The area of the shaded region and the length of the boundary is 86.59 cm^2 and 44cm respectively.
A semicircle is a shape that is half of a circle. It is defined by a center point and a radius, and it is made up of an arc that is 180 degrees of the full circle.
The circumference of a semicircle is given by the formula: C = π * d, where C is the circumference and d is the diameter of the semicircle.
Diameter of the biggest semi-circle = 14cm.
Diameter to two small semi-circles = 3.5cm.
Diameter of other semi-circle = 14 - 2(Diameter to two small semi-circles)
=14 - 7 cm
= 7cm
Length of boundary = Circumference of bigger semi-circle + Circumference of small semi-circle + 2 ×circumference of the smaller semi-circles
∴Length of boundary= [tex]\pi R+\pi r_{1}+2\pi r_{2}[/tex]
=> Length of boundary=[tex]\pi (R+r_{1})+2\pi r_{2}[/tex]
=> [tex]\frac{22}{7}(7+3.5)+2X\frac{22}{7}X1.75[/tex]
=> 44cm
Area of the biggest semi-circle = [tex]\frac{1}{2}\pi (7)^{2} cm^{2}[/tex]
Area of two small semi-circles = [tex]\pi (1.75)^{2}cm^{2}[/tex]
Area of other semi-circle= [tex]\frac{1}{2}\pi (3.5)^{2}cm^{2}[/tex]
Area of shaded region= π×(24.5−3.0625+12.25)
=π×27.5625 cm^2 =86.59 cm^2
Therefore, the area of the shaded region and the length of the boundary is 86.59 cm^2 and 44cm respectively.
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the relationship between the magnitude of the restoring force f and the resultant displacement x from equilibrium for a nonlinear spring is given by the equation f
The work done by stretching the spring to the given distance is:
[tex]W=\frac{kx_{0} }{3}[/tex]
The given parameters:
Applied force on the spring = F
Extension of the spring, = x₀
The work done by stretching the spring to the given distance is calculated as follows:
[tex]W=\int\limits^b_a {F} \, dx[/tex]
Where:
F - Force.
W- Work.
x- Distance.
If we know that F=k.x², then the work of the nonlinear spring is:
[tex]W=\int\limits^b_a {F} \, dx \\W=\int\limits^b_a {kx^2} \, dx \\W=k\int\limits^b_a {x^2} \, dx \\\\W=k[\frac{x^3}{3}]\\\\W=k[\frac{x_b-x_a}{3} ]\\\\W=k[\frac{x_o-0}{3} ][/tex]
W=kx₀/3
Thus, the work done by stretching the spring to the given distance is: W=kx₀/3
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Which represents the reflection of f(x) = StartRoot x EndRoot over the y-axis?
Answer:
I tink D?
Step-by-step explanation:
The function after the reflection over y-axis is f' ( x ) = √( -x )
What is Reflection?Reflection is a type of transformation that flips a shape along a line of reflection, also known as a mirror line, such that each point is at the same distance from the mirror line as its mirrored point. The line of reflection is the line that a figure is reflected over. If a point is on the line of reflection then the image is the same as the pre-image. Images are always congruent to pre-images.
The reflection of point (x, y) across the x-axis is (x, -y). When you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y).
Given data ,
Let the function be represented as f ( x )
Now , the value of f ( x ) is
f ( x ) = √x
Now , when you reflect a point across the y-axis, the y-coordinate remains the same, but the x-coordinate is taken to be the additive inverse. The reflection of point (x, y) across the y-axis is (-x, y)
So , the reflected function is f' ( x ) = √( -x ) and the graph is plotted
Hence , the reflected function is f' ( x ) = √( -x )
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segment from ( − 8 , 10 )to ( − 8 , − 5 )that partitions the segment into a ratio of 2 to 1?
