Find a function of the form y = A sin ( k x ) + C or y = A cos ( k x ) + C whose graph matches the function shown below:
Leave your answer in exact form.
Answers
The sine function that matches the graph is given as follows:
y = sin(2πx/7) - 1.
How to define the sine function?The sine function is given as follows:
y = Asin(Bx) + C.
For which the parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: vertical shift.The maximum value is of 0, while the minimum value is of -2, hence the amplitude A is obtained as follows:
2A = 2. (as the difference of the maximum value and the minimum value is of 2).
A = 1.
A sine function with amplitude 1 should oscillate between -1 and 1, while this one oscillates between -2 and 0, hence the vertical shift is given as follows:
C = -1.
The period of the function is of 7 units, hence:
2π/B = 7
7B = 2π
B = 2π/7.
Then the function is defined as follows:
y = sin(2πx/7) - 1.
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Related Questions
What is 1% of 800?
Hint: We can think of 1% as a common fraction.
Answers
Reason:
1% converts to the decimal form 0.01
0.01*800 = 8
Basically we move the decimal point two spots to the left
So the 800.0 becomes 8.000 or simply 8
Answer:
8
Step-by-step explanation:
Anything in percentage format can be expressed as a fraction by dividing by 100
Thus
[tex]\textrm{1\% }= \dfrac{1}{100}[/tex]
1% of 800 is found by multiplying 800 by the above fraction
[tex]\textrm{1\% of 800 } = 800\cdot \dfrac{1}{100} = 8[/tex]
The range of a set of numbers is 16.
The minimum value is 6.
What is the maximum value?
Answers
Answer:
22
Step-by-step explanation:
Range : Maximum - Minimum
Minimum = 6
Maximum = A (Let maximum be A)
Hence,
16 = A - 6
A = 22
Maximum = 22
Use the digits in 2023 (2, 0, 2 and 3) exactly once time each along with any mathematical symbol or operation of your choosing to create expressions equivalent to the numbers between 1 and 100. 6th Grade.
Answers
The number-finding assignment to a subset of the numbers depending on the age and arithmetic proficiency .
what is expressions ?A mathematical expression is a sentence with at least two variables or integers and one mathematical action. Addition, subtraction, multiplication, or division are all possible outcomes of this mathematical process. The following are the fundamental parts of an expression: Expression: (Math Operator, Number/Variable, Math Operator). A statement that has a least two numbers or variables, at least one mathematical operation, and is called a mathematical expression. Let's get acquainted with expressive writing. A number is 6 more than half of another number, which is known as x.
given
It is possible to locate more numbers in the challenge in some years than in others.
You might want to limit the number-finding assignment to a subset of the numbers depending on the age and arithmetic proficiency of your pupils as well as the amount of class time you want to allot to this task. The 2023 Challenge is available in 6 distinct iterations this year, which you can print and utilize with your pupils. Using the digits in 2023, set a challenge for your students to discover the numbers 1-10, 1-20, 1-30, 1-40, 1-50, or 1-100.
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A manufacturing firm want to determine the proportion of defects in a manufacturing process. How many of its products does it need to sample if it wants to achieve a ±5% accuracy at a 95% confidence level, given that it believes that the true proportion of defects is no greater than 10%?
Answers
The firm needs to sample 138.297 products to achieve a ±5% accuracy at a 95% confidence level, given that it believes that the true proportion of defects is no greater than 10%.
What is a manufacturing firm?Generally, To determine the sample size needed to achieve a ±5% accuracy at a 95% confidence level, with a maximum expected proportion of defects of 10%, you can use the formula for sample size for a proportion. The formula is:
n = (z^2 * p * (1-p)) / E^2
Where:
n is the sample sizez is the standard normal deviate corresponding to the desired level of confidence (1.96 for a 95% confidence level)p is the maximum expected proportion of defects (0.10 in this case)E is the margin of error (0.05 in this case)Plugging in the given values, we get:
n = (1.96^2 * 0.10 * (1-0.10)) / 0.05^2
n =138.297
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Some students collected the data below month and average temperatures. They will graph the data. What is the y-intercept? Your answer should be an ordered pair/
Answers
The y intercept of the data collected is 42°C
What is an equation?An equation is an expression composed of variables and numbers linked together by mathematical operations.
