Answer:
As the number of sides of the bases of a prism increases, the shape of the prism becomes more complex and closer in form to a cylinder. For example, a prism with two identical polygonal bases, such as a rectangular prism or a triangular prism, will have a more blocky or pyramidal shape. However, as the number of sides of the base increases, the shape of the prism becomes more cylindrical and less pyramidal in appearance. This is because the more sides a polygon has, the more closely it approximates a circle, and the cross-section of the prism becomes more circular in shape.
When the number of sides of the base of a prism increases, the prism becomes more like a cylinder.
Find the surface area of the following figure. Round your final answer to the nearest
tenth.
The surface area is approximately 41.7 square units.
The rectangle has dimensions 18 units by 6 units, so its area is:
A(rectangle) = l x h = 18 x 6 = 108 square units
The semicircle has a radius of 5 units, so its area is half that of a full circle:
A(semicircle)
= 1/2 x π x r²
= 1/2 x π x 5²
= 1/2 x 25π
= 12.5π
To find the total surface area, we need to add the areas of the rectangle and the semicircle. However, since the semicircle is attached to the top of the rectangle, we need to subtract the area of the portion of the circle that overlaps with the rectangle. This overlapping area is equal to the width of the rectangle (18 units) times half the circumference of the circle (1/2 x π x r), or:
A(overlap)
= w x 1/2 x π x r
= 18 x 1/2 x π x 5
= 45π
Therefore, the total surface area is:
Surface area = A(rectangle) + A(semicircle) - A(overlap) = 108 + 12.5π - 45π ≈ 41.7 square units
Rounding to the nearest tenth, the surface area is approximately 41.7 square units.
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Q1: Use the image to determine the type of transformation shown.
Preimage of polygon ABCD. A second image, polygon A prime B prime C prime D prime to the right of the first image with all points in the same position.
Reflection across the x-axis
90° clockwise rotation
Horizontal translation
Vertical translation
the correct answer is a reflection across the x-axis.
How to solve questions?
Based on the given image, the type of transformation shown is a reflection across the x-axis.
A reflection is a transformation that flips a figure over a line of reflection, in this case, the x-axis. The resulting image is a mirror image of the original figure, with corresponding points on either side of the line of reflection equidistant from it.
In the given image, polygon ABCD is the preimage, and polygon A'B'C'D' is the resulting image. We can see that the two polygons are mirror images of each other across the x-axis. For example, point A in the preimage is reflected across the x-axis to point A' in the resulting image, which is directly below point A. Similarly, point B in the preimage is reflected to point B', point C to C', and point D to D'.
A 90° clockwise rotation would result in a different orientation of the polygon, where point A would move to the position of point B, point B to C, point C to D, and point D to A. A horizontal or vertical translation would result in a shift of the polygon in the respective direction, which is not the case here.
Therefore, the correct answer is a reflection across the x-axis.
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Study the coordinate plane below.
A certain polygon has its vertices at the following points.
(1,8), (4,3), (7,3), and (8,8)
What is the best description of this polygon?
A.
parallelogram
B.
trapezoid
C.
rhombus
D.
square
Reset
Based on the information provided, the polygon can be classified as a trapezoid.
What is the shape of the polygon?A parallelogram has opposite sides parallel and equal in length, but in this case, the sides are not parallel.A rhombus has all sides of equal length but opposite angles are not congruent in this case, so it's not a rhombus.A square has all sides of equal length and all angles are right angles, which is not the case in this polygon.A trapezoid is a quadrilateral with one pair of opposite sides parallel. In this polygon, the bottom side (4,3) to (7,3) is parallel to the top side (1,8) to (8,8), so it is a trapezoid.Learn more about trapezoids in https://brainly.com/question/8643562
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The vectors v and w lie in the coordinate plane such that their initial points are at the origin. Vector v has a magnitude of 2 and direction of 45° North of East. Vector w has a magnitude of 2 and a direction of 45° South of East. What is the magnitude of the vector v+w?
The vector v+w has a magnitude of 2√2 and its direction is along the positive x-axis.
What is meant by vector?
A vector is a quantity that has both magnitude and direction. It is represented as an arrow with its length representing the magnitude and its direction representing the direction of the quantity.
