The polar coordinate (3, 45°) lies in the same location on the polar plane as (-3, Ø), where -360° < Ø < 0. Then, the value of Ø is 45°.
The polar coordinates (r, θ) represent a point on the polar plane, where r is the radial distance from the origin (in this case, 3 units) and θ is the angle measured counterclockwise from the positive x-axis (in this case, 45°).
According to the given statement, the polar coordinate (-3, Ø) lies in the same location on the polar plane as (3, 45°). This means that these two points represent the same location, and their radial distances and angles must be equivalent.
Comparing the radial distances;
|r| = 3 (for (3, 45°))
|-r| = 3 (for (-3, Ø))
Since |-r| = |r|, we can conclude that r = -r, which implies r = 0, as r cannot be negative in polar coordinates.
Comparing the angles;
θ = 45° (for (3, 45°))
θ = Ø (for (-3, Ø))
Since the angles are equivalent, we can equate them:
45° = Ø
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From a group of 10 people, you randomly select 2 of them. What is the probability that they are the 2 oldest people in the group?
The probability that they are the 2 oldest people in the group is 0.011
Understanding probabilityProbability is a measure of the likelihood or chance of an event occurring. It is expressed as a number between 0 and 1, where 0 indicates that the event is impossible, and 1 indicates that the event is certain.
The probability of an event A is denoted by P(A)
From the question above, let us calculate the probability.
The probability that the first person selected is the oldest is 1/10.
Then, the probability that the second person selected is the second oldest is 1/9, since there are only 9 people left to choose from.
Therefore, the probability of selecting the two oldest people in the group is:
1/10 * 1/9 = 1/90
So, the probability of selecting the two oldest people in the group is 1/90 or approximately 0.011 or 1.1%.
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Jay’s mean score for four quizzes is 9 . His scores for the first three quizzes are 8,5, and, 9. What is Jay’s score for the last quiz?
Jay's score for the last quiz is 14.
Let's use the formula for finding the mean:
Mean = (Sum of all scores) / (Number of scores)
We can rearrange this formula to solve for the unknown score:
Unknown score = (Mean x Number of scores) - (Sum of all other scores)
Given that Jay's mean score for four quizzes is 9, we have:
Mean = 9
Number of scores = 4
Jay's scores for the first three quizzes are 8, 5, and 9. The sum of these scores is:
Sum of first three scores = 8 + 5 + 9 = 22
Using the formula above, we can find Jay's score on the fourth quiz:
Unknown score = (Mean x Number of scores) - (Sum of all other scores)
Unknown score = (9 x 4) - 22
Unknown score = 36 - 22
Unknown score = 14
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6. Error Analysis Dakota said the third term of the expansion of (2g + 3h) is 36g2h². Explain Dakota's error. Then correct the error.
The binomial expansion is solved and the error in Dakota's statement is the incorrect substitution of 36g^2h^2 for the correct expression
Given data ,
Dakota made a mistake because the third term of the expansion of (2g + 3h) should have been 36g2h2. The binomial theorem asserts that the expansion of (2g + 3h) is as follows:
( x + y )ⁿ = ⁿCₐ ( x )ⁿ⁻ᵃ ( y )ᵃ
Here, x = 2g and y = 3h. Since term numbers begin at 0, since we are seeking for the third term, r = 2.
So , on simplifying the equation , we get
= nC2 * (2g)⁽ⁿ⁻²⁾ * (3h)²
= (n! / (2! * (n - 2)!)) * (2g)⁽ⁿ⁻²⁾ * (3h)²
= ((n * (n - 1)) / 2) * (2g)⁽ⁿ⁻²⁾ * (3h)²
Hence , the correct expression for the third term of the expansion of (2g + 3h) is ((n * (n - 1)) / 2) * (2g)^(n - 2) * (3h)², where n is the exponent in the binomial expansion.
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A student transformed the system of
equations shown below by multiplying
the second equation by a constant and
then adding the resulting equation to the
first equation.
x + 4y = 12
3x - y = 10
Answer:
The answer to your problem is, 3x+6y=9 then -2x-4y=4
Step-by-step explanation:
So first we are going to multiply the first equation by 2 and second equation by 3 and add it.
If there is both x and y terms gets cancelled then we can say there were no solutions at all.
Shown;
A) -2x+4y=4
-3x+6y=6
Which then becomes;
-4x + 8y = 8
-9x + 18y = 18
For, -13x + 26y = 26
B) 3x+y=12-
3x+6y=6
Which we then multiply first equation by 2 and second equation by 3
6x + 2y = 24
-9x + 18x = 18
For, -3x + 20y = 42
C)3x+6y=9
-2x-4y=4
Again multiply first equation by 2 and second equation by 3
6x + 12y = 18
-6x - 12y = 12
Which can equal to:
30
Which both x and y terms becomes 0.
