Answer:
(4,π/6)
Step-by-step explanation:
The correct polar coordinates of the point (2√3, 2) are (r, θ) = (4, π/6).
Explanation:
Using the formulas for converting Cartesian coordinates to polar coordinates:
r = √(x^2 + y^2)
θ = atan2(y, x)
Plugging in the given values:
r = √((2√3)^2 + 2^2)
= √(12 + 4)
= √16
= 4
θ = atan2(2, 2√3)
≈ 0.5236 radians
However, in the polar coordinate system, angles are typically expressed in radians between 0 and 2π. The angle π/6 is equivalent to 0.5236 radians, so the correct polar coordinates of the point (2√3, 2) are (r, θ) = (4, π/6).
Select all numbers that are irrational.
Answer:
The irrational numbers are:
368.5468432...
14.19274128...
√.156
7
Select the correct answer from the drop-down menu.
Which term best fits the sentence?
After you make a decision, the next step in the decision-making process is to
whether you made the right choice.
Reset
Next
This step will help you det
Answer:
Step-by-step explanation: bot
whose graph passes through the points (-1, 0) and (-5, 0)
The graph of the line passing through the points (-1, 0) and (-5, 0) is attached.
Given are two points we need to find the equation of line passing through them,
We know that the equation of a line passing through two points, (x₁, y₁) and (x₂, y₂) is,
y-y₁ = y₂-y₁ / x₂-x₁ (x-x₁)
Here, (x₁, y₁) and (x₂, y₂) are (-1, 0) and (-5, 0).
So,
y-0 = 0-0 / -5+1 (x+1)
y = 0
Hence, the equation of the line is y = 0.
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The sales data for July and August of a frozen yogurt shop are approximately normal.
The mean daily sales for July was $270 with a standard deviation of $30. On the 15th of July, the shop sold $315 of yogurt.
The mean daily sales for August was $250 with a standard deviation of $25. On the 15th of August, the shop sold $300 of yogurt.
Which month had a higher z-score for sales on the 15th, and what is the value of that z-score?
a.)
August, with a z-score of 1.67.
b.)
July, with a z-score of 1.5.
c.)
July, with a z-score of 1.8.
d.)
August, with a z-score of 2.
Answer: D
Step-by-step explanation:
To determine which month had a higher z-score for sales on the 15th, we need to calculate the z-scores for each month's sales.
For July:
z-score = (x - μ) / σ
where x is the sales on the 15th, μ is the mean daily sales for July, and σ is the standard deviation of daily sales for July.
Plugging in the values, we get:
z-score for July = (315 - 270) / 30 = 1.5
For August:
z-score = (x - μ) / σ
where x is the sales on the 15th, μ is the mean daily sales for August, and σ is the standard deviation of daily sales for August.
Plugging in the values, we get:
z-score for August = (300 - 250) / 25 = 2
Since the z-score for August is higher than the z-score for July, August had a higher z-score for sales on the 15th.
The value of the z-score for August's sales on the 15th was 2.
write a quadratic function that passes through points (5,0) (9,0) (7,-20)
The quadratic function that passes through points is P(x) = 5(x - 5)(x - 9)
Writing the quadratic function that passes through pointsFrom the question, we have the following requirements that can be used in our computation:
Zeros at (5,0) (9,0) Point (7,-20)The quadratic function, P(x), in factored form is represented as
P(x) = a * product of (x - zeros)
So, we have
P(x) = a(x - 5)(x - 9)
Using the point (7, -20), we have
a(7 - 5)(7 - 9) = -20
So, we have
a = 5
Recall that
P(x) = a(x - 5)(x - 9)
So, we have
P(x) = 5(x - 5)(x - 9)
Hence, the function is P(x) = 5(x - 5)(x - 9)
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A runner sets up her training schedule. Each week she will increase the number of miles she runs. The number of miles she runs this week will be 2 more than the number she ran last week. Let x = miles she ran last week Let y = miles she runs this week Which equation represents the situation? O A. y = 2x OB. y= 2/ OC. y=x-2 O D. y = x + 2
y = x + 2 represents the correct equation for the situation.
Option D is the correct answer.
We have,
The problem states that the number of miles the runner runs this week (y) will be 2 more than the number of miles she ran last week (x).
