Answer:
y = 4 sin(2x/3)
Step-by-step explanation:
The parent function for sine functions is: y = a sin b(x - c) + d
"a" defines amplitude/vertical dilation
"b" defines the change to the period/horizontal dilation
"c" defines the phase shift/horizontal translation
"d" defines the midline/vertical translation
We can already set "a = 4" because 4 is the amplitude.
However, to include the period into the function, we have to take note of the parent sine function already having a period of 2π.
This means: 2π/b = period
2π/period = b
2π/3π = b
2/3 = b
Knowing the "a" and "b" values, we can set up the equation:
y = 4 sin(2x/3)
No horizontal/vertical translations were applied, so "c" and "d" are both zero.
2 market women shared a basket full of oranges in order to sell them.the share of the first woman is twice the other if the are 300 oranges in the basket what is the share of each women
Answer:
Step-by-step explanation:
no idea
The number of oranges with first women are 200 and the number of oranges with other women are 100.
What is an equation?In mathematics, an equation is a formula that expresses the equality of two expressions, by connecting them with the equals sign =.
Given that, 2 market women shared 300 oranges.
The share of first woman is twice the other.
Let the number of oranges with other women be x.
Then, the number of oranges with first women will be 2x.
Now, x+2x=300
3x=300
x=100
So, 2x=200
Therefore, the number of oranges with first women are 200 and the number of oranges with other women are 100.
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Determine which set of side measurements could be used to form a triangle.
8, 14, 20
7, 8, 15
2, 19, 22
1, 4, 8
The set of side measurements that could be used to form a triangle are 8, 14, 20.
How can the set of side measurements be identified?The concept that will be used is the concept of triangle inequality theorem.
To know if the given 3 side lengths are a triangle, then the use of the triangle inequality theorem comes into play.
This rule tells us that when we sum 2 sides of a triangle the value must be greater than the third side.
Then this rule can be applied as
The first option; 8, 14, 20
a+b>c = 8+14>20
a+c>b = 8+20>14
b+c>a = 20+14>8
Therefore, first option is correct.
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Find the midpoint of the line segment with end coordinates of:
(0, 2) and (8,8)
The mid point of the line segment with the end coordinates of:
(0, 2) and (8,8) is (4,5).
Define the term mid point?A mathematical expression known as the midpoint formula is used to determine where two data points meet midway. This formula is also used in the study of economics to determine this same coefficient of elasticity, etc.The midpoint is the point on the center of the line that is equally distant as from 2 points if a line is created connecting the two points.For the given question;
The given coordinates are-
(x1, y1) = (0, 2)
(x2, y2) = (8,8)
The mid point is found by the formula;
x = (x1 + x2 )/2
y = (y1 + y2)/2
Put teh values,
x = (0 + 8)/2
x = 4
y = (2 + 8)/2
y = 5
Thus, the mid point of the line segment with the end coordinates of:
(0, 2) and (8,8) is (4,5).
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f(x)=−x 2 −2x+3 \text{Find }f(1) Find f(1)
Joseph invested $7,850 in an account that pays 7.5% interest per year. How much interest will Juan have earned at the end of 36 months?
Juan have earned of interest after 36 months at the rate of 7.5% interest per year.
What is Simple Interest?Simple interest is a quick and simple formula for figuring out how much interest will be charged on a loan. The daily interest rate, the principle, and the number of days between payments are multiplied to calculate simple interest. The formula of simple interest is as follows:
S.I = p×r×t
Where p is principle value, r is rate and t is time in years.
Here, the principle amount is $7,850 and rate is 7.5% i.e [tex]\frac{7.5}{100}=0.075[/tex] and time is 36 months i.e 3 years.
Now, putting the values,
SI = 7850×0.075×3
= $ 1766
Therefore, the interest Juan have earned in 36 months is $1,766.
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for any integer p, show that p^3+11p will always be a multiple of 6
By the principle of mathematical induction, it has been proved that
[tex]p^3 + 11p[/tex] is divisible by 6
What is Principle of mathematical induction?