Thus the anwer to your problem is, 3x+6y=9 then -2x-4y=4
Solve the following system of equations. If there is no solution, write DNE in each coordinate of the ordered triplet. If there are an infinite number of solution, write each coordinate in terms of z
x+3=y+12
z+13=x+8
y-7=z-11
PLS
Which of the following is not a characteristic of both experiments and
surveys?
O A. Data are collected about a population.
B. Subjects should be randomly selected.
OC. The data collected might be studied for patterns.
OD. The researcher exercises direct control over at least one variable.
SUBMIT
"Data are collected about a population," is not a characteristic of both experiments and surveys. Option A
What is the difference between survey and experiment?A survey is a technique for gathering data about a study variable from the respondents of the population. An experiment is a technique used in science to isolate the problem being examined and test a theory.
Options B, C, and D are characteristics obtained in the case of the experiments and surveys. In both types of research, subjects may be randomly selected (option B), the data collected may be studied for patterns (option C).
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Question 1 نت You are interested in constructing a 99% confidence interval for the proportion of all caterpillars that eventually become butterflies. Of the 369 randomly selected caterpillars observed, 45 lived to become butterflies. Round answers to 4 decimal places where possible. a. With 99% confidence the proportion of all caterpillars that lived to become a butterfly is between and b. If many groups of 369 randomly selected caterpillars were observed, then a different confidence interval would be produced from each group. About percent of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about percent will not contain the true population proportion. Hint: Hints Video [+]
a) The 99% confidence interval for the proportion of all caterpillars that lived to become a butterfly is between 0.078 and 0.166.
b) About 99% of these confidence intervals will contain the true population proportion of caterpillars that become butterflies and about percent will not contain the true population proportion.
What is a confidence interval of proportions?A confidence interval of proportions has the bounds given by the rule presented as follows:
[tex]\pi \pm z\sqrt{\frac{\pi(1-\pi)}{n}}[/tex]
In which the variables used to calculated these bounds are listed as follows:
[tex]\pi[/tex] is the sample proportion, which is also the estimate of the parameter.z is the critical value.n is the sample size.The confidence level is of 99%, hence the critical value z is the value of Z that has a p-value of [tex]\frac{1+0.99}{2} = 0.995[/tex], so the critical value is z = 2.575.
The sample size and the estimate for this problem are given as follows:
[tex]n = 369, \pi = \frac{45}{369} = 0.122[/tex]
The lower bound of the interval is given as follows:
0.122 - 2.575 x sqrt(0.122 x 0.878/369) = 0.078.
The upper bound of the interval is given as follows:
0.122 + 2.575 x sqrt(0.122 x 0.878/369) = 0.166.
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Activity
After an intensive search, Philip has narrowed his choices to four houses. Now he wants to buy the one that fits his budget. He has saved $40,000
for the down payment. Use the fixed-rate calculator to find the monthly payment for each house.
House Purchase Price Monthly Payment Affordability
A
$250,000
B
$200,000
C
$195,000
D
$180,000
Answer:
A
Step-by-step explanation:
A
Highschool geometry please answer questions 8-10 in the attachment added
The Winberg apartment complex rents out units at $200x monthly for each of their 9 units. The Hensing apartment complex has 3x more units and rents out each unit for $20 less monthly.
Which of the following equations could be used to determine the amount of money the Hensing apartment complex bills in rent each month when all of their units are rented out?
A. y = $(600x^2 - 180)
B. y = $(600x^2)
C. y = $(600x^2 + 1,740x - 180)
D. y = $(600x^2 + 1,860x - 180)
The equation that could be used to determine the amount of money the Hensing apartment complex bills in rent each month when all of their units are rented out is A. y = $(600x^2 - 180).
How to calculate the equationThe Hensing apartment complex rents out each unit for $20 less monthly than the Winberg complex, so the rent for each unit is $200x - $20 = $180x.
The equation that represents this situation is: y = $(600x^2 - 180
So the answer is (A) y = $(600x^2 - 180).
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Use the numbers in the multiplication equation 28 times 1/7 = 4 to write a division equation involving divison by a fraction
Changing the multiplication sign to a division sign, we will have 28 ÷ 7
Multiplication and division rule :-
Given the product of 28 and 1/7, we are to write a division equation involving division by a fraction.
