Answer:
Circle
Step-by-step explanation:
r = 2 cos θ
Multiply both sides by r.
r² = 2r cos θ
Convert to rectangular.
x² + y² = 2x
x² − 2x + y² = 0
Complete the square.
x² − 2x + 1 + y² = 1
(x − 1)² + y² = 1
This is a circle with center (1, 0) and radius 1.
The given function r = 2 cos θ is a circle with a center (1, 0) and radius of 1.
What is a circle?A circle is a shape consisting of all points in a plane that are given the same distance from a given point called the center.
Given function is r = 2 cos θ
Now, Multiply both sides by r.
r² = 2r cos θ
Convert to rectangular form;
x² + y² = 2x
x² − 2x + y² = 0
Using Complete the square.
x² − 2x + 1 + y² = 1
(x − 1)² + y² = 1
Hence, This is a circle with a center (1, 0) and radius of 1.
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The results of a linear regression are shown below.
y= ax + b
a = -1.15785
b= 139.3171772
r= -0.896557832
r2 = 0.8038159461
Which phrase best describes the relationship between x and y?
1)Strong Postive Correlation
2)Strong Negative Correlation
3)Weak Positive Correlation
4)Weak Negative Correlation
Answer:
2) Strong Negative Correlation
Step-by-step explanation:
With the value of r we have both the information about the sign of the relationship and the strength of this relationship.
As the value of r is negative, we can conclude that the correlation between x and y is negative.
Also, as the absolute value of r is close to 1, we can conclude that this relationship is strong.
The strength can also be seen in the value of r2, which is also close to 1, but this value does not give information about the sign.
The value of the slope a, being negative, can also tell us that the relation between x and y is a negative correlation.
Use a significance level of α= 0.05 and use the given information for the following:
Required:
a. State a conclusion about the null hypothesis. (Reject H0 or fail to reject H0.)
b. Without using technical terms or symbols, state a final conclusion that addresses the original claim.
"we dont gaf abt no bii, we dont giveeaf abt no bii and if i was you i wouldnt kiss her on the lips"
Square A"B"C"D" is the final image after the rule was applied to square ABCD. On a coordinate plane, a square A double-prime B double-prime C double-prime D double-prime has points (negative 5, negative 3), (negative 3, negative 1), (negative 1, negative 3), (negative 3, negative 5). What are the coordinates of vertex A of square ABCD? (–1, –6) (–1, –2) (–1, 6) (–2, 1)
Answer:
The answer is (-2 , 1 ) or D on Edge
Step-by-step explanation:
The coordinates of vertex A of square ABCD is (-1, -2).
What are coordinates?Coordinates are two numbers (Cartesian coordinates), or sometimes a letter and a number, that locate a specific point on a grid, known as a coordinate plane.
Given:
A(-5, -3), B(-3, -1), C(-1, -3) and D(-3, -5)
By using the rule
T(-4, -1)
So, the coordinate of Vertex A will be
A( -5 + 4, -3 + 1)
=A(-1, -2)
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Please help. I’ll mark you as brainliest if correct!
Answer:
(0. 4)
(-2, 0)
Step-by-step explanation:
The y- coordinates (output) at the highest and lowest points are called the absolute maximum and absolute minimum, respectively.As per given graph,
absolute maximum is 4, point (0, 4)absolute minimum is 0, point (-2, 0)if f(x) =2x^2+5 (x-2) completel the following statement f(3)=
Answer:
41
Step-by-step explanation:
f(3) = 2(3)^2 +5(x-2)
= 2(18)+ 5
= 41
please help me explain your answer only answer if you are sure
Answer:
The answer of top prism is 262
and down prism is 478
The upper figure is triangular prism.
so, we use bh+2ls+lb formula
B=5
h=3
s=4
l=19
Now,
surface area of triangular prism = bh+2ls+lb
= 5×3+2×19×4+19×5
= 262
The down figure is rectangular prism.
so, we use 2lw+2lh+2hw
l=5
h=6
w=19
Now,
The area of rectangular prism = 2lw+2lh+2hw
= 2×5×19+2×19×6+2×5×6
= 478
The function f(x)=2x2−x+4; f ( x ) = 2 x 2 − x + 4 is defined over the domain 0 ≤ x ≤ 3 Find the range of this function. A. 4 < f(x) < 7 B. 4 < f(x )< 19 C. 4 ≤ f(x) ≤ 19 D. 4 ≤ f(x) ≤ 25
Answer:
C. 4 ≤ f(x) ≤ 19 . . . . . . best of bad answer choices
Step-by-step explanation:
When looking for the range of a function on an interval, one must check the function values at the ends of the interval, along with any local maxima or minima.
