The sinusoidal function of the form y = A·sin(k·x) + C that matches the function in the graph is; y = 4·sin((π/5)·x) - 1
What is a sinusoidal function?A sinusoidal function is a periodic function based on the sine or cosine functions.
The form of the function is y = A·sin(k·x)
The peak and trough of the graph are; (-7.5, 3), (-2.5, -5)
The amplitude of the function is therefore; A = (3 - (-5))/2 = 4
The vertical shift of the function is; C = (3 + (-5))/2 = -1
The period of the graph (Number of input x-values required to complete a cycle) = 2.5 - (-7.5) = 10 = 2·π/k
Therefore; k = 2·π/10 = π/5
The horizontal shift can be found as follows;
When x = 0, y = -1, therefore;
-1 = 4 × sin(π/5 × (0 - θ)) - 1
arcsin(0/4) = π/5 × (- θ)
θ = 0
The sinusoidal function is therefore;
y = 4·sin((π/5)·x) - 1
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Let f(x) = 1/x+2 and g (x) = 1/x-3. Find (f/g) (x). Assume all appropriate restrictions to the domain. help!!!!
Answer:
x ≠ -2 or 3
Step-by-step explanation:
No denominator can be zero, so ...
x +2 ≠ 0
x ≠ -2
__
x -3 ≠ 0
x ≠ 3
__
g(x) ≠ 0 . . . . . true for all x; no restriction needed for this
__
The appropriate restrictions are x ∉ { -2, 3 }.
Find the measure of the numbered angles in each rhombus
Answer:
Step-by-step explanation:
I thought those lines mean that they are equal meaning that the number is 68.
Mr. Lai buys 2 1/4 pounds of red apples and 1 3/8 pounds of green apples. How many more pounds of red apples does he buy?
Answer:
Mr. Lai buys 2 1/4 pounds of red apples and 1 3/8 pounds of green apples. How many more pounds of red apples does he buy?
2. Amir's community center has an evening art class. He pays $5 every time he goes to the class. His cost, C(a), is given by C(a) = 5a, where a is the number of art classes Amir attends.
a. Identify the independent variable and tell what it represents.
b. Identify the dependent variable and tell what it represents.
Answer: a. The independent variable in the equation C(a) = 5a is a. It represents the number of art classes Amir attends.
b. The dependent variable in the equation C(a) = 5a is C(a). It represents the cost Amir incurs as he attends art classes. The dependent variable is dependent on the independent variable because the cost will change as the number of classes attended changes.
PLS HELP IMA MARK BRAINLIEST
Answer:
3/5
Step-by-step explanation:
The probability of a number greater than 6 is 4/10 or 2/5
The probability of getting a blue is 2/10 or 1/5
U add 1/5 and 2/5 which gives u 3/5
Hope this helps
Mark em brainiest pls
14. Which shows how to find 5 x 72 mentally by using the Distributive
Property?
A. 5(7) + 5(2) B. 5(70) + 5(2) C. 205 + 70) D. 5(70)+2
Answer:
B
Step-by-step explanation:
5(70)= 350
5(2)= 10
350+10=360
72(5)= 360
i hope this helps!
i really need help, can someone please help me with this math question
The functions for this problem are defined as follows:
(t + s)(x) = x³ + 5x².(ts)(x) = \(5x^5\)(t - s)(-2) = -28.How to obtain the functions?The functions for this problem are given as follows:
s(x) = 5x².t(x) = x³.The addition and subtraction functions for this problem are given as follows:
(t + s)(x) = x³ + 5x².(t - s)(x) = x³ - 5x².At x = -2, the numeric value of the subtraction function is given as follows:
(t - s)(-2) = -2³ - 5(-2)²
(t - s)(-2) = -28.
The product function for this problem is given as follows:
(ts)(x) = \(5x^5\)
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find the area of a triangle whose sides are 5 m, 6 m and 9m,( use root 2 =-1.41 m)
Answer: 14.1 sq meters
Step-by-step explanation:
this question has already been answered
During practice, the players on a softball team warm up by running the bases. This graph shows the relationship between the number of hours, x, of practice the players attend and the number of minutes, y, the players spend running the bases.
How many minutes do the players spend running the bases during each hour of practice?
The number of minutes that the players spend running bases during each hour of practice is the constant of proportionality of the proportional relationship.
What is a proportional relationship?A proportional relationship is defined as follows:
y = kx.
In which k is the constant of proportionality.