What is meant by the x-axis?
The x-axis is the horizontal line on a coordinate plane that is used as a reference for plotting and describing the positions of points in two-dimensional space. It is often referred to as the "horizontal axis" or the "abscissa".
According to the given information
Here the vector v has a magnitude of 2 and a direction of 45° so the components of vector v are:
v_x = 2 cos 45° = √2
v_y = 2 sin 45° = √2
Vector w has a magnitude of 2 and a direction of 45° South of East. This means that the angle between vector w and the positive x-axis is 45°, and the angle between vector w and the negative y-axis is 45°. Therefore, the components of vector w are:
w_x = 2 cos 45° = √2
w_y = -2 sin 45° = -√2
Now we can add the components of vectors v and w to find the components of the vector v+w:
(v+w)_x = v_x + w_x = √2 + √2 = 2√2
(v+w)_y = v_y + w_y = √2 - √2 = 0
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poppy seed muffins 1
cinnamon rolls 3
bran muffins 2
apple fritters 2
croissants 2
Considering this data, how many of the next 20 pastries served should you expect to be bran muffins?
We can expect 4 of the next 20 pastries served to be bran muffins based on the given data.
What is meant by the term data?
Data refers to a collection of facts, statistics, measurements, or observations that are gathered and analyzed to gain insights or information about a particular topic or subject. Data can be both quantitative (numerical) and qualitative (descriptive) in nature, and it can be obtained from various sources, such as surveys, experiments, sensors, or records. The processing and interpretation of data can lead to new discoveries, trends, or predictions in various fields, including science, business, and technology.
According to the given information
The proportion of bran muffins out of the total pastries served can be calculated by dividing the number of bran muffins by the total number of pastries:
The proportion of bran muffins = 2 / (1 + 3 + 2 + 2 + 2) = 2 / 10 = 0.2
This means that 20% of the pastries served are bran muffins. To find out how many of the next 20 pastries served should be expected to be bran muffins, we can multiply 20% by 20:
The number of expected bran muffins = 0.2 * 20 = 4
Therefore, we can expect 4 of the next 20 pastries served to be bran muffins based on the given data.
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ction: Fill each blank with the correct answer.
1. The method in identifying part of the respondents of the
Study.
2. The samples are selected based on availability.
3. A technique that divides the elements of the population into small
subgroups(strata) based on the similarity in such a way that the
elements within the group are homogenous and heterogeneous
among the other subgroups formed.
4. It is based on the intention or the purpose of the study.
5. This type of sampling depends on some pre-set standard. It selects
the representative sample from the population.
6. A technique that uses randomization to make sure that every
element of the population gets an equal chance to be part of the
selected sample.
7. It is used in situations where the population is completely unknown
and rare.
8. It is guided specifically by a hypothesis.
9. A systematic subjective approach used to describe life experiences
and give them meaning. To gain insight, explore depth, richness and
complexity inherent in the phenomenon.
10. An objective, systematic empirical investigation of observable
phenomena through the use of computational techniques.
Step-by-step explanation:
1. Quota Sampling: This method involves identifying specific subgroups of respondents that need to be included in the study in a specific proportion to the population.
2. Convenience Sampling: This sampling technique involves selecting the sample based on the availability of participants at the time of the study.
3. Stratified Sampling: This technique divides the population into subgroups or strata based on similarities, with the elements within each group being relatively homogeneous and heterogeneous among the other subgroups.
4. Purposive Sampling: This type of sampling is based on the intention or purpose of the study, and the sample is selected based on the researcher's judgment or knowledge of the population.
5. Judgment Sampling: This sampling technique depends on some pre-set standards, and the representative sample is selected based on the researcher's judgment or experience. 6. Simple Random Sampling: This technique involves using randomization to ensure that every element of the population has an equal chance of being selected for the sample. 7. Snowball Sampling: This sampling method is used in situations where the population is completely unknown or rare, and it relies on referrals from the initial participants to identify subsequent participants.
8. Hypothesis Sampling: This type of sampling is guided specifically by a hypothesis, and the sample is selected based on the research question being asked.
9. Qualitative Sampling: This technique is used in qualitative research and involves a systematic, subjective approach used to describe life experiences and give them meaning.
