1. Yearly total dividends paid are $151,250.
2. The dividends per share are $1.25 for common stockholders
3. The dividends per share are $4 for preferred stockholders.
What are yearly total dividends and dividends per share?We must calculate amount of dividends paid to the preferred stockholders in order to get dividends per share for common and preferred stockholders.
The per dividends paid to the preferred stockholders is:
= $50 par value x 8% guaranteed rate of return
= $4 per share
The total dividends paid to preferred stockholders:
= $4 per share x 5,000 shares
= $20,000
The per dividends paid to those stockholder is calculated as:
= Common stock + Preferred stock
= $1.25 per share + $4 per share
= $5.25 per share
The total dividends paid to common stockholders:
= $5.25 per share x 25,000 shares
= $131,250.
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So-hee and Ethan are at the arcade in the amusement park. They play a game in which they earn points by collecting coins and gems. So-hee collects 3 coins and 5 gems for a total of 70 points. Ethan collects 6 coins and 2 gems for a total of 52 points. How many points is 1 coin worth? How many points is 1 gem worth?
please help meee
The answer of the given question based on the equation problem is , one coin is worth 5 points and one gem is worth 11 points.
What is Equation?An equation is the mathematical statement that shows equality between the two expressions. It consists of two parts: the left-hand side (LHS) and the right-hand side (RHS), separated by an equals sign (=). The LHS and RHS may contain one or more variables, constants, mathematical operations, and functions.
Let's denote the value of one coin by x and the value of one gem by y. We can set up two equations based on the given information:
3x + 5y = 70 (equation 1)
6x + 2y = 52 (equation 2)
We can use these equations to solve for x and y. One way to do this is to multiply equation 2 by 5 and subtract it from equation 1 multiplied by 2:
6x + 10y = 140 (equation 1 multiplied by 2)
-30x - 10y = -260 (equation 2 multiplied by 5, with signs flipped)
-24x = -120
x = 5
Now that we know that one coin is worth 5 points, we can substitute this value into either of the original equations to solve for y. Let's use equation 1:
3(5) + 5y = 70
15 + 5y = 70
5y = 55
y = 11
Therefore, one gem is worth 11 points.
In summary, one coin is worth 5 points and one gem is worth 11 points.
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(solve for h) geometry
The value of h in the right triangle is 3 units.
How to find the side of a right triangle?A right angle triangle is a triangle that has one of its angles as 90 degrees. The sum of angles in a triangle is 180 degrees.
Therefore, let's find h in the right triangle as follows:
Let's find the angle.
cos ∅ = adjacent / hypotenuse
cos ∅ = 6 / 6.5
∅ = cos⁻¹ 0.92307692307
∅ = 22.6208962498
Therefore,
sin 22.62° = h / 7.8
cross multiply
h = 7.8 × sin 22.62°
h = 7.8 × 0.3846175604
h = 3.00001697112
h ≈ 3 units
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Given that x = 7.7 m and = 25°, work out AB rounded to 3 SF. B A X 0⁰ C
Given that x = 7.7 m and = 25° the value of AB is given as 3.254
How to solve for ABWe have the following data to work with
x = 7.7 m and = 25°,
then we have sin 25 = ∅ = 25 degrees
sin 25 = ab / 7.7
cross multiply from here
AB = sin25 x 7.7
= 0.4226 x 7.7
= 3.254
Hence we would say that in the triangle if x = 7.7 m and = 25°, the value of AB would be solved to be 3.254
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The function f(x) = 1.62x² models
the cost of a square carpet, where
x is the length in feet. Find the
average rate of change for f, to the
nearest tenth, over the interval
15 ≤ x ≤ 25. Explain your steps.
Answer:
Step-by-step explanation:
use integration
A device used to come in four models, each with nine colors to choose from. How many combinations were possible? (Select all that apply. )
n(A ⨯ B) = n(A)n(B)
n(A') = n(S) − n(A)
n(A) = number of elements in A
n(A ∪ B) = n(A) + n(B) − n(A ∩ B)
There are 36 possible combinations of the four models and nine colors to choose from.