The coordinate of the point that partitions the given line in the ratio 2:1 is; (-8, 0)
How to partition line segments?If the coordinates are given as;
P (x₁ , y₁) and Q (x₂ , y₂) and the partition of the line segment is divided internally in the ratio m : n, then its coordinate ( x, y) given by :
( x ,y ) = [(mx₂ + nx₁)/ ( m + n), (my₂ + ny₁)/ ( m + n)]
We are given the coordinates as ( − 8 , 10 )to ( − 8 , − 5 ) and if it is partitioned in the ratio 2: 1, the coordinates of the points of partition are;
(x, y) = [(2(-8) + 1(-8))/ (2 + 1), (2(-5) + 1(10))/ (2 + 1)]
(x, y) = (-24/3), (0/3)
(x, y) = (-8, 0)
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shawna reads a scatterplot that displays the relationship between the number of cars owned per household and the average number of citizens who have health insurance in neighborhoods across the country. the plot shows a strong positive correlation. shawna recalls that correlation does not imply causation. in this example, shawna sees that increasing the number of cars per household would not cause members of her community to purchase health insurance. identify the lurking variable that is causing an increase in both the number of cars owned and the average number of citizens with health insurance.
The average income per household that is causing an increase in both the number of cars owned and the average number of citizens with health insurance.
The correlation of variables is the statistical relationship between two variables.
A correlation is positive if both variables move in the same direction and negative if the variables move in different directions - as one variable increases, the other decreases.
Correlation does not imply causation: This means that one can not legitimately associate a cause-and-effect relationship between the two variables.
In this example, it cannot be legitimately shown that increasing the number of cars per household would cause members of the community members to purchase health insurance, but when we bring in the lurking variable.
which is the increase in average income per household, we can see that this possibility might cause more people to buy more health insurance even after they have purchased cars, because they have more money to spend.
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Consider the expression given below. Simplify this expression into the form A/B and place the appropriate expressions into the boxes shown below: V4219 Answer: 4x19 = AB, where A= 2x9 âand B = 4.19 Ð¥
the simplified expression is 2x9/4.19, which can be written as A/B, where A = 2x9 and B = 4.19. Therefore, the value of A is 18 and the value of B is 4.
To simplify the expression V4219, first divide it into two separate terms by breaking the number 4219 into 4 and 2119.
Now, we need to simplify the terms 4 and 2119 separately.
To simplify the term 4, we need to divide it by 4, which gives us 1.
To simplify the term 2119, we need to divide it by 19, which gives us 2x9.
Hence, the simplified expression is 2x9/4.19, which can be written as A/B, where A = 2x9 and B = 4.19. Therefore, the value of A is 18 and the value of B is 4.
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The roof shingles are arranged so that each row has 7 fewer shingles than the row below it. If the first row has 75 shingles, how many shingles are in the 6th row?
The shingles are in the 6th row is 110 using arithmetic process.
What is arithmetic process?A subject of mathematics known as arithmetic operations deals with the study and use of numbers in all other branches of mathematics. Basic operations including addition, subtraction, multiplication, and division are included.
The study of numbers and the operations on those numbers, which are relevant to all other branches of mathematics, is the focus of a branch of mathematics known as arithmetic operations. It includes addition, subtraction, multiplication, and division as its fundamental operations.
Given that A = 75 and d = 7, n = 6
A₆ = A + (n-1)d
A₆ = 75 + (6-1)7
A₆ = 75 + 5 * 7
A₆ = 75 + 35
A₆ = 110
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Answer:
33
Step-by-step explanation:
it starts with 75 and decreases by 7 for each row. on the 6th row youll be at 33!
STARTS AT 75
row one: 68
row two: 61
row three:54
row four: 47
row five: 40
row six: 33
A 2D depiction of what a 3D shape would look like if it was opened out and laid flat is called a
Answer: Net (of a shape)
Step-by-step explanation:
Answer:
Step-by-step explanation:
no need for step by step its called a net
A company mix concrete brick shaped like rectangular prism is birth is 10 inches long 9 inches wide and 4 inches tall if they used 18,000 in 3 (the tree is to the power of / tiny three) of concrete how many breaks do they make?
50 breaks do they make.
What is equation?An equation is a mathematical statement that shows the relationship between two values, or variables. It is formed by using an equal sign between two expressions that have the same value. Equations are used to solve for unknown values, or to describe a relationship between two or more variables. Equations can be used to solve for a single variable or multiple variables, and can be used to solve problems in both mathematics and science.
To find the answer to this question we must use the formula V = L x W x H. In this case, V = 10 x 9 x 4 = 360. We now know that there is 360 cubic inches in each brick. To find the total number of bricks that can be made from 18,000 cubic inches of concrete, we must divide 18,000 by 360. The answer is 50, which means that the company can make 50 concrete bricks from 18,000 cubic inches of concrete.