LO. Quantitative Sampling: This technique involves an objective, systematic, empirical investigation of observable phenomena through the use of computational techniques.
35 Points! Multiple choice. State the domain and range of the function graphed. Photo attached. Thank you!
Domain and range of function is (D)=D={x|x≥2}, R={y|y≥0}.
Define domain and range of functionIn mathematics, the domain of a function is the set of all possible input values for which the function is defined. The range of a function is the set of all possible output values that the function can produce, based on its input values. In other words, the domain is the set of all x-values that the function can take, while the range is the set of all corresponding y-values that the function can take.
The given graph is oriented toward x direction
Domain of function =x≥2
For every value of x the y is always positive
So, range =y≥0
Hence, domain and range of function is (D)=D={x|x≥2}, R={y|y≥0}
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If 31.2 out of every 100 pregnant women in Indiana deliver their babies by C-section, how many pregnant women out of 85,733 would be expected to deliver by C-section?
If 31.2 out of every 100 pregnant women in India deliver their babies by C-section.
First, we need to find the fraction of pregnant women who deliver by C-section
31.2 out of 100 = 31.2/100 = 0.312
Then, we can use this fraction to find the number of pregnant women out of 85,733 who would be expected to deliver by C-section.
0.312 x 85,733 = 26,723.896
Rounding to the nearest whole number, we get
26,724 pregnant women.
26,724 pregnant women out of 85,733 would be expected to deliver by C-section.
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What should be added to
[tex] \frac{17}{24} [/tex]
get
[tex] \frac{ - 5}{12} [/tex]
Answer:
See the below process
Step-by-step explanation:
let the Unknown value be x.
Now
[tex] \frac{17}{24} + x = \frac{ - 5}{12} [/tex]
[tex]x = \frac{ - 5}{12} - \frac{17}{24}[/tex]
Taking LCM
[tex]x = \frac{ - 10 - 17}{24} [/tex]
[tex]x = \frac{ - 27}{24} \\ = \frac{8}{9} [/tex]
we should add 8/9 to 17/24 to get -5/12
I hope it helped you
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what is 5x-9 and 3x+9
Answer:
5x - 9 and 3x + 9 are two mathematical expressions. The first expression, 5x - 9, represents a value obtained by multiplying 5 by x and then subtracting 9. The second expression, 3x + 9, represents a value obtained by multiplying 3 by x and then adding 9. Both expressions can be simplified further or used in various mathematical operations depending on the context of the problem or equation in which they are being used.
Answer:-45 and -3
Step-by-step explanation:
for justin beibers part only pls help
On day zero, the number of students who know the rumor are 2 people who are Susanna and Liz.
On day 2, the number of students would be 12 students.
The number of days till 32 students know the rumor is 6 days.
2 students (Susanna and Liz) know the rumor on day 0.
On day 2, the number of students who know the rumor will be the initial number of students (2) plus 5 students for each day that has passed (5 * 2 = 10). So, on day 2, 2 + 10 = 12 students know the rumor.
To find the number of days it will take for 32 students to know the rumor, we can set up an equation using the given information:
2 (Susanna and Liz) + 5 x number of days = 32
Now, we can solve for the number of days:
5 x number of days = 32 - 2
5 x number of days = 30
number of days = 30 / 5
number of days = 6
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On July 26, 2005, it rained a record
37 inches in Mumbai, India, in a 24-hour
period. Which equation of direct
variation relates the number of inches
of rain y to the number of hours x?
F. y=24/37x
G.y=37/24x
H.y=24x
J.y=37x
G. y = 37/24x
Direct variation means that the number of inches of rain (y) is directly proportional to the number of hours (x). In this case, 37 inches of rain fell in a 24-hour period. To find the constant of proportionality, divide the total inches of rain by the total hours:
k = 37 inches / 24 hours
Now, we can write the equation of direct variation:
y = kx
Substitute the value of k:
y = (37/24)x
You have 7 people in a work group if you each worked 38 hours last week how many total hours worked by the group
Answer:
266
Step-by-step explanation:
36 hours x 7 people.
Hope this helps...
Please mark me brainliest.