The slope intercept form of a linear equation is:
y = mx + b
Where m is the slope (rate of change) and b is the y intercept.
Let y represent the average temperature and x represent the month. x = 0 represent the month January.
From the table, at January, the average temperature is 42°C. Hence the y intercept is 42°C.
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Hi can someone help me do this math problem? How would you do it in a ti-84 calculator or by hand?
Answers
The value of x, if x is a real number and the expression, [tex]\frac{x + 2\cdot \mathbf{i}}{1 + \mathbf{i}}[/tex] is a purely imaginary number is x = -2. The correct option is option b.
b. -2
What is an imaginary number?An imaginary number is a number which is obtained by finding the square root of a negative number.
The specified expression is; [tex]\frac{x+2\cdot \mathbf{i}}{1 + \mathbf{i}}[/tex]
Multiplying the numerator and the denominator by the complex conjugate of the denominator, (1 - i), we get;
[tex]\frac{x+2\cdot \mathbf{i}}{1 + \mathbf{i}}\times \frac{1 - \mathbf{i}}{1 - \mathbf{i}} =\frac{x - x \cdot \mathbf{i}+2 \cdot \mathbf{i}-2\cdot \mathbf{i}^2}{1 - \mathbf{i}^2}[/tex]
[tex]\frac{x - x \cdot \mathbf{i}+2 \cdot \mathbf{i}-2\cdot \mathbf{i}^2}{1 - \mathbf{i}^2} = \frac{x + (2 - x)\cdot \mathbf{i} + 2}{1 - (-1)} =\frac{x + (2 - x)\cdot \mathbf{i} + 2}{2}[/tex]
Where x is real, for the number to be purely an imaginary number, we get;
[tex]\dfrac{x + (2 - x)\cdot \mathbf{i} + 2}{2} = \dfrac{x +2+ (2 - x)\cdot \mathbf{i} }{2} = \dfrac{0+ (2 - x)\cdot \mathbf{i} }{2}[/tex]
[tex]\frac{0+ (2 - x)\cdot \mathbf{i} }{2} = \frac{(2 - x)\cdot \mathbf{i} }{2} = \frac{(2-x)}{2} \cdot \mathbf{i}[/tex]
Therefore, for the number to be a purely imaginary number, then; x + 2 in the numerator following the multiplication of the numerator and the denominator by the complex conjugate of 1 + i, which is 1 - i, should be 0, and we get;
x + 2 = 0
x = 0 - 2 = -2
x = -2
The value of x such that the expression (x + 2·i)/(1 + i) is a purely imaginary number is; x = -2
The correct option is; b. -2
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Sally bought a soft drink for $3 and seven candy bars. she spent a total of $31. how much did each candy bar cost? Write an equation to represent the problem, and show the steps to solve it.
Answers
Answer:
31=3+x
31=-3+x
28=x
28/7
$4
Each Candy bar cost $4 each
Step-by-step explanation:
. The cylinder shown below
has a diameter of 5.2 cm on
the base and a height of 7.1
cm. Label the
measurements and find the
volume of the cylinder.
Answers
We are given the diameter of 5.2 and the formula requires the radius so that would be (5.2/2) 2.6. The height of 7.1 is given. Now plug everything into the formula.
V=pi 2.6^2 7.1
Note: I am using 3.14 for pi
v= 150.7074 cm^3
Solve for n. 7n - 2 = 5n + 6
Answers
Answer:
n = 4
Step-by-step explanation:
Pre-SolvingWe are given the equation 7n - 2 = 5n + 6, ans we want to solve it for n.
To do this, we need to isolate n one one side.
SolvingLet's start by adding 2 to both sides.
7n - 2 = 5n + 6
+2 +2
_______________
7n = 5n + 8
Now, subtract 5n from both sides.
7n = 5n + 8
-5n -5n
_______________
2n = 8
Divide both sides by 8 to get the value of n.