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please help will mark BRAINLIEST thank you
Answer: <3, 1>
Step-by-step explanation: A translation of a vector is simply moving it a certain distance in a certain direction. In this case, the first translation of <6, -4> moves the vector 6 units to the right and 4 units down. The second translation of <-3, -5> then moves the vector an additional 3 units left and 5 units down. The net result of these two translations is to move the vector 3 units to the right and 1 unit up, which is equivalent to a single translation of <3, 1>.
Write an expression for "5 decreased by 2.
Answer:
5 (less than sign) 2
Step-by-step explanation:
Answer:
5n-20
Step-by-step explanation:
Product means multiply and so the product of 5 and n is 5n. To decrease this value by 20 , means to subtract 20 from it hence: 5n - 20 is algebraic expression for the statement
sale of eggs that are contaminated with salmonella can cause food poisoning in consumers. a large egg producer takes an srs of 200 eggs from all the eggs shipped in one day. the laboratory reports that 9 of these eggs had salmonella contamination. unknown to the producer, 0.1% (one-tenth of 1%) of all eggs shipped had salmonella. identify the population, the parameter, the sample, and the statistic.
The simple random sample of 200 eggs
Statistic=Proportion of eggs in the sample that contain salmonella.
p = 0.045
The population is the individuals that are being studied.
population=All eggs in one day
A sample is the part of the population of which information was actually collected.
Sample=The simple random sample of 200 eggs
A parameter is a descriptive measure for a population.
Parameter=Proportion of eggs shipped that day that contain salmonella.
p = 0.1 % =0.001
A statistic is a descriptive measure for a sample.
STATISTIC=Proportion of eggs in the sample that contain salmonella.
p=9÷200 = 0.045
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PLEASE HELP ITS DUE TODAY WOULD GIVE ALOT OF POINTS IF SOMEONE SHOWS THE ANSWER ANY SPAM ANSWERS WILL BE REPORTED!
THANK YOU!
Answer:
y ≥ -x -7
Step-by-step explanation:
The inequality is greater than or equal to because it is above the line and it is a solid line.
The slope is -1. If you select a point on the line, you go down one unit and one unit to the right to get back on the line. The slope is the rise over the run. -1/1 = -1
The y intercept is where the graph crosses the y axis (0,-7) So the y intercept is -7
A fashion store is planning its end–of–season sale. It sells 40 of its signature jeans every week at $175 per pair. Last year, the store's sales increased to 60 pairs per week when the price was dropped by $25. By what amount should the store discount the price this year to maximize its revenue?
A. $112.50
B. $103.50
C. $62.50
D. $71.50
Answer:
A
Step-by-step Explanation:
Every $1 decrease in price corresponds to a 0.8 increase in the number of pairs of jeans sold.
So, if [tex]x[/tex] pairs of jeans are sold, the revenue in dollars is [tex](175-x)(40+0.8x)[/tex].
The roots of this function are [tex]x=175[/tex] and [tex]x=-50[/tex]. The maximum is achieved halfway between these roots at [tex]x=62.5[/tex].
When 62.5 pairs of jeans are sold, the price is $112.50.
The store should discount the price to $112.50 to maximize its revenue
What is Discount?Discount is a deduction from the usual cost of something, typically given for prompt or advance payment or to a special category of buyers.
From the above question, every $1 decrease in price corresponds to a 0.8 increase in the number of pairs of jeans sold.
So, if pairs of jeans are sold, the revenue in dollars is (175 - x)(40 + 0.8x)
The roots of this function are x = 175 and x = -50. The maximum is achieved halfway between these roots at x = 62.50.
Therefore, When 62.5 pairs of jeans are sold, the price is $112.50.
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Please help with their question
If f(x) = x⁴ + 2, g(x) = x-6 and h(x) = √x , then the simplified form of f(g(h(x))) is f(g(h(x))) = (√x - 6)⁴ + 2.
What is the polynomial expression?
Any expression which consists of variables, constants, and exponents, and is combined using mathematical operators like addition, subtraction, multiplication, and division is a polynomial expression.