To find the total number of combinations possible, we can use the formula: n(A ⨯ B) = n(A) x n(B), where n(A) is the number of models and n(B) is the number of colors to choose from.
In this case, there are four models and nine colors to choose from for each model. Therefore, the number of combinations possible would be:
n(A ⨯ B) = 4 x 9 = 36
So there are 36 possible combinations. This can also be calculated by using the formula n(A') = n(S) - n(A), where n(A') is the complement of the set A, n(S) is the total number of possible options, and n(A) is the number of options we are not interested in.
In this case, the complement of the set A (which represents all possible combinations) would be the empty set, since we are interested in all possible combinations. Therefore, n(A') = 0, and n(S) = 36.
We could also use the formula n(A ∪ B) = n(A) + n(B) - n(A ∩ B), where n(A ∪ B) represents the total number of options in both set A and set B, n(A) is the number of options in set A, n(B) is the number of options in set B, and n(A ∩ B) is the number of options that are common to both set A and set B.
In this case, we could consider set A to be the four models, and set B to be the nine colors for each model. The intersection of set A and set B would be the combinations where each model is paired with a specific color. Therefore, n(A ∩ B) = 4 x 9 = 36.
Using the formula, we can find the total number of options:
n(A ∪ B) = n(A) + n(B) - n(A ∩ B)
n(A ∪ B) = 4 + 9 x 4 - 36
n(A ∪ B) = 36
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Solve for z : 15 = − 45
Answer:
z = -675
Step-by-step explanation:
z : 15 = -45
For that, we can change it into
z/15 = -45
z = -45*15
z = -675
The volume of the prism is 90 cubic meters. Find the value of x.
x=
Answer: 5 meters
Step-by-step explanation:
volume of a rectangular prism: V=whl
90=6*h*3
h=90/(6*3)
h=90/18
h=5 meters
the volume of a large aquarium is 625 ft³ . It is 16[tex]\frac{2}{3}[/tex] wide and 3[tex]\frac{1}{3}[/tex] high. What is the length of the aquarium.
Length of the aquarium is 11.25 ft
We have,
Volume of the aquarium = 625 ft³
given by
Volume = length × width × height.
Width = 16 2/3 ft
= 50/3
and Height = 3 1/3 ft
= 10/3 ft
Length = Volume/Width × Height
= 625/ 50/3 × 10/3
= 625/ 500/9
= 11.25 ft
Hence, Length of the aquarium is 11.25 ft
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Is brainly freee for students the whole time they use it?
Answer:
there is brainly free and other options if you do not want to watch ads. but it is free if you do not want to upgrade.
Step-by-step explanation:
Answer:
yes
Step-by-step explanation:
A volume of a cone is 37.7 cubic inches, and its height is 4 inches. Find the diameter of the base of the cone.
Answer:
Approximately 5.988 inches
Step-by-Step Explanation:
The formula for the volume of a cone is:
V = (1/3)πr^2h
where V is the volume, r is the radius of the base, h is the height, and π is the mathematical constant pi.
We are given that the volume of the cone is 37.7 cubic inches, and the height is 4 inches. We can plug these values into the formula and solve for the radius:
37.7 = (1/3)πr^2(4)
37.7 = (4/3)πr^2
r^2 = (37.7 x 3) / (4 x π)
r^2 = 8.9717
r ≈ 2.994 inches
Now that we know the radius of the base, we can find the diameter by doubling the radius:
d = 2r ≈ 5.988 inches
Therefore, the diameter of the base of the cone is approximately 5.988 inches.
Given two cones of the same height, the first has a radius of 8 inches and the second has a radius of 12 inches with a height of 9 inches.
How much more water can the second cone hold than the first cone? Round your
answer to the nearest hundredth.
603.19 in.3
753.98 in.3
1,357.17 in.3
1,960.36 in.3
Answer :
753.98 in³Step-by-step explanation:
According to the question It's given that :
Two cones of the same height, the first has a radius of 8 inches and the second has a radius of 12 inches with a height of 9 inches.
Here,
Radius of 1st cone = 8 inchesRadius of 2nd cone = 12 inchesSince, Both the cones are of the same height.