Let the statement be given by P(n). At first P(n) is proved to be true for 1. Then it is assumed that P(n) is true for all n. If P(n) is true for (n+1) then by Principle of Mathematical induction, P(n) is true for all natural numbers
The given expression is [tex]p^3 + 11p[/tex]
For p = 1
[tex](1)^3 + 11 \times 1\\12[/tex]
which is a multiple of 6
Let it be true for p = m
[tex]m^3 + 11m[/tex] is a multiple of 6
[tex]m^3 + 11m = 6k[/tex], where k is any integer
For p = m + 1
[tex](m+1)^3 + 11(m+1) \\m^3+3m^2+ 3m +1+11m+11\\m^3+11m +3m^2+3m+12\\m^3+11m + 3m(m+1) + 12[/tex]
Now,
[tex]m^3 + 11m[/tex] is divisible by 6
We know that the product of two consecutive integers are divisible by 6
[tex]3m(m+1)[/tex] is divisible by 6
12 is divisible by 6
[tex](m+1)^3 + 11(m+1)[/tex] is divisible by 6
So it is true for p = m + 1
By the principle of Mathematical induction, it is true for all natural numbers and eventually for all integers
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can someone
help with this
Step-by-step explanation:
let angles of a triangle a=86
b= 180-3z , c= 180-4z
a+b+c = 180 {angle sum property}
86 +180+180-3z-4z=180
446 -7z = 180
-7z = -266
[tex]z = \frac{ - 266}{ - 7} = 38[/tex]
so other angle are
3z = 3 x 38 = 114
4z = 4 x 38 = 152
The names or notes of all the white notes on a piano are written in pieces of paper and placed in a cup. There are 7 sets of the notes D E F and G and 8 sets of the notes A B and C. If a person draws one note out of the cup without looking what are the chances of them getting a c
The probability that the person obtains a note with C written in it is of:
0.1538 = 15.38%.
How to calculate a probability?The probability of an event in an experiment is obtained as the number of desired outcomes in the context of the experiment divided by the number of total outcomes in the context of the experiment.
The total number of notes in this problem is composed as follows:
7 notes of each of D, E, F and G.8 notes of each of A, B and C.Hence the total number is of:
Total = 7 x 4 + 8 x 3 = 52 notes.
The desired number of outcomes is the number of notes with C, hence:
Desired = 8 notes.
Thus the probability is calculated as follows:
Probability = Desired/Total = 8/52 = 0.1538 = 15.38%.
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A rectangular garden has an area of 72 square yards. The dimensions of the
garden are not prime numbers. What are the possible dimensions of the
garden
Answers:
1 yard by 72 yards
4 yards by 18 yards
6 yards by 12 yards
8 yards by 9 yards
==========================================================
Explanation:
Let's list out all the ways to multiply to 72 using two values
1*72
2*36
3*24
4*18
6*12
8*9
Then cross off something like 2*36 since 2 is prime. We also cross off 3*24 since 3 is prime.
We're left with this list
1*72
4*18
6*12
8*9
which represent the possible dimensions of this rectangle.
Keep in mind that 1 is not prime.
Find the image vertices for a dilation with center (0,0) and a scale factor of 4.
After dilation with center (0, 0) and scale factor 4 the required image vertices of the given image is given by A' =(-12 , 4), B' =(16 , -12),
C' = (8 , 12), D' = (-4 , 16).
As given in the question,
From the given graph of quadrilateral the vertices of the given image is given by :
A and D are second quadrant , C is first quadrant and B is in fourth quadrant.
Each unit on both the axis represents 1 unit only.
Coordinates of each vertices are:
A = (-3 , 1) , B = (4 , -3) ,C = (2 , 3), D = (-1 , 4)
Now for dilation scale factor is equal to 4
Image vertices for a dilation with center (0 , 0) multiply the vertices by scale factor 4.
Required image vertices are given by:
A' = (-12 , 4),
B' = (16 , -12)
C' = (8 , 12)
D' = (-4 , 16)
Therefore, after dilation with center (0, 0) and scale factor 4 the required image vertices of the given image is given by A' =(-12 , 4), B' =(16 , -12),
C' = (8 , 12), D' = (-4 , 16).
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4
The height of a cone is two times its base diameter. What is the volume of the cone in terms of its base radius r
The volume of cone will be [tex]\frac{88r^{3} }{21}[/tex]
Cone:
A cone is a three-dimensional geometric shape that tapers smoothly from a flat base.