2n = 8
÷2 ÷2
________
n = 4
A track runner counted the number of races he had during a season. The graph shows the relationship between the number of track meets, x, and the number of races, y.
coordinate plane with the x axis labeled number of track meets and the y axis labeled number of races with a line that passes through the points 0 comma 5 and 1 comma 7
Part A: Calculate the slope of the linear equation shown in the graph. Show all necessary work. (3 points)
Part B: What does the slope mean for the relationship between the number of races and the number of track meets? (3 points)
Part C: Interpret the y-intercept in the situation. (3 points)
Part D: Write the equation of the line shown on the graph in slope-intercept form. (3 points)
Answers
A. The slope of the linear function is given as follows: m = 2.
B. The slope means that the number of races increases by two when the number of track meets increases by one.
C. The y-intercept of 5 means that when there are 5 races when there are 0 track races.
D. The slope-intercept definition of the linear function is given as follows: y = 2x + 5.
How to define the linear function?The slope-intercept definition of a linear function is given as follows:
y = mx + b.
In which:
m is the slope, representing the rate of change of the output variable relative to the input variable.b is the intercept, representing the value of y when x assumes a value of zero.The input and output variables for this problem are given as follows:
Input x: number of track meets.Output y: number of races.Two points in the function are given as follows:
(0,5) and (1,7).
Hence the slope and the intercept are given as follows:
Slope of 2, as when x increases by one, y increases by two.Intercept of 5, as when x = 0, y = 5.Meaning that the function is defined as follows:
y = 2x + 5.
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To which set does the number
11 belong. Choose the most descriptive answer.
O rational
O irrational
O whole
O natural
Answers
Answer:
Step-by-step explanation:
The number 11 belongs to the set of natural numbers. Natural numbers are the set of all positive whole numbers, including 0, and the number 11 is a positive whole number.
simplify 7m-2(3m^2 +mn)
Answers
Answer: 7m-6m²-2mn
Step-by-step explanation:
Multiply each term in parenthesis by -2
Calculate product (2x3=6)
7m-6m²-2mn
Pleaseeeeew i beg you
Answers
The sum of three consecutive integers is 42. Which of the equations could represent this relationship? Select the two correct answers. x + (x + 1) + (x + 2) = 42 x + (x + 2) + (x + 4) = 42 (x minus 1) + x + (x + 1) = 42 (x minus 2) + x + (x + 2) = 42 x + 2 x + 3 x = 42
Answers
The equation that represents the relationship is:
x + (x + 1) + (x + 2) = 42
And the 3 consecutive numbers are 13, 14, and 15.
Which equation represents the relationship?Here we know that the sum of three consecutive integers is 42.
If the first number is x, then the two consecutive numbers are:
x + 1
x + 1 + 1 = x + 2
Then the sum of these 3 consecutive numbers can be written as:
x + (x + 1) + (x + 2)
And that is equal to 42, then the equation is:
x + (x + 1) + (x + 2) = 42
So the first option is the correct one.
And the solution is:
x + (x + 1) + (x + 2) = 42
3x + 3 = 42
3x = 42 - 3
3x = 39
x = 39/3
x = 13
The 3 numbers are:
13, 14, and 15.
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Jonathan Rodero operates a booth selling T-shirts during concerts. Following each event, he makes : deposit to his savings account. Today he has checks: $40.00, $50.00, and $35.00; cash and coins: 8 fifty-dollar bills. 12 twenty-dollar bills, 12 ten-dollar bills, 8 five-dollar bills, 22 one-dollar bills; less $100 in cash.
Answers
Jonathan deposited $847 in his saving account.
What is deposit slip?This bank deposit slip is the record of the total amount that a person is depositing into a bank account. It includes the details of the items being deposited, that is, the number of checks and notes or coins of each type in the form of cash.
Given,
Amount in checks = $40 + $50 + $35 = $125
8 fifty-dollar bills = 8 × $50 =$400
12 twenty-dollar bills = 12 × $20 = $240
12 ten-dollar bills = 12 × $10 = $120
8 five- dollar bills = 8 × $5 = $40
22 1-dollar bills = 22 × $1 = $22
Subtotal = $125 + $400 + $240 + $120 + $40 + $22 = $947
Less cash = $100
Total = $947 - $100
Total = $847
Hence, $847 is the total deposited amount by Jonathan.