Answer: 266 hours
Step-by-step explanation:
38 x 7 = 266 hours. Each worker worked 38 hours, and there are 7 people. So, multiply worker by time.
The length of one side of a golden rectangle is 4.9 metersFind the length of the other side that the other side could be other longer or shorter than the given side
The length of the other side will be 3.
How to obtain the lengthTo obtain the length of the other side of the rectangle, given the approximation of 1.62, we will first divide 4.9, the known side by x, the unknown side, and equate this to 1.62.
If we are using the approximation of 1.62, then the length of the other side of the rectangle will be 4.9/x = 1.62
1.62x = 4.9
x = 3
So, the length of the other side, which in this case is shorter is 3.
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Pls help with this homework pls
Answer: 480 in²
Step-by-step explanation:
To calculate the surface area, we will find the area of each side and add it together.
Area of the rectangular sides can be found with A = LW:
A = LW
A = (12 in)(10 in)
A = 120 in²
A = LW
A = (12 in)(10 in)
A = 120 in²
A = LW
A = (12 in)(12 in)
A = 144 in²
All the rectangular sides added together:
120 in² + 120 in² + 144 in² = 384 in²
Now, we will find the triangle sides. The formula for a triangle is [tex]A=\frac{BH}{2}[/tex], but since we have two congruent triangles I will not be dividing by 2.
A = BH
A = (12 in)(8 in)
A = 96 in²
Lastly, I will add them both together:
384 in² + 96 in² = 480 in²
What is 7x7 using an exponent
Answer:
7²
Step-by-step explanation:
You want to know what 7×7 is when it is written using an exponent.
ExponentAt its most basic, an exponent signifies repeated multiplication. It represents the number of times a value appears as a factor in the product.
The expression 7×7 has 7 as a factor 2 times. It can be written as 7 with an exponent of 2.
7×7 = 7²
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Select the correct answer. Which expression is equivalent to the given expression? (6n^-5)(3n^-3)^2
The equivalenet expression is 54[tex]n^{-11}[/tex]
What is expression?Any mathematical statement that includes numbers, variables, and an arithmetic operation between them is known as an expression or algebraic expression.
What is exponent?The way of representing huge numbers in terms of powers is known as an exponent. Exponent, then, is the number of times a number has been multiplied by itself.
To simplify the given expression, we need to apply the power of a power rule, which states that to raise a power to another power, we need to multiply the exponents.
Starting with:
([tex]6n^-5[/tex])([tex]3n^-3[/tex])²
We can simplify as follows:
([tex]6n^-5[/tex])([tex]9n^-6[/tex])
Now, we can use the product of powers rule, which states that when multiplying two powers with the same base, we add their exponents.
Therefore:
6 x 9 = 54
[tex]n^-5 * n^-6 = n^-11[/tex]
So the simplified expression is:
[tex]54n^-11[/tex]
Therefore, the expression [tex](6n^-5)(3n^-3)^2[/tex] is equivalent to [tex]54n^-11.[/tex]
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The expression that is equal to (6n-5)(3n-3) option D, 54n11.
What is expression?Mathematical expressions consist of at least two numbers or variables, at least one arithmetic operation, and a statement.
We can use the distributive property of multiplication to expand the expression (6n - 5)(3n - 3) as follows:
(6n - 5)(3n - 3) = 6n(3n) - 6n(3) - 5(3n) + 5(3)
= 18n² - 18n - 15n + 15
= 18n² - 33n + 15
Therefore, the expression that is equivalent to (6n - 5)(3n - 3) is 18n² - 33n + 15, which is option D.
So, the answer is option D, 54n11.
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Is (9,8) a solution to this system of equations?
6x - 5y = 16
X = 9
yes
no
Calculate the length of IG. *
3
square root 20
square root 50
square root 10
square root 25
The length of LG in the plane is
square root 50How to find the length of LGTo find the distance between two points in a 2D plane, we can use the distance formula:
distance = √((x2 - x1)^2 + (y2 - y1)^2)
Using this formula, we can find the distance between L(4,4) and G(9,9):
distance = √((9 - 4)^2 + (9 - 4)^2)
= √(5^2 + 5^2)
= √50
= 5√2
Therefore, the distance between L(4,4) and G(9,9) is 5√2, which is approximately 7.07 units.