We can simplify f(g(h(x))) by first evaluating h(x), then substituting the result into g(x), and finally substituting the result into f(x).
Starting with h(x) = √x, we can substitute this into g(x) to get:
g(h(x)) = g(√x) = √x - 6
Next, we can substitute g(h(x)) = √x - 6 into f(x) to get:
f(g(h(x))) = f(√x - 6) = (√x - 6)⁴ + 2
Simplifying this expression requires some algebraic manipulation, but we can expand (√x - 6)⁴ using the binomial theorem or by using the method of FOIL (first, outer, inner, last) repeatedly. Either way, we will end up with a polynomial expression in x with terms of various degrees.
Therefore, the simplified form of f(g(h(x))) is f(g(h(x))) = (√x - 6)⁴ + 2.
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Three vertices of a parallelogram are shown in the figure below.
Give the coordinates of the fourth vertex.
(-4,8)
(-6,-2)
(4,5)
The coordinates of the fourth vertex is (1,-8).
Find the coordinates of the fourth vertex?As three of a parallelogram's vertices, we were given:
(3,-2), (-1,-4), (5,-6). (5,-6).
We see that (3,-2) and (-1,-4) form a diagonal after charting the points as in the attachment.
The midpoint formula determines what point on this diagonal is in the middle.
Keep in mind that both diagonals' midpoints are identical.
Specify the coordinates of the fourth point (x,y).
As a result of once more applying the midpoint formula to (3, -2), we get:
x=1 and y=-8
The fourth point's locational details are as follows:
(1,-8).
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The complete question is,
A good can be produced for a total cost of 600 or 850 when making 100 units and 150 units, respectively. Discover an equation for TC in terms of Q, the number of generated units, presuming that the total cost function is linear.
The table represents the number of pairs of shoes bought when customers bought a dress from Famous Formalwear,
Which value represents the correlation coefficient of this data set?
O 0.18
O 0.32
O 0.43
O 0.99
Number of dresses purchased
1
4
3
1
4
6
2
6
2
Number of Pairs of Shoes Purchased
2
3
3
1
2
2
1
2
1
The correlation coefficient for this data-set is given as follows:
r = 0.43.
How to obtain the correlation coefficient for the data-set?The coefficient is obtained inserting the points in a data-set in a correlation coefficient calculator.
The points for the data-set in this problem are given as follows:
(1,2), (4,3), (3,4), (1,1), (4,2), (6,2), (2,1), (6,2), (2,1).
Inserting these points into a correlation coefficient calculator, the correlation coefficient for this data-set is given as follows:
r = 0.43.
Meaning that the correct option is given by the third option.
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This is a 2-page document! **
Include a congruency statement for all congruent triangles.
State whether the triangles could be proven congruent, if possible, by SSS or SAS.
1. W
M
3.
5.
U
1.
2.
3.
4.
5.
1.
2.
3.
4.
Statements
8. Given: PO SR, ZPORZSRQ
Prove: APOR ASRO
2.
4.
Statements
6.
7. Given: AMCP, CM GP, C is the midpoint of AG
Prove: AACM ACGP
W
Complete the proofs below using the most appropriate method, SSS or SAS.
X
4
M
1.
2.
B
3.
5.
N
1.
2.
3.
SSS & SAS
4.
P
A
Reasons
P
G
R
Reasons
M
P
S
Gina Wilson (All Things Algebra. L
The following congruence theorems can be applied to every triangle in the provided pair:
1) SSS
2) SAS
3)SAS
4) SSS
5) SAS
6) SAS
How to find the Calculation?1) We can observe from the that;
FY ≅ CW
FP ≅ CM
YP ≅ MW
This proves the Side-Side-Side (SSS) congruency theorem, which states that the three corresponding sides of the two triangles are congruent.
2) We can observe from the picture that;
CBD and BCA are congruent because they both have alternate interior angles. Thus;
CBD and BCA
We can also see that
EB ≅ EC
DB ≅ CA
Inferring from the fact that two corresponding sides and an angle of the two triangles are congruent
Using the Side-Angle-Side (SAS) congruency theorem, construct BED and AEC.