In the context of this problem, the variables x and y are given as follows:
Variable x: number of hours.Variable y: time spent running the bases.The equation for the constant is given as follows:
k = y/x.
Representing the hourly time spent running times, you can calculate it taking any point (x,y) on the graph of the function.
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5/8 dived by 3/5
Help please
Answer:
5/6
Step-by-step explanation:
you must flip 3 over 5 and multiply
Please help me !! I need help asap
In given fractions 8/9 is 1/36 large than 31/36
Comparing Fractions:Finding the larger and smallest fraction in between two or more fractions is known as comparing fractions.
We need to change fractions with unlike denominators into fractions with similar denominators in order to compare them. For this, we will find the denominators' Least Common Multiple (LCM).
If the denominators are the same then it is easy to compare the fractions.
Here we have
31/36 and 8/9
To find the largest fraction convert both denominators into the same
Here LCM(36, 9) = 36
Now multiply both numerator and denominators of fractions with a number to change the denominators
=> \(\frac{31}{36} \times \frac{1}{1} = \frac{31}{36}\)
=> \(\frac{8}{9} \times \frac{4}{4} = \frac{32}{36}\)
From the above calculations given fractions are 31/36 and 32/36
Difference = \(\frac{32}{36} - \frac{31}{36} = \frac{1}{36}\)
Therefore,
In given fractions 8/9 is 1/36 large than 31/36
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Gambling is an issue of great concern to those involved in college athletics. Because of this concern, the National Collegiate Athletic Association (NCAA) surveyed randomly selected student athletes concerning their gambling-related behaviors. Of the 5594 Division I male athletes in the survey, 3547 reported participation in some gambling behavior. This includes playing cards, betting on games of skill, buying lottery tickets, betting on sports, and similar activities. A report of this study cited a 1% margin of error. The confidence level was not stated in the report. Use what you have learned to find the confidence level, assuming that the NCAA took an SRS.
The confidence level in this report of survey of student atheletes concerning their gambling-related behaviors is equals to 87.88%.
The confidence interval when calculated with the two tails methods then it can be used to test the two tail hypothesis for the same parameter provided that the confidence level. We have, National Collegiate Athletic Association (NCAA) take a survey of randomly selected student athletes concerning their gambling-related behaviors.
repoted participation of students, x = 3547
Sample size,n = 5594
Margin of error, E = 1% = 0.01
The sample proportion is a number of successes divided by the sample size, p-cap = 3547/5594
= 0.6341
The margin of error is for a confidence interval for a proportion, which is determined by using the following formula is
\(CL = Zα/₂ \sqrt{ \frac{ \hat{p} \: (1- \hat{p})}{n} }\)
= Zα/₂√(1 - 0.6341)0.6341/5594
= 0.0064 Zα/₂
This margin of error also has to be equal to 1% or
0.0064 Zα/₂ = 0.01
=> Zα/₂ = 0.01/0.0064 ~ 1.55
The confidence level is the probability of obtaining this value or less extreme, determine the probability using z- table,
P(-1.55< Z < 1.55) = P(Z < 1.55) - P(Z < -1.55)
= 0.9394 - 0.0606 = 0.8788 = 87.8
Thus the confidence level is 87.88%.
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At Hearth and Home the price for 2 candles is $8.00. At Homeland the price for 3 candles is $15.00. How many dollars will you save if you buy 6 candles from Hearth and Home instead of Homeland?
Answer:
answer is 6
Step-by-step explanation:
hard to explain but you have to find the price of 1 candle
Using Intermediate Value Theorem determine which of the following
function has a real root on [1,2].
Answer:
Use the Intermediate Value Theorem to prove that every cubic function has at least one real root. You will have to first argue that you can find real numbers a and b so that f(a) is negative and f(b) is positive.
Reflect (6,-4) across the -axis. Then reflect the result across the -axis. What are the coordinates of the final point?”
The coordinates of the final point after the reflections across the x-axis twice is (6, -4)
What are the coordinates of the final point?Reflecting a point across the x-axis means that we keep the x-coordinate the same, but change the sign of the y-coordinate.
So reflecting (6,-4) across the x-axis gives us the point (6,4).
Reflecting this result again across the x-axis means that we keep the x-coordinate the same, but change the sign of the y-coordinate again.
So reflecting (6,4) across the x-axis gives us the point (6,-4).
Therefore, the final point after both reflections is (6, -4).