Given,
The height of a cone is two times its base diameter.
we have to find the volume of cone in terms of base radius.
let us assume the base radius of cone is equal to r units
so diameter(d) of cone will be, d= 2r units
so,
height(h) of cone will be equal to, h = 2d units
h = 2x2r units
h = 4r units
We know,
Volume of the cone(V) = [tex]\pi r^{2} h/3[/tex]
Where,
r = radius of base
h = height of cone
π = 22/7
Thus by using formula,
Volume of cone(V) = [tex]\pi r^{2} h/3[/tex]
= 22/7 * [tex]r^{2}[/tex] * 4r/3
= 88[tex]r^{3}[/tex]/21
= [tex]\frac{88r^{3} }{21}[/tex]
Hence,
The volume of cone will be [tex]\frac{88r^{3} }{21}[/tex]
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An entry level architect's annual pay is $47,008 based on 52 weeks per year. Due to the economy, his company is having to cut back on the number of weeks that it employs its architects. If the firm cuts the work year to 48 weeks but keeps the same rate of pay, how much should the architect expect his annual pay to decrease? Round your answer to the nearest dollar.
After the firm work year reduced to 48 weeks at the same rate, the architect annual pay decrease to 43,392 dollars.
How to find the annual pay decrease?An entry level architect's annual pay is $47,008 based on 52 weeks per year. Due to the economy, his company is having to cut back on the number of weeks that it employs its architects
The company cuts the work year to 48 weeks but keeps the same rate of pay. The amount the architect should expect his annual pay to decrease can be calculated as follows:
Let's find the rate.
Therefore,
52 weeks = 47008
1 week = ?
cross multiply
rate = 47008 / 52
rate = 904 dollars per weeks
He collects the same rate after the company cuts the work year to 48 weeks.
Therefore,
annual pay of the architect after the cut = 48 × 904
annual pay of the architect after the cut = 43,392 dollars
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What is the value of x?
Thank you.
Answer:
x would be 3 by 2
I am 90% sure but I hope this helps!
To prepare for his mountain biking trip, Rhyan bought four tire patches. Rhyan paid using a gift card that had $22.20 on it. After the sale, Rhyan’s gift card had $1.90 remaining. Which equations could you use to find the price of one tire patch? Select all that apply. 4x – 1.9 = 22.2 4x – 22.2 = 1.9 4x + 1.9 = 22.2 4x + 22.2 = –1.9 22.2 – 4x = 1.9
The equations you use to find the price of one tire patch are 4x + 1.9 = 22.20 and 22.2 – 4x = 1.9, so options A and E are correct.
What is equation?A formula known as an equation uses the equals sign to denote the equality of two expressions.
Given:
The Balance on the gift card = $22.20,
The no of patches bought = 4,
The left balance on the card = $1.90.
The equation for the statement in the question is,
The no of patches bought × The price of patches + The left balance on the card = The Balance on the gift card
Let x be the price of one batch
Substitute the values,
4x + 1.9 = 22.20 or 22.2 – 4x = 1.9
Therefore, the equations you use to find the price of one tire patch are 4x + 1.9 = 22.20 and 22.2 – 4x = 1.9.
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An investment portfolio is shown below.
Investment Amount Invested ROR
Savings Account $3,200 2.1%
Municipal Bond $4,900 4.5%
Preferred Stock $940 10.5%
Common Stock A $1,675 −3.5%
Using technology, calculate the weighted dollar amount of the savings account.
−$58.63
$58.63
−$67.20
$67.20
The weighted dollar amount of the savings account as per the an investment portfolio is; $67.20.
What is the percentage?A percentage is a minimum number or ratio that is measured by a fraction of 100.
Given that An investment portfolio is;
Investment Amount Invested ROR
Savings Account $3,200 2.1%
Municipal Bond $4,900 4.5%
Preferred Stock $940 10.5%
Common Stock A $1,675 -3.5%
The weighted dollar amount of the savings account is;
= 2.1% of $3200
= ( 2.1 / 100) × $3200
= ($6720) /100
= $ 67.20
Therefore, the weighted dollar amount of the savings account as per the an investment portfolio is; $67.20.
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55555555555555555555555555555555555555555555555555555555555555555555555555x0
Answer:
Step-by-step explanation:
Ok:
1. Anything times zero always equals zero.
So: 55555555555555555555555555555555555555555555555555555555555555555555555555x0=
Answer:0
log 4(x+8) + log 4(x+5) = 1
rewrite the equation
According to the product rule of logarithms, the given equation is written as, log₄(x² + 13x + 40) = 1
Product rule of logarithm
Basically, the product rule states that the sum of two logarithms is equal to the product of the logarithms.