We can express this relationship using the equation:
y = x + 2
This equation means that if we know the number of miles the runner ran last week (x), we can find the number of miles she runs this week (y) by adding 2.
Thus,
y = x + 2 represents the correct equation for the situation.
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What is the area of the lawn of Serena's front yard, in square yards?
12 ft-
Driveway
Serena's Front Yard
72 ft
Lawn
-15 ft
Flower
Bed
15 ft
48 ft
My Progress
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3
Our square yard calculator allows you to easily find the total area of a surface. Additionally, if you wish to cover that surface with some material or to do some construction work, such as painting or gardening, it gives you an estimation of your material cost and labor cost.
The square yard calculator also allows you to use different units (imperial and metric) and seamlessly convert between the two. Want to enter your measurements in feet and get your area in square yards or square meters? We've got you covered. You can easily switch between units and get answers to questions like "How to convert from feet to yards?" or "How many square feet in a square yard?"
what is the solution to the equation 0.5x - 1.25 = 3.5?
Answer:
Step-by-step explanation:
Add '-1.25' to each side of the equation.
1.25 + -1.25 + -0.5x = 0.75 + -1.25 + 3.5n
Combine like terms: 1.25 + -1.25 = 0.00
0.00 + -0.5x = 0.75 + -1.25 + 3.5n
-0.5x = 0.75 + -1.25 + 3.5n
Combine like terms: 0.75 + -1.25 = -0.5
-0.5x = -0.5 + 3.5n
Divide each side by '-0.5'.
x = 1 + -7n
Simplifying
x = 1 + -7n
what is the area of the square if it’s 15 by 15
Answer:
225 is the answer
15 times 15
Step-by-step explanation:
Which diagram depicts as a positive angle in standard position?
Answer:
A.
Step-by-step explanation:
A positive angle has the initial side at the positive x-axis and the terminal side rotated counterclockwise from it.
That is shown in diagram A.
Find the value of x in the figure below 53° ,24° and x°
Answer:46
Step-by-step explanation:
traingle ABD = 53 + 24 + 47 + x = 180
134+x=180
x=180-134
x=46
can someone please help me what is 11 1/8 + 2 3/4??? please
Answer: 13 7/8
Step-by-step explanation:
11 + 1/8 + 3/4 + 2 = 13 7/8
Find a quadratic equation which has solutions x=7 and x=-9. Write the quadratic form in the simplest standard form x^2+bx+c=0
Answer: x^2+2x-63
Step-by-step explanation:
Quadratic Equation = x^2-(Sum of Solution)x+(Product of Solution)
=x^2-(7-9)+(7*(-9))
=x^2+2x-63
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Yui is buying beverages for her friends. She buys a total of 6 bottles of water and sports drinks. Bottles of water cost $1.50 each, and sports drinks cost $2.50 each, she spends a total of $10. Write a system of equations to represent the information, and use substitution to determine how many of each type of drink yui buys
Answer:
Let x be the number of bottles of water that Yui buys, and let y be the number of sports drinks she buys.
Since Yui buys a total of 6 bottles of water and sports drinks, we know that:
x + y = 6
We also know that each bottle of water costs $1.50 and each sports drink costs $2.50, and that Yui spends a total of $10. Therefore, we can write another equation based on the total cost:
1.5x + 2.5y = 10
We now have a system of two equations with two variables:
x + y = 6
1.5x + 2.5y = 10
To solve for x and y, we can use substitution. Rearranging the first equation, we get:
x = 6 - y
Substituting this expression for x into the second equation, we get:
1.5(6 - y) + 2.5y = 10
Expanding and simplifying, we get:
9 - 1.5y + 2.5y = 10
Combining like terms, we get:
y = 2
Substituting this value of y back into the equation x + y = 6, we get:
x + 2 = 6
Solving for x, we get:
x = 4
Therefore, Yui buys 4 bottles of water and 2 sports drinks.
Laura is 3 ft tall how tall is Laura in inches
The directional derivative of f= x^2 y z^3 along x = e^-t , y = 1 + 2 sint , z = t -cost at t =0
The directional derivative of f = x²yz³ along vector i + 2j + 2k at x = [tex]e^{-t}[/tex] , y = 1 + 2 sin t , z = t -cost at t =0 is 2/3.