Height of 1st cone = 9 inchesHeight of 2nd cone = 9 inchesFormula of volume of cone = 1/3 πr²h
where,
π = 3.14 r = radius h = heightFor first cone,
[tex] \implies [/tex] Volume = 1/3 × 3.14 × (8)² × 9
[tex] \implies [/tex] 1/3 × 3.14 × 64 × 9
[tex] \implies [/tex] 1/3 × 3.14 × 576
[tex] \implies [/tex] 1/3 × 1808.64
[tex] \implies [/tex] 602.88 in³
For second cone,
[tex] \implies [/tex] Volume = 1/3 × 3.14 × (12)² × 9
[tex] \implies [/tex] 1/3 × 3.14 × 144 × 9
[tex] \implies [/tex] 1/3 × 3.14 × 1296
[tex] \implies [/tex] 1/3 × 4069.44
[tex] \implies [/tex] 1356.48 in³
Now, How much more water can the second cone hold than the first cone?
Volume of 2nd cone - Volume of 1st cone
[tex] \implies [/tex] 1356.48 - 602.88
[tex] \implies [/tex] 753 (approximately)
Therefore, 753.98 in³ is the answer .
nicole is flying two kites. she has 97 feet of string out to one kite and 115 feet out to the other kite. the angle formed by the two strings is 28 degrees. find the distance between the kites
The distance between the two kites is approximately 145.8 feet.
The Law of Cosines is a trigonometric formula that relates the sides and angles of a triangle. Specifically, it relates the length of one side of a triangle to the other two sides and the angle between them
We can use the Law of Cosines to solve for the distance between the two kites. Let's call the distance between the kites "d".
From the problem statement, we have two sides of the triangle formed by the two strings (97 feet and 115 feet) and the included angle (28 degrees). We can use the Law of Cosines to solve for the third side
d^2 = 97^2 + 115^2 - 2(97)(115)cos(28)
Using a calculator, we get
d² ≈ 21251.4
Taking the square root of both sides, we get
d ≈ 145.8 feet
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Hello this is my first time on brainly and I saw you could get some help with assignments so this is what I need help with.and Thank you:
A skewed distribution is neither symmetrical nor normal as the data values trail off more sharply on one side than on the other. It occurs due to the lower or upper bounds on data. In symmetric distribution left and right sides mirror each other.
a. The given data distribution is skewed as the data is not even on either side.
b. The median is defined as the middle value of a data set. Here 20 is the median as it is the mid point.
c. The average of the given numbers is known as mean and it is obtained by dividing sum of numbers divided by total numbers.
Mean = 207 / 11 = 18.81
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a ball is drawn randomly from a jar that contains 6 red balls, 7 white balls, and 8 yellow balls. find the probability of the given event. write your answers as reduced fractions or whole numbers.
The probability of drawing a white ball is 0.4, then drawing a red ball probability is 0.3, and drawing a yellow ball or a red ball probability is 0.6.
Given data:
Number of red balls = 6
Number of yellow balls = 6
Number of white balls = 8
Number of balls in a jar = n = 6 + 8 +6 = 20 balls
Where assume that:
R = event where you draw a red ball.
W =event where you draw a white ball.
Y = event where you draw a yellow ball.
P(R) = 6/20 = 3/10 = 0.3
P(W) = 8/20 = 2/5 = 0.4
P(R) or P(Y) = P(Y) + P(R) - P(Y or R)
= 6/20 + 6/20 - 0
= 12/20
= 3/5 = 0.6
Therefore, The probability of drawing a red ball is 0.3, a white ball is 0.4, and a yellow ball or a red ball is 0.6.
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Monticello, located in Charlottesville, was the home to Thomas Jefferson. The entrance hall in Monticello is shaped like a rectangular prism with the approximate dimensions shown.
How would the volume of the entrance hall change if the height of this room is doubled?
A It would be half the original volume.
B It would be doubled the original volume.
C It would be doubled the original volume.
D It would be triple the original volume.
Answer:
C: It would be double the original volume.