3) The image demonstrates that;
SVU and SVT
The shared sides provide using the reflexive property;
SV ≅ SV
VT ≅ VU
Inferring from the fact that two corresponding sides and an angle of the two triangles are congruent
Side-Angle-Side (SAS) congruency theory is used by VSU and VST.
4) The picture shows what;
MN ≅ QP
MQ ≅ NP
The shared sides provide using the reflexive property;
NQ ≅ NQ
This implies that the three corresponding sides of the two triangles are congruent, which, according to the Side-Side-Side (SSS) congruency theorem, means that QNM QNP.
5) The image demonstrates that;
GL ≅ HL
GJ ≅ HK
JLG and HLK are incongruent angles in the vertical direction;
JLG and HLK
Inferring from the fact that two corresponding sides and an angle of the two triangles are congruent
employing the Side-Angle-Side (SAS) congruency theorem, QNM and QNP.
6) From the triangles provided, we note that;
XZY and XZW (They both form a straight angle of 90 degrees.)
The shared side is congruent to itself using reflexive property, therefore;
XZ ≅ XZ
Also;
ZW ≅ ZY
Inferring from the fact that two corresponding sides and an angle of the two triangles are congruent
Using the Side-Angle-Side (SAS) congruency theorem, XYZ = XWZ.
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Complete question:
What is the equation of the line that passes through the point (3, -7) and has a slope of
−4/3?
[tex](\stackrel{x_1}{3}~,~\stackrel{y_1}{-7})\hspace{10em} \stackrel{slope}{m} ~=~ - \cfrac{4}{3} \\\\\\ \begin{array}{|c|ll} \cline{1-1} \textit{point-slope form}\\ \cline{1-1} \\ y-y_1=m(x-x_1) \\\\ \cline{1-1} \end{array}\implies y-\stackrel{y_1}{(-7)}=\stackrel{m}{- \cfrac{4}{3}}(x-\stackrel{x_1}{3}) \implies y +7= -\cfrac{4}{3} (x -3) \\\\\\ y+7=-\cfrac{4}{3}x+4\implies {\Large \begin{array}{llll} y=-\cfrac{4}{3}x-3 \end{array}}[/tex]
Write an exponential function for a graph that passes through the points (2, 336) and (3, 2688). Write the function in the form y = a(b). please I need help
Answer:
y = 5.25 [tex](8)^{x}[/tex]
Step-by-step explanation:
the general form of an exponential function is
y = a [tex](b)^{x}[/tex]
to find a and b , substitute the coordinates of the given points into the equation.
using (2, 336 )
336 = a b² → (1)
using (3, 2688 )
2688 = a b³ → (2)
divide (2) by (1)
[tex]\frac{ab^3}{ab^2}[/tex] = [tex]\frac{2688}{336}[/tex] ( cancel ab on numerator/denominator of left side )
b = 8
substitute b = 8 into (1) and solve for a
336 = a × 8² = 64a ( divide both sides by 64 )
5.25 = a
then exponential function is
y = 5.25 [tex](8)^{x}[/tex]
(50 points and brainlyest)
Because the diameter of the circle is now known 19.8, the base area of the cylinder can be calculated. Ignore the square base of the prism.
Answer:
307,8
Step-by-step explanation:
The area of a circle is 3.14 times the radius squared, and the radius is the diameter divided by 2. Hence the area is 307.8
suppose that 40% of all adults regularly consume coffee, 60% regularly consume carbonated soda, and 35% regularly consumes both coffee and soda. draw a venn diagram, then answer the following:(a) What is the chance a randomly selected adult regularly drinks coffee but doesn't drink soda?(b) What is the probability that a randomly selected adult consumes coffee, soda or both?(c) What is the probability that a randomly selected adult doesn't regularly consume at least one of these two products?
The probabilities of adults who drinks only coffee , both/ coffee ,soda and doesn't drink any are 5% , 65% and 35%.
Let A be the event that an adult consumes coffee.
Let B be the event that an adult consumes carbonated soda.
Given probabilities of the events.
P (A) = 0.4
P (B) = 0.6
P(A∩B) = 0.35
(a). P(A) - P(A∩B) = 0.4 - 0.35
= 0.05 OR 5 %
(b). P(AUB) = P (A) + P (B) - P(A∩B)
= 0.4 + 0.6 - 0.35
= 0.65 OR 65%
(c). The given case represents compliment of the event when the adult consumes at least one of the drink. According to probability axiom, the probability is given by:
P ((AUB)') = 1 - P (AUB) = 1-0.65 = 0.35
Therefore,
P ((AUB)') = 0.35 or 35 %.
