient.
16/8
And we want to rewrite this as a product by using the multiplicative inverse of number 8.
Remember that for any number x, the multiplicative inverse y is such:
x*y = 1
Solving that for y we get:
y = 1/x
Then the multiplicative inverse of 8 is:
1/8
So, dividing by 8 (like in the quotient) is equivalent to multiply by (1/8), then we can rewrite the quotient as:
16/8 = 16*(1/8)
So the equivalent expression is 16*(1/8)
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to determine whether the relation is a function. {(-6,15). (-12, -10), (-15, 11), (8, -14), (16, 1), (-10, -7)}.
The relation; {(-6,15). (-12, -10), (-15, 11), (8, -14), (16, 1), (-10, -7)} as given in the task content is; a function.
What kind of relation is a function?It follows from the task content that the relation is to be determined as being a function or not.
Since the definition of is such that; a function from a set X to a set Y assigns only one element of Y to each value of X.
In this regard, the set of possible values of x is called the domain of the function while the set y is called the range/codomain of the function.
Hence, since the relation given assigns only one y-value to each x-value, the relation given is therefore a function.
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please help I feel like I get it buy I don't know the answer
To find the area of the figure you can find the area of the figures that make it up and then add these areas, in other words
[tex]A_f=A_r+A_R[/tex]Where
The formula to find the area of a rectangle is
[tex]\begin{gathered} A=l\cdot w \\ \text{ Where A is the area,} \\ \text{l is the length and} \\ w\text{ is the width of the rectangle } \end{gathered}[/tex]So, you have
[tex]\begin{gathered} l_r=3\text{ mm} \\ w_r=1\text{ mm} \\ A_r=l_r\cdot w_r \\ A_r=3\operatorname{mm}\cdot1\operatorname{mm} \\ A_r=3\operatorname{mm}^2 \end{gathered}[/tex][tex]\begin{gathered} l_R=6\text{ mm} \\ w_R=2\text{ mm} \\ A_R=l_R\cdot w_R \\ A_R=6\operatorname{mm}\cdot2\operatorname{mm} \\ A_R=12\operatorname{mm}^2 \end{gathered}[/tex]Finally, adding the areas you have
[tex]\begin{gathered} A_f=A_r+A_R \\ A_f=3\operatorname{mm}^2+12\operatorname{mm}^2 \\ A_f=15\operatorname{mm}^2 \end{gathered}[/tex]Therefore, the area of the figure is 15 square milimeters.
To determine his net worth, Albert has gathered information on all of his assets and liabilities. He has $4,350 in household assets, $400 in liquid assets, and Series EE bonds currently worth $785. Albert only liability is the remaining balance of his car loan, which is $1,250. What is Albert’s net worth?
He has $400 in cash assets, $4,350 in home assets, and $785 worth of Series EE bonds. $4294 money is Albert worth.
Given that,
Albert has gathered data on all of his assets and obligations in order to calculate his net worth. He has $400 in cash assets, $4,350 in home assets, and $785 worth of Series EE bonds. The only debt Albert has is the $1,250 remaining on his auto loan.
We have to find how much money is Albert worth.
To get the Albert worth
Adding the assets
$400+$4359+$785
$5544
Now, we substract
$5544 -$1250
$4294
Therefore, $4294 money is Albert worth.
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