Step-by-step explanation:
The volume of a rectangular prism is given by the formula:
Volume = length × width × height
If the height of the rectangular prism is doubled, then the new volume would be:
New volume = length × width × (2 × height)
= 2 × (length × width × height)
= 2 × (original volume)
Therefore, if the height of the entrance hall is doubled, the new volume would be double the original volume.
So the answer is option C: It would be double the original volume.
I do not understand what do I have to do here
Step-by-step explanation:
I think u have to find the degrees of x
The value of x in the figure is,
⇒ x = 65 degree
What is mean by Triangle?A triangle is a three sided polygon, which has three vertices and three angles which has the sum 180 degrees.
Now, We can formulate;
The value of third angle in first triangle is,
180 - (50 + 62)
180 - 112
68 degree
And, The value of third angle in second triangle is,
180 - (53 + 80)
180 - 133
47 degree
Thus, The value of third angle in mid triangle is,
180 - (47 + 68)
180 - 115
65 degree
So, By definition of vertically opposite angle is,
⇒ x = 65 degree
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two sides of a right triangle measure 8 inches and 9 inches find the two possible lengths of the third side
c =
a
sin(α)
= 51.13963
b = √c2 - a2
= √51.1396257719972 - 82
= √2551.2613240999
= 50.51001
∠β = 90° - ∠α
= 81° = 1.41372 rad = 9/20π
area =
a × b
2
=
8 × 50.5100121174
2
= 202.04005
perimeter = a + b + c
= 8 + 50.5100121174 + 51.139625771997
= 109.64964
inradius =
a × b
a + b + c
=
404.0800969392
109.6496378894
= 3.68519
circumradius =
c
2
=
51.139625771997
2
= 25.56981
Please help me with this homework
Answer:
36 cm²
Step-by-step explanation:
Area of a triangle = 1/2bh = 1/2(9)(8) = 36
x^2+12x+35
work required
The solution or roots of this quadratic function are x = -7 and x = -5.
What is the general form of a quadratic function?In Mathematics and Geometry, the general form of a quadratic function can be modeled and represented by using the following quadratic equation;
y = ax² + bx + c
Where:
a and b represents the coefficients of the first and second term in the quadratic function.c represents the constant term.Next, we would solve the quadratic function by using the factorization method as follows;
x² + 12x + 35 = 0
x² + 7x + 5x + 35 = 0
x(x + 7) + 5(x + 7) = 0
(x + 7)(x + 5) = 0
x = -7 or x = -5.
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Write a sentence that describes the distribution of the data shown on the dot plot.
OFFERING 50 points HELP PLEASE
There's a picture too
The distribution of the data shown on the dot plot is Skewed.
We have to given that;
The data shown on the dot plot.
Now, We know that;
A graph is symmetric if the left and right side of the graph are mirror images of each other. A graph is skewed if it has more data on one side rather than the other.
Here, it has more data on one side rather than the other.
Hence, the distribution of the data shown on the dot plot is Skewed.
Thus, the distribution of the data shown on the dot plot is Skewed.
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Which is a diagonal through the interior of the cube?
C
G
O AH
EL-
Mark this and return
-
D
H
B
F
Save and Exit
Mext
Subm
AH is the diagonal of the cube through the interior.
Option A is the correct answer.
We have,
A diagonal through the interior of a cube refers to a straight line that passes through the interior of the cube and connects two opposite corners of the cube.
It does not lie on any of the faces of the cube but passes through the center of the cube.
From the cube,
The diagonal through the interior of the cube is:
AH, CF, BG, and DE.
Thus,
AH is the diagonal of the cube through the interior.
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A random sample of 100 middle schoolers were asked about their favorite sport. The following data was collected from the students.
Sport Baseball Basketball Tennis Soccer
Number of Students 17 12 27 44
Which of the following graphs correctly displays the data?
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled basketball going to a value of 17, the second bar labeled baseball going to a value of 12, the third bar labeled soccer going to a value of 27, and the fourth bar labeled tennis going to a value of 44
bar graph with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
Answer:
The second answer: histogram with the title favorite sport and the x axis labeled sport and the y axis labeled number of students, with the first bar labeled baseball going to a value of 17, the second bar labeled basketball going to a value of 12, the third bar labeled tennis going to a value of 27, and the fourth bar labeled soccer going to a value of 44
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A spherical hot-air balloon has a diameter of 55 feet . When the balloon is inflated , the radius increases at a rate of 1.5 feet per minute .