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a) What is the area of the top face of this
cuboid?
b) What is the area of the bottom face of
this cuboid?
4 cm
9 cm
7 cm
The area of both the top face and the bottom face of the cuboid is 63 square centimeters (cm²).
To find the area of each face of the cuboid, we'll use the formulas for finding the area of a rectangle (which is the shape of each face of the cuboid).
Given dimensions:
Length (L) = 9 cm
Width (W) = 7 cm
Height (H) = 4 cm
a) Area of the top face of the cuboid:
The top face is a rectangle with dimensions 9 cm (length) and 7 cm (width).
Area = Length × Width
Area = 9 cm × 7 cm
Area = 63 square centimeters (cm²)
b) Area of the bottom face of the cuboid:
The bottom face is also a rectangle with dimensions 9 cm (length) and 7 cm (width).
Area = Length × Width
Area = 9 cm × 7 cm
Area = 63 square centimeters (cm²)
Therefore, the area of both the top face and the bottom face of the cuboid is 63 square centimeters (cm²).
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Need help with a congruent answer! NEED IT FAST PLEASEE
• What can you say about the values of 180 and 2x2x3x3x5?
Answer:
2×2×3×3×5 are the prime factors of 180
Step-by-step explanation:
If you draw a factor tree, you would find that 2x2x3x3x5 are the prime factors of 180
hope this helps :)
Question 3: Mathematical proficiency and the construction of mathematics ideas. To answer this question, you need to understand paragraphs 2.12 and 2.13 in your study guide: Key to note the following concepts: constructivism and behaviourism. inductive and deductive thinking or reasoning. instrumental and relational understanding conceptual and procedural knowledge; and ● elements of mathematics proficiency. . e . (10 marks) ● 3.1 Create an activity where procedural and conceptual understanding co-exists. Revisit your content areas and choose a problem to solve and demonstrate how procedural and conceptual knowledge can be linked to the teaching and learning process. (6) 3.2 Provide an example to explain the difference between conceptual knowledge and procedural knowledge.
Given statement solution is :- Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.
3.1 Activity: Procedural and Conceptual Understanding in Action
Content Area: Fractions
Problem: Comparing Fractions
Objective: Students will demonstrate both procedural and conceptual understanding of comparing fractions.
Activity Steps:
Begin by introducing the concept of fractions and reviewing the basic procedures for comparing fractions (e.g., finding a common denominator, cross-multiplying).
Provide students with a set of fraction comparison problems (e.g., 2/3 vs. 3/4, 5/8 vs. 7/12) and ask them to solve the problems using the traditional procedural approach.
After students have solved the problems procedurally, engage them in a group discussion to explore the underlying concepts and relationships between fractions. Ask questions such as:
What does it mean for one fraction to be greater than or less than another?
Can you explain why we need a common denominator when comparing fractions?
How can you visually represent and compare fractions to better understand their relative sizes?
Introduce visual aids, such as fraction bars or manipulatives, to help students visualize the fractions and compare them conceptually. Encourage students to reason and explain their thinking.
Have students revisit the fraction comparison problems and solve them again, this time using the conceptual understanding gained from the group discussion and visual aids.
Compare the students' procedural solutions with their conceptual solutions, and discuss the similarities and differences.
Conclude the activity by emphasizing the importance of both procedural and conceptual understanding in solving fraction comparison problems effectively.
By incorporating both procedural and conceptual approaches, this activity allows students to develop a deeper understanding of comparing fractions. The procedural approach provides them with the necessary steps to solve problems efficiently, while the conceptual approach helps them grasp the underlying principles and relationships involved in fraction comparison.
3.2 Example: Conceptual Knowledge vs. Procedural Knowledge
Conceptual knowledge refers to the understanding of underlying concepts, principles, and relationships within a domain, whereas procedural knowledge focuses on knowing the specific steps or procedures to perform a task without necessarily understanding the underlying concepts.
Example: Division of Fractions
Conceptual Knowledge: Understanding the concept of division as the inverse operation of multiplication, and recognizing that dividing fractions is equivalent to multiplying by the reciprocal of the divisor. This understanding allows for generalization and application of division concepts to various fractions.
Procedural Knowledge: Following the specific steps to divide fractions, such as "invert the divisor and multiply" or "keep-change-flip" method. This knowledge involves applying the procedure without necessarily grasping the underlying concept or reasoning behind it.