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If 28% of 581 people replied newton ate the apple what’s the margin of error %
The margin of error, given the percentage who replied that Newton ate the apple, is 3.5%.
How to find margin of error ?The margin of error is a measure of how much the sample results are likely to vary from the true population value.
To calculate the margin of error, you need to know the sample size, the proportion of the sample that gave a particular response, and the level of confidence.
The formula for the margin of error is:
Margin of Error = z x √(p x ( 1 - p) / n)
where:
z = the critical value from the standard normal distribution table
p = the proportion of the sample that gave a particular response
n = the sample size
The margin of error for Newton eating the apple is therefore:
Margin of Error = 1.96 x √(0.28 x (1 - 0.28) / 581)
Margin of Error = 1.96 * √(0.00035)
Margin of Error = 1.96 * 0.018
Margin of Error = 0.035
The margin of error is therefore 3.5%.
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Find the smallest value of m such that the product of 189m is a perfect square
Answer: 7
Step-by-step explanation:
First, we need to prime factorize the number 189,
189 = 3 × 3 × 3 × 7 × m
From the factors we can see that there is no pair of same numbers for 7, so if we replace m with 7, we can get a perfect square.
Hence the answer is 7
if we apply an alpha level of .05, and there really is no effect of the experimental manipulation, then one should make a type i error .
Answer:
6 votes
Step-by-step explanation:
if you were in a spaceship accelerating at 1g how long would it take you to reach the speed of light
To reach the speed of light, the spaceship will take 3.1 × 10⁷ seconds. The result is obtained by using the formula for acceleration.
What is acceleration?Acceleration is the rate of change in velocity of an object with respect to time. It can be expressed as
[tex]a = \frac{\Delta v}{\Delta t}[/tex]
Where
a = accelerationΔv = change in velocityΔt = change in timeIf we were in a spaceship with an acceleration of g, determine the time we reach the speed of light!
We have
Acceleration, a = 1g = 9.8 m/s²Speed of light, c = 3 × 10⁸ m/sTo find the time so that we can reach the speed of light, we use the formula for acceleration.
[tex]a = \frac{\Delta v}{\Delta t}[/tex]
[tex]g = \frac{c - 0}{\Delta t}[/tex]
[tex]9.8 = \frac{3 \times 10^{8}}{\Delta t}[/tex]
[tex]\Delta t = \frac{3 \times 10^{8}}{9.8}[/tex]
Δt = 0.306 × 10⁸
Δt = 3.1 × 10⁷ s
Hence, the spaceship will take 3.1 × 10⁷ seconds to reach the speed of light.
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The Colossus Ferris wheel debuted at the 1984 New Orleans World's Fair. The ride is 180 ft tall, and passengers board the ride at an initial height of 15 ft above the ground. The height above ground, h, of a passenger on the ride is a periodic function of time, t. The graph displays the height above ground of the last passenger to board over the course of the 15 min.
Sine function model: h=-82.5 cos 3pi(t)+97.5 where h is the height of the passenger above the ground measured in feet and t is the time of operation of the ride in minutes
If the Colossus Ferris wheel debuted at the 1984 New Orleans World's Fair and the ride is 180 ft tall, and passengers board the ride at an initial height of 15 ft above the ground. The period of the sine function model is: 2/3 minutes.
How to find the period of the sine function model?Given equation:
h=-82.5 cos 3pi(t)+97.5
Where:
h= height of the passenger above the ground measured in feet
t = time of operation of the ride in minutes
So,
h=-82.5× cos [2 × π ×t /T) +97.5
2 ×π / T = 3 × π
T = 2/3 minutes
Therefore the period of the sine function model is: 2/3 minutes.