The amount of time it would take to inflate the balloon to two-thirds of its maximum volume is 16 minutes.
How to calculate the volume of a sphere?In Mathematics and Geometry, the volume of a sphere can be calculated by using the following mathematical equation (formula):
Volume of a sphere = 4/3 × πr³
Where:
r represents the radius.
Note: Radius = diameter/2 = 55/2 = 27.5 feet.
For maximum volume, we have the following:
V ∝ R³
2/3V = v
2/3R³ = r³
r = 27.5 × ∛(2/3)
Radius, r = 24
Since the radius of this spherical hot-air balloon increases at a rate of 1.5 feet per minute, time to reach a radius of 24 feet can be calculated as follows;
Time = 24/1.5
Time = 16 minutes
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Complete Question:
A spherical hot-air balloon has a diameter of 55 feet. When the balloon is inflated, the radius increases at a rate of 1.5 feet per minute. Approximately how long does it take to inflate the balloon to Two-thirds of its maximum volume? Use π = 3.14 and V = four-thirds pi r cubed.
Solve for X.
Z=(x+h)k
Answer:
Step-by-step explanation:
You have to try to eliminate all the other variables and isolate 'x':
Z=(x+h)k
Subtract 'h' from both sides:
Z-h=x(k)
Divide 'k' from both sides:
[tex]\frac{Z}{k} -h[/tex]
So, [tex]x=\frac{Z}{k}-h[/tex].
Find an equation in slope-intercept form for the line passing through each pair of points: (-4, 4), (-5, -3)
Answer:
y = 7x + 32
Step-by-step explanation:
The general equation of the slope-intercept form is
y = mx + b, where x and y are any point on the linem is the slope (change in y / change in x) and b is the y-intercept (point at which the line intersects the y-axis)Given two points which line on the same line, we can find the slope, m, using the slope formula, which is
[tex]m=\frac{y_{2} -y_{1} }{x_{2}-x_{1} }[/tex],
where x1 and x2 are one of the points on the line and y1 and y2 are the other point.If we allow (-4, 4) to be our x1 and x2 point and (-5, -3) to be our y1 and y2 point, we can find the slope by plugging the points into the slope formula:
[tex]m=\frac{-3-4}{-5-(-4)}\\ \\m=\frac{-7}{-5+4}\\ \\m=\frac{-7}{-1}\\ \\m=7[/tex]
Since we now know the slope, we can b, the y-intercept by plugging in any of the two points for x and y and the slope (7) and solving for b:
Let's try the first point (-4, 4):
4 = 7(-4) + b
4 = -28 + b
32 = b
Thus, the equation of the line passing through the points (-4, 4) and (-5, -3) in slope-intercept form is y = 7x + 32
You are surveying students to find out whir opinion of the quality of food served in the school cafeteria. You decide to poll only those students who buy hot lunch on a particular day. Is your sample random? Explain.
Answer:
The sample is not random because he only poll the person that bought a hot lunch on a particular day and not random people so the sample is not random.
Disjoint vs. independent. In parts (a) and (b), identify whether the events are disjoint, independent, or neither (events cannot be both disjoint and independent) (a) You and a randomly selected student from your class both earn A's in this course. (b) You and your class study partner both earn A's in this course. (c) If two events can occur at the same time, must they be dependent?
a) Independent
b) Dependent
c) No
(a) The events are independent because the grade each person earns does not affect the other person's grade.
(b) The events are dependent because the grades of you and your study partner are likely to be influenced by each other's study habits and collaboration.
(c) Not necessarily. Two events can occur at the same time and still be independent, such as flipping two coins at the same time. However, if the occurrence of one event affects the probability of the other event happening, then they are dependent.
(a) You and a randomly selected student from your class both earn A's in this course.
Answer: Independent
Explanation: The events are independent because your performance in the course does not affect the performance of the randomly selected student, and vice versa. They are not disjoint, as both events can occur at the same time.