Given that the functions are,
x = [tex]e^{-t}[/tex]
y = 1 + 2 sin t
z = t - cos t
At t = 0 the point will be,
x = e⁰ = 1
y = 1 + 2 sin 0 = 1
z = 0 - cos 0 = -1
So the point is (1, 1, -1).
The vector is,
a = i + 2j + 2k
unit vector of a = (i + 2j + 2k)/√(1² + 2² + 2²) = (i + 2j + 2k)/3
Given the function is, f = x²yz³
Grad. f = 2xyz³.i + x²z³.j + 3x²yz².k
directional derivative is given by
= (Grad. f)*(unit vector of a) at (1, 1, -1)
= (2xyz³.i + x²z³.j + 3x²yz².k)*(i + 2j + 2k)/3 at (1, 1, -1)
= (2xyz³ + 2x²z³ + 6x²yz²)/3 at (1, 1, -1)
= (-2 - 2 +6)/3
= 2/3
Hence required directional derivative is 2/3.
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The question is incomplete. The complete question will be -
"The directional derivative of f= x^2 y z^3 along vector i + 2j + 2k at x = e^-t , y = 1 + 2 sin t , z = t -cost at t =0"
A restaurant hired 18 servers for one banquet. They pay a full time server $21.00 per hour and a part time server $15.50 per hour. If the labor cost of the restaurant was $312.00 per hour, how many full time and part time servers were there for the banquet?
Let's assume that x servers were full-time and y servers were part-time. Then we can write two equations based on the given information:
x + y = 18 (since there were 18 servers in total)
21x + 15.5y = 312 (since the labor cost was $312 per hour)
To solve for x and y, we can use elimination or substitution. Here's one way to use elimination:
Multiply the first equation by 15.5 to get 15.5x + 15.5y = 279.
Subtract the first equation from the second equation to get 5.5x = 33.
Divide both sides by 5.5 to get x = 6.
Now we know that there were 6 full-time servers. We can substitute this value into either of the two equations to solve for y:
6 + y = 18
y = 12
Therefore, there were 6 full-time servers and 12 part-time servers at the banquet.
Area/ Perimeter question. Any help? i have an assignment to complete.
Answer:
13 + 8 + 13 + (1/2)(8π) = 34 + 4π feet
= 46.57 feet
The students at Kayla's school are forming teams of three students for a quiz bowl competition. Kayla is assuming that each member of a team is equally likely to be male or female. She uses a coin toss (heads = female, tails = male) to simulate this probability. Here is Kayla's data from 50 trials of 3 coin tosses:
thh tth tth tht thh htt hth hht hth tth tth hht hth tht tht tth tth thh thh htt tht thh tth hht hth thh tht tth hht thh hhh tth tth hth htt tht thh hhh htt thh htt ttt tht ttt thh hht hth htt hht hth
According to this data, what is the experimental probability that a team will consist of two girls and a boy?
0.33
0.375
0.23
0.46
The required, experimental probability that a team will consist of two girls and a boy is 0.33. Option A is correct.
To find the experimental probability that a team will consist of two girls and a boy, we need to count the number of times that Kayla got a team with two girls and one boy and divide that by the total number of trials.
So, out of 50 trials, there were 17 trials where the team had two girls and one boy. Therefore, the experimental probability is:
17/50 = 0.34
Therefore, it is 0.34, which is closest to option (A) 0.33.
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Write an equation then find the value of y when x =16. Show all work.
Answer:
Answer is A
Step-by-step explanation:
A) y = -1/2x represents a proportional relationship because the equation can be written in the form y = kx, where k is a constant. In this case, k = -1/2, which means that y is proportional to x with a constant of proportionality of -1/2.
B) y = 2x - 4 does not represent a proportional relationship because the equation cannot be written in the form y = kx. If we try to write it in this form, we get y/x = 2 - 4/x, which means that y/x is not constant. Therefore, y is not proportional to x with a constant of proportionality.
-12 divided by 3 5/9
your answer is 3.375
tia's favorite stargergy for multiplying polynomials is to make a box that fits the two factors
Using Tia's box method, the multiplication of the polynomials (x + 2)(x² -3x + 5) in the standard form is x³ - x² - x + 10
Here, we need to multiply the polynomials (x + 2)(x² -3x + 5)
Tia's stargergy for multiplying polynomials is to make a box that fits the two factors.