And it is the first law and it can be represented as;
logₐ(x) + logₐ(y) = logₐ(xy)
Given,
Here we have the logarithmic equation log 4(x+8) + log 4(x+5) = 1
And we have to rewrite the equation.
Here we have the logarithmic equation,
=> log₄(x+8) + log₄(x+5) = 1
By using the product property of logarithms,
We have to rewrite the equation as,
=> log₄(x+8)(x+5) = 1
Now, we have to expand (x+8)(x+3) using the FOIL Method.
Then we get,
=> log₄(x² + 5x + 8x + 40) = 1
=> log₄(x² + 13x + 40) = 1
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Michelle sells new and used kayaks. She makes a 10.5% commission on every kayak she sells and she also gets paid $495.50 per week.
a) Develop an equation for the way Michelle is paid.
b) Last month, the total value of the kayaks she sold was $19 425. Use the equation you’ve developed to find out how much Michelle was paid for that month.
Part a
The equation for the way Michelle is paid is
Total weekly payment y = 495.50 + 0.105x
Part b
The total payment in a month = $4021.625
She makes a 10.5% commission on every kayak she sells
Consider the total value of kayaks she sold = x
The rate of commission = 10.5%
The amount of commission = x × (10.5/100)
= 0.105x
The weekly fixed payment = $495.50
Total weekly payment y = 495.50 + 0.105x
Part b
The total value of the kayaks she sold = $19425
Total number of weeks in a month = 4
Then the total payment in a month = (4 × 495.50) + (0.105×19425)
= 1982 + 2039.625
= $4021.625
Hence,
part a
The equation for the way Michelle is paid is
Total weekly payment y = 495.50 + 0.105x
Part b
The total payment in a month = $4021.625
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Status:
Frank borrowed $56022 from the bank at 4.0% for 69 days to expand his bike shop.
Find the total amount Frank pays back to the bank.
The total amount Frank pays back to the bank = $210642.72
Assuming the given interest rate- that is the simple interest rate.
so the future value A for the simple interest rate is given by,
A = P(1 + rt)
here, P = $56022
r = 0.04
t = 69
Substitute these values in above formula.
A = 56022 (1 + 0.04 * 69)
A = 56022 * 3.76
A = $210642.72
Therefore, the total amount Frank pays back to the bank = $210642.72
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A store is having a sale on chocolate chips and walnuts. For 3 pounds of chocolate chips and 2 pounds of walnuts, the total cost is $14. For 5 pounds of
chocolate chips and 6 pounds of walnuts, the total cost is $28. Find the cost for each pound of chocolate chips and each pound of walnuts.
Cost for each pound of chocolate chips: $
Cost for each pound of walnuts: $
Cost for each pound of chocolate chips is equal to $3.5.
Cost for each pound of walnuts is equal to $1.75
How to determine the cost for each pound of chocolate chips and each pound of walnuts?In order to solve this word problem, we would assign variables to the cost for each pound of chocolate chips and each pound of walnuts respectively, and then translate the word problem into algebraic equation as follows:
Let the variable c represent the amount of cost for each pound of chocolate chips.Let the variable w represent the cost for each pound of walnuts.For 3 pounds of chocolate chips and 2 pounds of walnuts, we have:
3c + 2w = 14 .....equation 1.
For 5 pounds of chocolate chips and 6 pounds of walnuts, we have:
5c + 6w = 28 .....equation 2.
Solving the system of equations by using the elimination method, we have:
3 × (3c + 2w = 14) = 9c + 6w = 42
5c + 6w = 28_
4c = 14
c = 14/4
c = $3.5
For the cost for each pound of walnuts, we have:
3c + 2w = 14
3(3.5) + 2w = 14
10.5 + 2w = 14
2w = 14 - 10.5
2w = 3.5
w = 3.5/2
w = $1.75.
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Add.
3/5+7/8+3/10
Enter as a mixed number in simplest form.
Answer:71/40 or 1 31/40 or 1.775
Step-by-step explanation:1 31/40 is the mixed number
(b) Tickets for a raffle are placed in a box. The box contains 25 blue tickets and 20 red
tickets. Tickets are drawn at random from the box, one at a time and are not replaced.
What is the probability that:
(i) the first ticket drawn is red and the second ticket drawn is blue?