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How many times smaller is 1.2 × 106 than 1.47 × 107?
Answer: It is 1.24x smaller.
Step-by-step explanation:
1.2(106)= 127.2
1.47(107)= 157.3
157.3/127.2 = 1.24x smaller
2) (8.7A) The volume of the prism shown is 241.92 in. What is the height of the prism?
Enter your answer in the box.
5.6 in.
5.4 in.
The height of the rectangular prism is 8 inches.
What is the height of the rectangular prism?A rectangular prism is simply a three-dimensional solid shape which has six faces that are rectangles.
The volume of a rectangular prism is expressed as;
V = w × h × l
Where w is the width, h is height and l is length
Given that:
Volume V = 241.92 in³
Length l = 5.6 in
Width w = 5.4 in
Height h = ?
Plug the given values into the above formula and solve for h
V = w × h × l
h = V / ( w × l )
h = 241.92 in³ / ( 5.4 in × 5.6 in )
h = 8 in
Therefore, the height is 8 inches.
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Need the answer quickly!!!
Matching each function with the transformation that took place gives:
g(x) = -(x - h)ⁿ: Reflection across the x-axis
j(x) = axⁿ + k: Translation of k units up
m(x) = (x + h)ⁿ - k: Translation of h units to the left
Vertical dilation: Functions of form f(x) = 2ⁿ are vertically dilated.
What is transformation?In mathematics, a transformation refers to a process of changing the size, position, or orientation of a geometric object or a function.
Transformations are usually expressed as a set of rules or equations that determine how each point or element in the original object or function maps to a corresponding point or element in the transformed object or function. Common types of transformations include translations, rotations, reflections, dilations, and combinations of these operations.
Transformations are widely used in many areas of mathematics, physics, engineering, and computer science to study and model complex systems and phenomena.
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Consider the following.
f(x) = x^5 − x^3 + 4, −1 ≤ x ≤ 1
(a) Use a graph to find the absolute maximum and minimum values of the function to two decimal places.
The function has a local maximum at x = 1 and a local minimum at x = 1/5, as shown in the graph, and the absolute maximum and minimum occur at x = 0 and x = (3/5), respectively.
what is function?Numbers and their variants, equations and related structures, forms and their arrangements, and the places where they might be found are all topics covered in mathematics. The term "function" describes the relationship between a collection of inputs, each of which has a corresponding output.
A function is an association between inputs and outputs that yields one unique outcome for each input. Every function has a domain and a codomain, often known as a scope. Functions are commonly represented with the letter f. (x). As input, an x is used. On functions, one-to-one functions, many-to-one functions, within functions, and on functions are the four fundamental types of functions available.
To obtain the absolute maximum and lowest values of the function over the interval −1 ≤ x ≤ 1, we must examine the critical points and the interval endpoints.
We first take the derivative of f(x) and set it to zero to determine the critical points:
The function is then assessed at these pivotal points and the interval's endpoints:
As we can see from the information above, f(x) has a maximum value of 4 and occurs at the values x = 0 and x = 1. The absolute minimum value of f(x) is approximately 2.65 for x = (3/5).
We can corroborate these findings by charting the graph of f(x) across the 1 x 1 interval: graph of f(x) = x5 x3 + 4
According to the graph, the function has a local maximum at x = 1 and a local minimum at x = 1/5, but the absolute maximum and lowest are, respectively, x = 0 and x = (3/5).
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The probability that the friend is at least 22 minutes late is
The probability that the friend is at least 22 minutes late is 0.266
Uniform density function for a friend = x minutes late
The Friend is at least 21 minutes late
Based on the above information, the probability that the friend is at least 21 minutes late is
= (Total minutes - minimum minutes)/Total minutes
=30-22/30
=8/30
=0.266
Based on the above formula we can easily find out the probability for the friend who is at least 22 minutes late
Hence, the probability that the friend is at least 22 minutes late is 0.266
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Which step is missing?
OA.
ADCA
ADCA
OC. ADAC
OD. ADAC
B.