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Please help me with the blanks.
Each answer can be used more than once, by the way.
Answers
I have 18 students that took a test. 4 of the students passed. What is the percentage of the students that passed and the students that didn't pass?
Answers
Step-by-step explanation:
as always with % calculations :
first find what is 100% or 1%. everything else can be calculated from that.
in our case, we got 100% = 18.
therefore, 1% = 100%/100 = 18/100 = 0.18
how many % are 4 students ?
as many as the times 1% (0.18) fits into 4 :
4 / 0.18 = 22.22222222... %
so,
22.22222222... %
of the students passed.
therefore,
100 - 22.22222222... = 77.77777777... %
of the students did not pass.
What is g(x)?
O A g(x)=-x
OB. g(x)=-lxi
OC. g(x)=-2*
O D. g(x)=-x²
Answers
Answer:
c.
Step-by-step explanation:
this graph is exponential equation
How much is 9.6 KB kilobytes
Answers
9.6 KB kilobytes is equal to 0.0096 MB
What is Unit of Measurement?A unit of measurement is a definite magnitude of a quantity, defined and adopted by convention or by law, that is used as a standard for measurement of the same kind of quantity.
1kB=1000 bytes
1MB=1000 KB
1kB=1/1000MB=0.001 MB
9.6 KB is nothing but 9600 bytes
9.6 KB in MB we have to convert
Now multiply 9.6 with 0.001
9.6×0.001
0.0096 MB
Hence, 9.6 KB kilobytes is equal to 0.0096 MB
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Simplificar -3+{4-2[6-3+4(5-7)]+3
Answers
Answer:
14
Step-by-step explanation:
Para simplificar esta expresión, debemos seguir el orden de las operaciones, también conocido como PEMDAS: paréntesis, exponentes, multiplicación y división (de izquierda a derecha), y suma y resta (de izquierda a derecha).
1. Comience por simplificar la expresión dentro de los paréntesis.
4-2[6-3+4(5-7)]
4-2[6-3+4(-2)]
4-2[6-3-8]
4-2[-5]
4+10 = 14
2. Ahora sustituya el valor simplificado dentro de los paréntesis en la expresión original:
-3+{14}+3
3. Ahora podemos sumar y restar de izquierda a derecha.
-3+14+3 = 14
Entonces, la expresión simplificada es 14.
At noon, a 36 foot building casts a 20 foot shadow. Find the shadow cast by a 6 foot tree. Set up a proportion and solve. Be sure to show all your work!
Answers
Answer:
3 1/3 ft
Step-by-step explanation:
Let SHADOW and HEIGHT pertain to the building, and let shadow and height pertain to the tree.
The proportion is:
HEIGHT/SHADOW = height/shadow
Now we fill in with the numbers we know, and "shadow" for the shadow of the tree.
(36 ft)/(20 ft) = (6 ft)/(shadow)
Cross multiply.
36 × shadow = 6 × 20
36 × shadow = 120
shadow = 120/36 = 10/3
shadow = 3 1/3
Answer: 3 1/3 ft
A mother gives birth to a 7-pound baby. Every 3 months, the baby gains 2 pounds. If x is the age of the baby in months, then y is the weight of the baby in pounds. Find an equation of a line in the form y=mx+b that describes the baby's weight.
y =___________________
Answers
Answer:
y = 2/3 x + 7
Step-by-step explanation:
At birth represents the beginning of time for the baby. Lets call this month zero. So here are your coordinates.
x = 0 y = 7 ----> at birth
x = 3 y = 9
x = 6 y = 11
x = 9 y = 13
Now we find the slope between each point. Since the common difference of y is 2 and the common difference in x is 3 , the slope will be
slope = y / x = 2 / 3
Therefore, the equation of the line that represents this relationship is
y = (2/3) x + 7
Select the correct answer.
Which type of investment offers both capital gains and interest income?