Probability of drawn ticket at random with the condition of first ticket drawn is red and for second ticket drawing blue is equal to 0.253.
As given in the question,
Number of blue tickets in a box is equal to 25
Number of red tickets in a box is equal to 20
Total number of tickets in a box = 25 + 20
= 45
Drawing a ticket one at a time and not replaced
Probability of drawing a ticket first is red and second drawn is blue
= ( 20 / 45 ) × ( 25 / 44 )
= ( 500 / 1980 )
= 0.2525..
= 0.253
Therefore, probability of drawn ticket at random with the condition of first ticket drawn is red and for second ticket drawing blue is equal to 0.253.
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Determine the x- and y-intercepts of the graph of x+2y=−4 .
Then plot the intercepts to graph the equation.
Keyboard Instructions
Initial graph state
The horizontal axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).
The vertical axis goes from -10.8 to 10.8 with ticks spaced every 1 unit(s).
Answer:
Step-by-step explanation:
1) first we find the x and y intercepts. Remember the intercepts are where x=0 and y=0
2) To find the x-intercept, substitute y = 0 and solve for x.
given equation: x +2y= -4
then substitute y=0 so
x+ 2(0) = -4 -> any number multiplied by 0 it will always equal zero
then, it will be x=-4
the coordinates will be (-4,0)
3) To find the y-intercept, substitute x =0 and solve for y.
given equation: x +2y= -4
then substitute x=0 so
(0)+ 2y = -4 -> x disappears since is zero
then, it will be 2y=-4
then we multiply by 2 :
2y/2 = -4/2
y=-2
the coordinates for the y-intercept will be (0,-2)
graph:
Which is the graph of y = 3¥x+2 + 3?
The graph of the equation y = 3x + 2 + 3 is shown below .
In the question ,
it is given that ,
the equation of the line is y [tex]=[/tex] 3x [tex]+[/tex] 2 [tex]+[/tex] 3 ,
we need to draw the graph of it .
Do draw the graph we need at least two points .
for the first point
put x = 0
we get ,
y = 3(0) + 2 + 3
y = 0 + 2 + 3
y = 2 + 3
y = 5
the first point is (0,5)
for the second point put y = 0,
we get ,
0 = 3x + 2 + 3
3x = - 2 - 3
3x = -5
x = -5/3 ,
So , the second point is (-5/3 , 0)
the graph of the given equation is shown below .
Therefore , The graph of the equation y [tex]=[/tex] 3x + 2 [tex]+[/tex] 3 is shown below .
The given question is incomplete , the complete question is
What is the graph of the equation y = 3x + 2 + 3 ?
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Suppose you are designing a cardboard box that must have a volume of 18 cubic feet. The cost of the cardboard is $6 per square foot. How much will the material for each box cost?
Answer:
I think its 108 each Box is going to cost 108
John worked 18 hours last week. He earned $216. What was his hourly rate?
Find the y-coordinate of the y-intercept of the polynomial function defined below.
f(x) = 3 + 5x² + 4x^4 - 3x³ - 6x
Answer:
3
Step-by-step explanation:
When you substitute 0 in for x in the equation. You are left with f(0) = 3.
If the function f(x) is thje absolute value of 3 more than the value of x. Select all the true statements. A. The x-intercept of the function is 3.
The absolute value function is represented by f(x) = |x+3| and the
x-intercept of the function is -3.
The function is represented as absolute value of 3 more than x.
hence the function 3 more than x is given by
f(x)=x+3
Now for absolute function:
f(x)=|x+3|
The graph of the function will have no negative value for f(x).
The graph will pass through the point (0,3) which is the y-intercept.
The x-intercept is at (-3,0) .
The domain of the function is all real vales of x.
The range of the function is (0,∞)
The parent function is given by y=|x| .
An procedure that establishes the absolute value of a number or variable is known as a modulus function. It produces the variable count's size.
It is also known as an absolute value function. No matter what input was given to this function, a positive result is always the result.
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1.3 x 10 to the power of negative 3
Answer:
The answer to this problem is 0.0013.
The equation y – 4 = 6(x + 7) represents a linear function. What is the y-intercept of the graph of the equation?
Step-by-step explanation:
In general equation, y = mx+c, c represents y-intercept.
So, y-4 = 6x+42
y = 6x+46
So, y intercept will be 46