Using Tia's box method,
x² -3x +5
x x³ -3x² +5x
+2 +2x² -6x +10
Consider (x + 2)(x² -3x + 5)
= (x . x²) - (x . 3x) + (x . 5) + (2x²) -(2 × 3x) + (2 × 5)
= x³ - 3x² + 5x + 2x² - 6x + 10
= x³ - 3x² + 2x² + 5x - 6x + 10
= x³ - x² - x + 10
This is the required polynomial.
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Find the complete question below.
Amber baked 120 cookies to give to five friends she wants to put the same number of cookies in each bag which of the following can she use to find out how many cookies to put in each bag
Answer:
she can divide the amount of cookies to friends
Step-by-step explanation:
120/5= 24
A total of $8000 is invested: part at 6% and the remainder at 10%
. How much is invested at each rate if the annual interest is $760
The requried, $1000 is invested at 6%, and $7000 is invested at 10%
Let x be the amount invested at 6%, and y be the amount invested at 10%. We know that x + y = $8000 since the total amount invested is $8000.
We also know that the annual interest earned on the 6% investment is 0.06x, and the annual interest earned on the 10% investment is 0.1y. The total annual interest earned is given as $760.
So we have the system of equations:
x + y = 8000 (1)
0.06x + 0.1y = 760 (2)
We can use either substitution or elimination to solve for x and y. Here, we'll use elimination. Multiplying equation 1 by 0.06, we get:
0.06x + 0.06y = 480 (3)
0.1y - 0.06y = 0.04y = 280
y = $7000.
Substituting y = $7000 into equation 1, we get:
x + $7000 = $8000
So x = $1000.
Therefore, $1000 is invested at 6%, and $7000 is invested at 10%.
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Use cramers rule to solve the system below
2x -3y = -8
4x + 3y = -34
A) Let A be to coefficient matrix, fill in matrix a below
b) Find the determinant of matrix A.
C) Let Matrix X be the matrix used to solve for the x variable. Write this matrix below
D) find the determinant of matrix X
E) Let Matrix Y be the matrix used to solve for the 'y' variable. Write this matrix below:
F) find the determinant of matrix y
G) write your solution to the system above as a coordinate
The solution to all parts from a to f is shown below.
A) Matrix A:
[ 2 -3 ]
[ 4 3 ]
B) The determinant of matrix A is:
det(A) = (2*3) - (-3*4) = 6 + 12 = 18
C) Matrix X:
[ -8 -3 ]
[ -34 3 ]
D) The determinant of matrix X is:
det(X) = (-8*3) - (-3*-34) = -24 - 102 = -126
E) Matrix Y:
[ 2 -8 ]
[ 4 -34 ]
F) The determinant of matrix Y is:
det(Y) = 2(-34) - (-8) (4) = -68 + 32 = -36
G) Using Cramer's rule, we can solve for x and y as follows:
x = det(X) / det(A) = -126 / 18 = -7
y = det(Y) / det(A) = -36 / 18 = -2
Therefore, the solution to the system is (-7, -2).
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can someone help me with this
The sine equation for the object's height is given as follows:
d = -5sin(0.24t).
How to define the sine function?The standard definition of the sine function is given as follows:
y = Asin(Bx) + C.
The parameters are given as follows:
A: amplitude.B: the period is 2π/B.C: vertical shift.The amplitude for this problem is of 5 inches, hence:
A = 5.
The period is of 1.5 seconds, hence the coefficient B is given as follows:
2π/B = 1.5
B = 1.5/2π
B = 0.24.
The function starts moving down, hence it is negative, so:
d = -5sin(0.24t).
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complete the table AB=1?, BC=3?
Answer:
angle B = 60 degree
AB = 2 cm
BC = 2 cm
Step-by-step explanation:
an equilateral triangle is a triangle with the following properties:
1. all sides equal
2. all angels equal to 60 degree
As a result:
angle B = 60 degree
AB = 2 cm
BC = 2 cm
According to the National Weather Service, the average monthly high temperature in the Dallas/Fort Worth, Texas area from the years of 2006-2008 is given by the following table:
Month
Average Maximum Monthly Temperature
Jan
48.1
Feb
50.9
Mar
62.4
Apr
67.0
May
76.5
Jun
83.9
Jul
86.8
Aug
88.1
Sep
79.2
Oct
69.9
Nov
59.5
Dec
49.6
Let x represent the months and y represent the average maximum monthly temperature.