Given,
28 * 1/7 = 4
Changing the multiplication sign to a division sign, we will have:
28 * 1/7 = 28/7
This can also be written as 28 ÷ 7
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Here is question 5 of 6. Thank you for the help
The critical value for a two-tailed test at the 0.05 significance level is 1.96.
The null hypothesis is that there is no difference in the proportion of men and women intending to vote for Donald Trump, and the alternative hypothesis is that there is a difference.
The test statistic is given by:
z = (p1 - p2) /√[(p×(1-p)×(1/n1 + 1/n2),
where p = (x1 + x2) / (n1 + n2) and x1 and x2 are the number of successes in samples 1 and 2 respectively, and n1 and n2 are the sample sizes of samples 1 and 2 respectively.
In this case, x1 = 120, x2 = 132, n1 = 250, and n2 = 240.
Plugging these values into the equation gives us z = 0.906.
Since the test statistic does not exceed the critical value, we fail to reject the null hypothesis. That is, there is not convincing evidence that there is a difference in the proportion of all men and the proportion of all women in this city who intended to vote for Trump at the 0.05 significance level.
Therefore, the critical value for a two-tailed test at the 0.05 significance level is 1.96.
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Select all of the values of x that make the inequality -x+6 ≥ 10 true.
NEED ANSWER ASAP PLEASE
Answer:
second one
the y intercept is 8, the slope is -6/8, reduced -3/4
Step-by-step explanation:
equation if a line in slope intercept form is y=mx+
A company's survey of 150 employees find that on average an employee drinks 10.2 cups of coffee during the workweek with a margin of error of #0.6. Using this data, it is estimated that a maximum of 6, 048 cups of coffee will be consumed during a workweek. What is the total number of employees in the company?
• 403
• 560
• 593
• 630
The total number of employees in the company is 560.
What is total number of employees?
The total number of employees in the company is calculated as follows;
the true average number of cups of coffee consumed per employee during the workweek is 10.2 ± 0.6 cups.
maximum = 10.8 cups/employee
minimum = 9.6 cups/employee
The minimum number of employees is calculated as;
n_m = 6,048 cups / 10.8
n_m = 560
The maximum number is calculated as;
n_max = 6,048 cups/9.6
n_max = 630
Based on the error margin, we take the minimum number.
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Please help me i need the answer and im so confused just tell me if its a b c or d please
Answer:
The answer would be option A
Step-by-step explanation:
-14 times 8=-122
explicit formula for an, the nth term of the sequence 6, 0, -6, ....
Answer:
12 - 6n
Step-by-step explanation:
As this sequence decreases, rather than increases, this tell us that the nth term of this sequence will be minus. The difference from 6 and 0 is 6, telling us that the decrease is by 6 each time. So now we know the nth term of this sequence; -6n, but the sequence of -6n is -6,-12,-18 and so on. We need 6,0,-6. To find out the second part of the nth term find the difference from the sequence given and the sequence of -6n. The difference is 12 because the 6--6 = 12. So now we get the nth term of the sequence -6n + 12 which is written as 12-6n.
a principle has given a class 75 dollars to help pay for a field trip to the zoo
Answer:
5p + 75> 386
Step-by-step explanation:
principal has given $75
Total cost of trip = $386
price of a pie = $5
5p + 75 ≥ 386
Solve the following for θ, in radians, where 0≤θ<2π.
−sin2(θ)−4sin(θ)+4=0
Select all that apply:
1.1
2.52
0.98
0.69
1.43
2.17
Answer:0.98
2.17 are correct
Step-by-step explanation:
-u^2 - 4u + 4 = 0
Multiplying both sides by -1, we get:
u^2 + 4u - 4 = 0
Now we can use the quadratic formula to solve for u:
u = (-b ± sqrt(b^2 - 4ac)) / 2a
where a = 1, b = 4, and c = -4. Substituting these values, we get:
u = (-4 ± sqrt(4^2 - 4(1)(-4))) / 2(1)
u = (-4 ± sqrt(32)) / 2
u = (-4 ± 4sqrt(2)) / 2
u = -2 ± 2sqrt(2)
Therefore, either:
2. Given: y varies inversely with x.
If y=-24 when x =36, what is the value of x
when y = 45?
Using inverse variation, the value of x = -19.2
What is inverse variation?Inverse variation is when a quantity varies inversely as the other.
Given: y varies inversely with x.
If y=-24 when x =36, what is the value of x when y = 45.