In this example, Math Proficiency conceptual knowledge involves understanding the fundamental concept of division and its relationship to fractions, enabling flexibility in solving division problems with different fractions. Procedural knowledge, on the other hand, focuses on following a specific set of steps to achieve a correct solution without necessarily comprehending the underlying concept.
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item 992316 imagine math
Answer: To look up an answer: Locate the Item Number for the particular problem for which you want the answer. This is at the top of the screen as.
Step-by-step explanation:
4
If f(x)=3(x+5) +-, what is f(a + 2)?
x
4
A. 3(f(a)+5) +-
+5) + f(a) +2
B. 3(a+2)++2
a
C. 3(a+7)+
ST
a+2
The value of f(a + 2) is 3(a + 7)
How to evaluate the function?The function is given as:
f(x) = 3(x+5)
Next, we substitute a + 2 for x in the above equation
f(a + 2) = 3(a + 2 + 5)
Evaluate the like terms
f(a + 2) = 3(a + 7)
Hence, the value of f(a + 2) is 3(a + 7)
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This is how many classes students at Bronx College take this semester with the probabilities courses1 2 3 4 5 probability (distribution) of taking that many courses.1.1.6.1.1 The variance for this distribution is approximately.
Answer:
1
Step-by-step explanation:
Given the question above :
The probability distribution :
X : ___ 1 ___ 2 ___ 3 ___ 4 ____ 5
P(x): _ 0.1 __ 0.1 __ 0.6 _ 0.1 __ 0.1
The Variance : Var(X) = (Σx²*p(x)) - μ²
μ = E(X) = Σ(X * p(x)) :
Σ(X * p(x)) = (1*0.1)+(2*0.1)+(3*0.6)+(4*0.1)+(5*0.1)
μ = 3
Var(X): [(1^2*0.1)+(2^2*0.1)+(3^2*0.6)+(4^2*0.1)+(5^2*0.1)] - 3²
= 10 - 9
= 1
Hence. Variance = 1
On a number line, point C is at 8, and the midpoint E of CD is at -3.
Point D is at
on the number line.
Answer: C
Step-by-step explanation:
Point D is at -14 on the number line.
How to determine the midpoint of a line segment?In Mathematics, the midpoint of a line segment with two end points can be calculated by adding each end point on a line segment together and then divide by two (2).
Since E is the midpoint of line segment CD, we can logically deduce the following relationship:
Line segment CD = Line segment C + Line segment D
Midpoint E = (point C + point D)/2
By substituting the given points into the equation above, we have the following:
-3 = (8 + D)/2
-6 = 8 + D
D = -6 - 8
D = -14
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Sam and Jo created a grocery list. To make it easier to look at, they each split the list into equal groups. Sam splits the list into groups of 4 and Jo split the list into groups of 6. What is the smallest number of items that could be on the grocery list?
Answer:
12
Step-by-step explanation:
The least common multiple of 4 and 6 is what we are looking for
4,8 ,12,16,20
6,12,18
The smallest number is 12
a person can pay $9 for a membership to the science museum and then go to the muses in for just $8 per visit. What is the maximum number of visits a member of the science museum can make for a total cost of $41?
If 15% of a number is 45 and 50% of the same number is 150, find 35% of that number.v
Answer:105
Step-by-step explanation:
let the number is x
Then 15% of x = 0.15x = 45 .
x= 45/0.15
x = 300
now 50 % of x = 0.5x =150
x = 150/0.5
x= 300 (crosscheck correct)
now 35% of 300 = 0.35 ×3000
= 105
which of the following points does not lie on the graph of y=1/2x+3?
A. (10,8)
B. (-2,2)
c. ( 0,3)
d. (-6,-3)
Answer:
B
Step-by-step explanation:
From the London Summer Olympics 2012 to the Rio Summer Olympics 2016, the number of medals awarded increased by 118.5%. If 962 medals were awarded in London, how many were awarded four years later in Rio?
Answer:
1,440
Step-by-step explanation:
London 962
Rio +118.5%
One percent of 962 is 9.62 you get that by moving the decimal place over one place, multiply by 118.5 to get 1,139.97 there is no partial medals so round to the nearest whole number and you get 1,140.
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5/8 divided by -1/10
Abraham Lincoln's statue in the Lincoln Memorial stands 19 feet tall. Emily creates a model of the statue for art class. If Emily creates her model in
exact proportion to the original with a a height of only 1 foot, which transformation did Emily make?
O None of the Above
O Reflection
O Translation
O Dilation