Α. property
B. CDs
C. stocks
D. bonds
Answers
Answer:
D
Step-by-step explanation:
evaluate -
[tex]\int \:{tan}^{ - 1} x \: dx[/tex]
tysm! :)
Answers
calculate 76.7 × 308.2 ÷ 8.04
Answers
Answer:
Step-by-step explanation:
2940.1667
Answer:
2940.16667
Step-by-step explanation:
casey draws a rectangle array that is 1,167 units long and 7 units wide. what is the area of caseys array?
Answers
The Casey's rectangular array that is 1,167 units long and 7 units wide has an area of
8169 square unitsHow to calculate the area of the rectangleThe formula for the area of a rectangle is the product of length and wide. This is written mathematically as
= length * wideness
In the problem the rectangular array made by Casey has a the following dimensions
length = 1167 units
wide = 7 units
Area of rectangle = length * wideness
substituting the values
Area of rectangle = 1167 * 7
Area of rectangle = 8169 square units
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Fiona is purchasing hammers and wrenches for her workshop, and she would like to
spend under $120. Each hammer costs $5, and each wrench costs $6. Let x be the
number of hammers and y be the number of wrenches.
Select the inequality that describes the situation.
O 6x + 5y< 120
5x + 6y> 120
O6x + 5y 120
5x + 6y< 120
Answers
Answer:
The inequality that describes the situation is 5x + 6y < 120
Step-by-step explanation:
This inequality states that the total cost of purchasing x hammers and y wrenches must be less than $120. Each hammer costs $5 and each wrench costs $6, so the total cost is represented by the expression 5x + 6y.
The inequality states that 5x + 6y < 120 which means for any number of hammers and wrenches she buys it should be less than 120.
The other options:
6x + 5y < 120: the coefficient of x is 6 instead of 5 and that of y is 5 instead of 6.
5x + 6y > 120: the inequality is greater than instead of less than, which means that the total cost should be greater than $120 which is not the case.
6x + 5y ≥ 120 : the inequality is greater than or equal to instead of less than, which means that the total cost should be greater than or equal to $120 which is not the case.
Are the two triangles below similar? If so, write a similarity statement, and stay with similar to criteria can be used to prove it.
Similarity statement-
1. PNK DKG
2. PNK GDK
3. PNK KGD
4. The triangles are not similar
Criteria-
1. AA
2. SAS
3.SSS
4. Not applicable, the triangles are not similar
Answers
The two triangles below show the property of similarity.
The first property is the Side.
The side PN is similar to the side DG.
The second property his angle.
∠PNK = ∠DGK = 90°
The third property would be side as well.
Side NK is similar to the side GK.
Thus, the two triangles are similar.
Similarity is the mathematical property of triangles, wherein two triangles are called similar if they have either two congruent angles and one similar side, or two similar sides in ratio with one another and a congruent angle.
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HELP PLSS
subtract the polynomials
Answers
The value from the subtraction of the polynomials is -5x³ - 6xy -17y²
The degree is 3
What is an algebraic expression?An algebraic expression is defined as an expression that consists of terms, coefficients, variables, constants and factors.
They are also made up of mathematical expressions, such as;
ParenthesesBracketAddiitionSubtractionMultiplicationDivisionAlso, polynomials are algebraic expressions that are made up of coefficients and indeterminants.
These polynomials have degree of the variable, x, greater than one.
From the information given, we have that;
x³ + 4xy -8y² - (6x³ + 10xy - 9y²)
expand the bracket
x³ + 4xy - 8y² - 6x³ - 10xy - 9y²
Now, collect like terms
x³ - 6x³ + 4xy - 10xy - 8y² - 9y²
Add or subtract like terms
-5x³ - 6xy -17y²
Hence, the value is 3
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A jailer carries a large key ring. The key ring has a diameter of 4 inches. What is the key ring's radius?
Answers
Answer:
2 inches
Step-by-step explanation:
The radius is simply the distance from the edge if you were at the center, which is equal to half the diameter. So given the diameter is 4 inches, we divide that by two, [tex]\frac{4\text{ inches}}{2}=2\text{ inches}[/tex] and that's our radius!