To splve this, we proceed as follows
Since y varies inversely with x, we have that
y ∝ 1/x
y = k/x where k = constant of proportionality
So, making k subject of the formula, we have that
k = yx
Now, If y=-24 when x =36, we have that
k = - 24 × 36
= -864
So, substituting k into y, we have that
y = k/x
= -864/x
So, to find the value of x when y = 45, making x subject of the formula, we have that
x = -864/y
So, substituting y into the equation, we have that
x = -864/y
= -864/45
= -19.2
So, the value of x = -19.2
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The table shows the results of rolling a die several times. Outcome 1 2 3 4 5 6 Number of times outcome occurred 7 4 4 5 6 4 To the nearest percent, what is the experimental probability of rolling a 6? Question 1 options: 17% 20% 13% 67%
The experimental probability of the rolling a 6 is 13%.
How to find the experimental probability of rolling a 6?Probability is the likelihood of a desired event happening. Experimental probability is a probability that relies mainly on a series of experiments.
From the table:
The total number of times all the numbers appear is:
total number of times = 7 + 4 + 4 + 5 + 6 + 4 = 30
The number six (6) occurred 4 times.
Experimental probability = (occurrence of 6 / total number of times)
Experimental probability = 4/30 * 100
Experimental probability = 13%
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Use the graph of g(x) to answer the following question. The graph of g(x) is a translation of f(x)=x^2 Write the equation for g(x) in vertex form.
The equation for g(x) in vertex form is g(x) = (x - 2)^ + 3
Writing the equation for g(x) in vertex form.From the question, we have the following parameters that can be used in our computation:
The graph of g(x)
Also, we have
The graph of g(x) is a translation of f(x)=x^2
From the graph, we can see that
Using the above as a guide, we have the following:
g(x) = f(x - 2) + 3
Substitute the known values in the above equation, so, we have the following representation
g(x) = (x - 2)^ + 3
Hence, the equation for g(x) in vertex form is g(x) = (x - 2)^ + 3
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Determine which function is represented by the graph. Do not use a calculator. (a) f ( x ) = 4 cos ( x + π ) (b) f ( x ) = 4 cos 4 x (c) f ( x ) = 4 sin ( x − π ) (d) f ( x ) = − 4 cos ( x + π ) (e) f ( x ) = 1 − sin x 2
Answer:
The graph of the function appears to be a cosine function that has been shifted to the left by π/2 units, and has an amplitude of 4.
Option (a) is a cosine function that has been shifted to the left by π units, but does not have the amplitude of 4.
Option (b) is a cosine function that has a period of π/2, which is much shorter than the period of the graph.
Option (c) is a sine function that has been shifted to the right by π units, but does not have the amplitude of 4.
Option (d) is a cosine function that has been shifted to the left by π units and has the correct amplitude of 4.
Option (e) is not a cosine or sine function, so it cannot be the correct answer.
Therefore, the function represented by the graph is:
f(x) = -4 cos(x + π)
which is Option (d).
Step-by-step explanation:
On a coordinate plane, a parabola opens down. It has an x-intercept at (negative 5, 0), a vertex at (negative 1, 16), a y-intercept at (0, 15), and an x-intercept at (3, 0).
The function f(x) = –x2 − 2x + 15 is shown on the graph. What are the domain and range of the function?
The domain is all real numbers. The range is {y|y < 16}.
The domain is all real numbers. The range is {y|y ≤ 16}.
The domain is {x|–5 < x < 3}. The range is {y|y < 16}.
The domain is {x|–5 ≤ x ≤ 3}. The range is {y|y ≤ 16}
The domain is all real numbers.
The range is {y|y ≤ 16}.
Option B is the correct answer.
We have,
The given parabola opens downwards and has a vertex at (-1,16).
So,
The parabola has a maximum value at y = 16.
Also, the y-intercept of the parabola is (0,15), which is below the vertex, and the parabola intersects the x-axis at (-5,0) and (3,0).
We can use the factored form of the equation of a parabola to find its equation in this case.
The factored form is:
y = a(x - h)² + k
where (h,k) is the vertex and "a" determines whether the parabola opens upwards or downwards.
Since the parabola opens downwards, "a" is negative.
Also, we know that the vertex is (-1,16), so we have:
y = a(x + 1)² + 16
To find "a", we can use one of the x-intercepts, say (-5,0).
Substituting these values into the equation gives:
0 = a(-5 + 1)² + 16
0 = 16a
a = 0
This indicates that the parabola is actually a line passing through (0,15) and (3,0). Therefore, the equation of the parabola is:
y = -x² - 2x + 15
The domain of this function is all real numbers because there are no restrictions on the values of x that can be plugged into the equation.