ABCA by ASA
ABCA by SAS
ABCA by SAS
ABCA by ASA
The missing step in the two column proof is
Statement Reason
Δ DAC ≅ ΔBCA ASA congruence theorem
What is ASA theorem?The ASA theorem, also known as the angle side angle theorem, is a rule used in geometry to determine whether two triangles are congruent (meaning they have the same shape and size).
The angle side angle theorem states uses the side two parameters which includes:
angle and included sideThe parameters are used for the theorem to say that if two angles and the included side of one triangle are congruent to two angles and the included side of another triangle, then the two triangles are congruent.
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Hallar la ecuación de la parábola cuya directriz es la recta x= - 6 y su foco es F(0,0).
The required equation of the parabola is y² = 24x for focus (6,0) and directrix x= -6 .
The focus and directrix of the required parabola are as,
Focus (6, 0)
and, Directrix x = - 6
Since the focus of the parabola lies on the x- axis, the x- axis is said to be the axis of the parabola.
Therefore, the equation of the parabola is either of the form,
y² = 4ax
or, y2 = - 4ax
depending on which axis the parabola is in, that is whether negative or positive axis.
It is also seen that the directrix, x = - 6 which implies it is to the left of the y- axis while the focus is (6, 0) which implies it is to the right of the y-axis.
Hence, the parabola is of the form y² = 4ax.
Since, a = 6
Thus, the equation of the parabola is y² = 4(6)x
⇒ y² = 24x
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Enter the value for x that makes the equation 3(2x+5)=x-10 true.
Answer:
Step-by-step explanation:
6x + 15 = x - 10
5x + 15 = -10
5x = -25
x = -5
89, 93, 54, 64, 91, 103, 46, 64, 82, 123, 112, 99
1188
median :
mean
mode
range
Let uequals
Start 3 By 1 Table 1st Row 1st Column 4 2nd Row 1st Column 20 3rd Row 1st Column 8 EndTable
and Aequals
Start 3 By 2 Table 1st Row 1st Column 5 2nd Column negative 3 2nd Row 1st Column negative 2 2nd Column 6 3rd Row 1st Column 1 2nd Column 1 EndTable
.
Is u in the plane in set of real numbers R
cubed
spanned by the columns of A? Why or why not?
Question content area bottom
Part 1
Select the correct choice below and fill in the answer box to complete your choice.
(Type an integer or decimal for each matrix element.)
A.
Yes, multiplying A by the vector enter your response here
writes u as a linear combination of the columns of A.
B.
No, the reduced echelon form of the augmented matrix is enter your response here
,
which is an inconsistent system.
U is located in the plane or vector that A's columns span.
Describe vector?A mathematical concept with both magnitude and direction is a vector. It is frequently used to symbolise forces like the gravitational pull of an object or the electrical forces that exist between charged particles. It can be expressed mathematically as a line segment with two ends, a direction, and a magnitude.
Part 1
To calculate the resulting vector, vector operations including addition, subtraction, multiplication, and division can be used. The individual x, y, and z components of a vector—which stand for its magnitude and direction—can also be determined.
Part 2
Why the answer in Part 1 is correct?
Part 1's answer I gave was A. Yes, writing u as a linear combination of the columns of A after multiplying A by the vector [4, 20, 8]. This is so because the vector [4, 20, 8] may be expressed as a linear combination of the columns of A since it is a solution to the system of linear equations generated by the augmented matrix [A|u]. U is thus in the plane that is covered by the columns of A.
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Joan has a square flower bed with a side length of 4 meters filled with tulips. There are a total of 354 tulips in the bed.
Find the density of tulips for the area of the bed. Round to the nearest tenth if necessary.
If Joan has a square flower bed with a side length of 4 meters filled with tulips, the density of tulips in the bed is 22.1 tulips per square meter.
To find the density of tulips for the area of the bed, we need to divide the total number of tulips by the area of the bed. The area of the square flower bed is the side length squared, so in this case, it is 4 meters x 4 meters = 16 square meters.
So, the density of tulips in the bed is 354/16 ≈ 22.1 tulips per square meter. This means that there are approximately 22.1 tulips growing in every square meter of the flower bed.
The density is a measure of the amount of something per unit of space, so in this case, it is the number of tulips per square meter. It is a useful metric for understanding how many of something is present in a given area, which can be important for planning and management purposes.
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