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In the command window in MATLAB generate a random 6 x 6 matrix with integer entries using the command G = round(10* rand(6)) For each of the following questions below, execute the given commands and match the result with the best explanation of how MATLAB got the answer (some explanations will not match). G(:,:) G(:) G(7,6) ✓ [Choose ] maximum entry in each column of G reshapes all elements of G into a single column vector assigns the value 4 to all entries of G that are greater than 4 reshapes the matrix G into a single row vector returns the matrix G in its original form maximum entry in each row of G returns an indexing error entries of G that are greater than 4 sum of the entries in each column of G sum of the entries in each row max(G) sum(G) [ Choose ] G(G>4) [Choose ] G(G>4)=4 [Choose]
G(:,:) returns the matrix G in its original form. This command takes all elements of G and reshapes them into a single row vector. This means that all elements of G are included in the output, and the output is in the same shape as the original matrix.
G(:) reshapes all elements of G into a single column vector. This command takes all elements of G and places them into a single column. This means that all elements of G are included in the output, and the output is in a column vector.
G(7,6) returns an indexing error. This command attempts to access an element outside of the range of the matrix G. Since G is a 6 x 6 matrix, there is no element at the index (7,6).
max(G) returns the maximum entry in each column of G. This command takes the maximum value from each column and returns them as a single row vector. This means that the output contains the maximum value from each column and the output is in a single row vector.
sum(G) returns the sum of the entries in each column of G. This command takes the sum of all entries in each column and returns them as a single row.
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Mario wants to mail three books with the following
weights:5/8 pound,7/16 pound, and 3/4
pound. Can Mario
mail the books in a box that can hold up to 2 1/2 pounds?
Use benchmarks to justify your answer.
Mario can mail the books in the box, as the weight of the books is less than the weight of the box.
How to obtain the total weight?The total weight is obtained applying proportions, converting the fractions to decimal, dividing the numerator by the denominator.
The weights of each book are given as follows:
5/8 pounds = 0.625 pounds.7/16 pounds = 0.4375 pounds.3/4 pounds = 0.75 pounds.Hence the total weight for the books is given as follows:
0.625 + 0.4375 + 0.75 = 1.8125 pounds.
The weight of the box is given as follows:
2 + 0.5 = 2.5 pounds.
Hence Mario can mail the books in the box, as the weight of the books is less than the weight of the box.
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Which ordered pairs are solutions to the equation X+2y=8?
Answer:
To find the ordered pairs that are solutions to the equation X+2y=8, we need to isolate the variable y on one side of the equation.
We can start by subtracting X from both sides:
X+2y = 8
X+2y-X = 8-X
2y = 8-X
Now we can divide both sides by 2:
y = (8-X)/2
So the ordered pairs (X, y) that are solutions to the equation X+2y=8 are the ones that satisfy the equation y = (8-X)/2.
We can substitute any value of x into the equation and find the corresponding y value.
For example, if we take X= 4, we can find the corresponding y value:
y = (8-4)/2 = 4/2 = 2.
so (4,2) is a solution to the equation X+2y=8.
We can also plot the equation on a Cartesian plane and find the points where the equation is true, those are the solutions.
Alternatively, we can solve the equation for X and find the solutions for y.
X = 8-2y
So the ordered pairs (X, y) that are solutions to the equation X+2y=8 are the ones that satisfy the equation X = 8-2y
We can substitute any value of y into the equation and find the corresponding X value.
For example, if we take y= 2, we can find the corresponding X value:
X = 8-2(2) = 8-4 = 4.
so (4,2) is a solution to the equation X+2y=8.
In this case, any value of X and y that satisfies the equations y = (8-X)/2 or X = 8-2y are solutions to the equation X+2y=8
reduce to simplest form
-3/2 - 3/8
Answer:
To add or subtract fractions, they must have a common denominator. In this case, the denominators of the fractions are 2 and 8, which are not the same. To find the least common multiple of 2 and 8, we can list the multiples of each number and find the smallest one that is common to both:
2: 2, 4, 6, 8, 10, 12, 14, ...
8: 8, 16, 24, 32, ...
The least common multiple of 2 and 8 is 8. Therefore, to add or subtract the fractions, we must convert them to have a denominator of 8.
-3/2 = -12/8 and 3/8 = 3/8
So, -3/2 - 3/8 = -12/8 - 3/8
Now we can subtract the fractions directly:
-12/8 - 3/8 = -12 - 3 / 8
= -15/8
Therefore, the simplified form of -3/2 - 3/8 is -15/8