(b) You and your class study partner both earn A's in this course.
Answer: Dependent
Explanation: In this case, the events are dependent because your performance and your study partner's performance could be related (e.g., by studying together, you both improve your chances of earning an A). They are not disjoint, as both events can occur at the same time.
(c) If two events can occur at the same time, must they be dependent?
Answer: No
Explanation: Two events can occur at the same time without being dependent. For example, independent events can both occur at the same time, but their occurrence is not influenced by each other. Only when the occurrence of one event affects the probability of the other event occurring are they considered dependent.
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Rewrite the expression in the form a^na n a, start superscript, n, end superscript. \dfrac{1}{a^{^{\scriptsize -\dfrac56}}}= a − 6 5 1 =start fraction, 1, divided by, a, start superscript, start superscript, minus, start fraction, 5, divided by, 6, end fraction, end superscript, end superscript, end fraction, equals
The given expression is needed to be written in the the form a^n.
The required expression is a ^ -5/4
We have,
The given expression is
1/ a^5/4
We know,
the identity that a negative exponent means the reciprocal.
1/ a^b = a^-b
So, the given expression is
1/ a^5/4
=a ^-5/4
The required expression is a ^-5/4
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The shape shown is a right-angled triangle together with two-quarter circles of radius r cm.
a) Find the formulae for the area A and the perimeter P of the shape.
Can someone show me how to find the area and perimeter of the shape and explain why its the formulae, so I can understand please.
The formulas for the area and perimeter of the given shape are:
A = 1/2 x b x h + 1/2 x πr²
P = b + h + 1/2r
We
To find the area and perimeter of the given shape, we need to break it down into its constituent parts:
The right-angled triangle and the two-quarter circles.
Let's label the sides of the right-angled triangle as follows:
The side adjacent to the right angle (the base) has length b.
The side opposite the right angle (the height) has length h.
Now, let's find the area of the triangle.
The formula for the area of a triangle is:
A = 1/2 x base x height
So, in this case, we have:
A (triangle) = 1/2 x b x h
Next, let's find the perimeter of the shape.
The perimeter is the total length of the boundary of the shape.
To find the perimeter, we need to add up the lengths of all the sides of the triangle and the two-quarter circles.
The base and height of the triangle are already labeled as b and h, respectively.
The two-quarter circles each have a radius of r.
The formula for the circumference of a circle is:
C = 2πr
But since we only have quarter circles, we need to divide the circumference by 4:
C (quarter circle) = 1/4 x 2πr = 1/2πr
Therefore, the length of each quarter circle is:
L (quarter circle) = 1/2πr x π/2 = 1/4r
So the total perimeter of the shape is:
P = b + h + 2 L (quarter circle) = b + h + 1/2r
Now, to find the area of the entire shape, we need to add the area of the triangle and the two-quarter circles.
The area of each quarter circle is:
A (quarter circle) = 1/4 x πr²
So the total area of the two-quarter circles is:
A (circles) = 2 A (quarter circle) = 1/2 x πr²
Therefore, the total area of the shape is:
A = A(triangle) + A(circles) = 1/2 x b x h + 1/2 x πr²
Thus,
The formulas for the area and perimeter of the given shape are:
A = 1/2 x b x h + 1/2 x πr²
P = b + h + 1/2r
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#SPJ1
What is the radius of a sphere with a
volume of 384 ft3, to the nearest tenth of
a foot?
[tex]\textit{volume of a sphere}\\\\ V=\cfrac{4\pi r^3}{3}~~ \begin{cases} r=radius\\[-0.5em] \hrulefill\\ V=384 \end{cases}\implies 384=\cfrac{4\pi r^3}{3}\implies 384(3)=4\pi r^3 \\\\\\ \cfrac{384(3)}{4\pi }=r^3\implies \sqrt[3]{\cfrac{384(3)}{4\pi }}=r\implies 4.5\approx r[/tex]
Answer:
[tex] \frac{4}{3} \pi {r}^{3} = 384[/tex]
[tex]r = 4.5 [/tex]
So the radius of this sphere is approximately 4.5 feet.