However, the range of the function is limited by the maximum value of y, which is 16.
Since the parabola opens downwards, all y values less than or equal to 16 are attainable.
Therefore, the domain is all real numbers, and the range is {y | y ≤ 16}.
Therefore,
The domain is all real numbers.
The range is {y|y ≤ 16}.
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Given this unit circle what is the value of x? HELP PLEASE
Answer:
x = - [tex]\frac{3}{5}[/tex]
Step-by-step explanation:
consider the right triangle formed by the x- axis, the y- coordinate of the given point and the radius of the circle 1 , to the point from the centre.
using Pythagoras' identity
x² + ( [tex]\frac{4}{5}[/tex] )² = 1²
x² + [tex]\frac{16}{25}[/tex] = 1 ( subtract [tex]\frac{16}{25}[/tex] from both sides )
x² = 1 - [tex]\frac{16}{25}[/tex] = [tex]\frac{9}{25}[/tex] ( take square root of both sides )
x² = ± [tex]\sqrt{\frac{9}{25} }[/tex] = ± [tex]\frac{\sqrt{9} }{\sqrt{25} }[/tex] = ± [tex]\frac{3}{5}[/tex]
since the given point is in the second quadrant , then
x = - [tex]\frac{3}{5}[/tex]
geometry pls help fast 13 and 14
Answer:
13: (2,3) 14: A. Yes, 90, 180, 270 B. No C. No
Step-by-step explanation:
13. Right: -2+4, Down: 5-2
14. If it can be rotated and be similar, it has rotational.
The letters of "EAGLES" should be evenly spaced across a 63 inch wide banner, with no margins. Each letter is 8 inches wide. How many inches (x) should exist between each pair of letter?
Answer:
To evenly space the letters of "EAGLES" across a 63 inch wide banner with no margins, you would need to divide the remaining space between each letter of the word equally. With five letters total and each letter being 8 inches wide, the total width occupied by the letters is 40 inches. Therefore, the remaining space is 23 inches (63-40=23). To find out how many inches should exist between each pair of letter, you would divide the remaining space by the number of gaps between the letters, which is 4 (one less than the total number of letters in the word).
23 inches ÷ 4 gaps = 5.75 inches between each pair of letters.
Step-by-step explanation:
What is the solution to this system?
(1, 0)
(1, 6)
(8, 26)
(8, –22)
x = –2
Answer:
Step-by-step explanation:The system of equations represented by the given points is:1x + 0y = 1 (equation 1)
1x + 6y = 1 (equation 2)
8x + 26y = 1 (equation 3)
8x - 22y = 1 (equation 4)
We can use the first equation to solve for x in terms of y:1x + 0y = 1
1x = 1
x = 1
Then we can substitute x=1 into equations 2-4 to obtain three equations in terms of y:1(1) + 6y = 1 => 6y = 0 => y = 0
8(1) + 26y = 1 => 26y = -7/8 => y = -7/208
8(1) - 22y = 1 => -22y = -7/8 - 7 => y = 15/44
Therefore, the solution to the system is x = 1 and y = -7/208 or y = 0 or y = 15/44.
However, we are given that x = -2, which contradicts our solution of x = 1. Therefore, there is no solution to the system with the given values.
a robotic vacum cleanervacumsonehotelroomin 3/10 hour. at this rate, how many rooms of the same size will it vaccum in 3 hours
The number of rooms of the same size it willl vaccum in 3 hours is 10
How many rooms of the same size will it vaccum in 3 hoursFrom the question, we have the following parameters that can be used in our computation:
Unit rate = 3/10 hour per room
Time = 3 hours
using the above as a guide, we have the following:
Number of rooms = Time/Unit rate
Substitute the known values in the above equation, so, we have the following representation
Number of rooms = 3/(3/10)
Evaluate the quotient
Number of rooms = 10
Hence, the number of rooms is 10
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For the given rectangular equation give its equivalent polar equation
Answer:
The last option
[tex]r = \dfrac{14}{6\cos\theta - \sin\theta}[/tex]
Step-by-step explanation:
Given equation is 6x - y = 14
To convert an equation in rectangular(cartesian) form, f(x, y) to polar f(r, θ) we use the following information
x = rcosθ
y = rsinθ
Substituting for x and y in the original rectangular equation 6x - y = 14,
6(rcosθ) - rsinθ = 14
Factoring out r on the left side,
r(6cosθ - sinθ) = 14
which gives
[tex]r = \dfrac{14}{6\cos\theta - \sin\theta}[/tex]
That would be choice 4