Plot the data on a scatterplot. Choose the plot that best represents the data.
a.
On a coordinate plane, points are at (1, 48.1), (2, 50.9), (3, 62.4), (4, 67), (5, 76.5), (6, 83.9), (7, 86.8), (8, 88.1), (9, 79.2), (10, 69.9), (11, 59.5), (12, 49.6).
b.
On a coordinate plane, points are around (5, 85), (6, 90), (7, 80), (8, 70), (9, 60), (10, 50), (48, 1), (50, 3), (62, 4), (66, 4), (76, 5), (82, 8).
c.
On a coordinate plane, points are around (0, 49), (1, 52), (2, 62), (3, 68), (4, 78), (5, 85), (50, 12), (60, 10), (70, 10), (80, 9), (88, 8), (87, 9), (89, 9).
d.
On a coordinate plane, points are around (0, 48), (2, 52), (13, 50).
Please select the best answer from the choices provided
a) On a coordinate plane, points are at (1, 48.1), (2, 50.9), (3, 62.4), (4, 67), (5, 76.5), (6, 83.9), (7, 86.8), (8, 88.1), (9, 79.2), (10, 69.9), (11, 59.5), (12, 49.6) best represents the data.
This is because the data represents a set of paired values, with the months as the independent variable (x) and the average maximum monthly temperature as the dependent variable (y). A scatter plot is the appropriate graph for displaying this type of data.
Option a shows the correct placement of the data points on a scatter plot, with the x-axis representing the months and the y-axis representing the average maximum monthly temperature. The points are clearly organized in a sequence from January to December, with an upward trend in temperature from the winter months to the summer months, followed by a gradual decrease in temperature in the fall and winter months.
Option b has the correct range of temperatures, but the points are not arranged in a logical sequence and are scattered randomly across the graph. Option c also has a similar issue with random placement of points and does not reflect the actual values in the data set. Option d only has three points and does not represent the complete data set.
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Help is appreciated!
Answer:
Snacks: $75
Alcohol: $200
Dairy: $300
Average delivery charge per week: $63.89 (rounded to two decimal places)
Step-by-step explanation:
To find the average delivery charge the store pays each week, first calculate the total delivery cost for each category and then find the total cost for all deliveries. Finally, divide the total cost by the total number of deliveries.
Snacks:
3 deliveries * $25 per delivery = $75
Alcohol:
2 deliveries * $100 per delivery = $200
Dairy:
4 deliveries * $75 per delivery = $300
Total cost for all deliveries:
$75 (Snacks) + $200 (Alcohol) + $300 (Dairy) = $575
Total number of deliveries:
3 (Snacks) + 2 (Alcohol) + 4 (Dairy) = 9
Average delivery charge per week:
$575 (total cost) / 9 (total number of deliveries) = $63.89 (rounded to two decimal places)
2. An equation for a line is = 6/5 . What will the new equation of this line be after it is rotated 90° counterclockwise around the origin
If new equation of this line be after it is rotated 90° counterclockwise around the origin, the equation of the new line after rotation is y = (-5/6)x
To find the new equation of a line after it is rotated 90° counterclockwise around the origin, we need to use the following formula:
(x', y') = (-y, x)
where (x, y) are the coordinates of a point on the original line, and (x', y') are the coordinates of the corresponding point on the new line after rotation.
We can start by finding the slope of the original line, which is given by:
y = (6x/5)
Rearranging this equation, we get:
x = (5/6)y
This tells us that the slope of the original line is 5/6.
To find the equation of the new line after rotation, we need to apply the formula above to two points on the original line. Let's choose two easy points to work with, such as (0,0) and (5,6).
Using the formula, we can find the new coordinates of these points after rotation:
(0', 0') = (-0, 0) = (0,0)
(5', 6') = (-6, 5)
Now we can find the slope of the new line using these two points:
slope = (6' - 0') / (5' - 0') = 5/-6 = -5/6
In summary, to find the new equation of a line after rotating 90° counterclockwise around the origin, we can use the formula (x', y') = (-y, x) to find the new coordinates of two points on the original line, and then use these points to find the slope of the new line. In this case, the new equation of the line is y = (-5/6)x.
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