Here, the function values at the interval ends are ...
f(0) = 4
f(3) = 2·3² -3 +4 = 19
The axis of symmetry is located at ...
x = -b/(2a) = -(-1)/(2(2)) = 1/4
This is a value in the interval, so will be the location of the minimum value of the function.
f(1/4) = 2(1/4)² -1/4 +4 = 3.875
The range of f(x) on the interval [0, 3] is [3.875, 19]:
3.875 ≤ f(x) ≤ 19
__
All of the answer choices are incorrect. Please discuss question this with your teacher.
To solve a polynomial inequality, we factor the polynomial
into irreducible factors and find all the real_______polynomial. Then we find the intervals determined by the real__________sign of the polynomial on that interval. Let
$$P(x)=x(x+2)(x-1)$$
Fill in the diagram to find the intervals on which
$P(x) \geq 0$
we see that $P(x) \geq 0$ on the
intervals_______and________.
Answer:
To solve a polynomial inequality, we factor the polynomial into irreducible factors and find all the real _zeros_ polynomial. Then we find the intervals determined by the real _zeros and use test points in each interval to find the_ sign of the polynomial on that interval.
If P(x) = x(x+2)(x-1)
And P(x) ≥ 0
We see that P(x) ≥ 0 on the intervals (-2, 0) and (1, ∞).
Step-by-step explanation:
The complete question is attached to this solution
To solve inequality of a polynomial, we first obtain the solutions of the polynomial. The solutions of the polynomial are called the zeros of the polynomial.
If P(x) = x(x+2)(x-1)
The solutions of this polynomial, that is the zeros of this polynomial are 0, -2 and 1.
To now solve the inequality that arises when
P(x) ≥ 0
We redraw the table and examine the intervals
The intervals to be examined as obtained from the zeros include (-∞, -2), (-2, 0), (0, 1) and (1, ∞)
Sign of | x<-2 | -2<x<0 | 0<x<1 | x>1
x | -ve | -ve | +ve | +ve
(x + 2) | -ve | +ve | +ve | +ve
(x - 1) | -ve | -ve | -ve | +ve
x(x+2)(x-1) | -ve | +ve | -ve | +ve
The intervals that satisfy the polynomial inequality P(x) = x(x+2)(x-1) ≥ 0 include
(-2, 0) and (1, ∞)
Hope this Helps!!!
What’s the correct answer for this question?
Answer:
S ≈ 9.8
Step-by-step explanation:
Finding central angle of circle A first
S=r∅
6.5 = (4)∅
Central angle = 6.5/4
C A = 1.63(in radians)
Now finding Arc EF
S = r∅
S = (6)(1.63)
S = 9.75
S ≈ 9.8
Antoinette needs to solve this system of equations by graphing. Which statements explain how she should graph the equations? Check all that apply.
Answer:
see below
Step-by-step explanation:
In my opinion, Antoinette should make use of a graphing calculator to find the solution. (second attachment)
__
Slope-intercept form can be useful for graphing, so it often works well to start with equations in that form. If that is Antoinette's strategy, she should rewrite the first equation to that form. The second equation is already in slope-intercept form.
In doing that rewrite, she will want to get the y-term on one side of the equal sign by itself. She can do that by subtracting 2x from the first equation:
-7y = -2x +56
As a final step in her rewrite, she would divide by -7 to get ...
y = 2/7x +56
This 2nd equation has a positive slope of 2/7. The slope of the second equation is similarly the x-coefficient, -2.5. Neither is 4 and they have different signs.
The appropriate answer choices are shown checked below.
Answer:
B and D
Step-by-step explanation:
I got it right m8. Good day
A student works at an on- campus job Monday through Friday. The student also participates in intramural volleyball on Tuesdays and Thursdays. Given Events A and B, are the two events mutually exclusive? Explain your answer.
Event A: On a random day of the week, the student is working at their on-campus job.
Event B: On a random day of the week, the student is playing intramural volleyball.
Answer:
No, the events are not mutually exclusive because they share the common outcomes of the student working and playing volleyball on certain days.
Step-by-step explanation:
A and B are mutually exclusive events if they cannot occur at the same time. This means that A and B do not share any outcomes and P(A AND B)=0.
In this case, A and B have outcomes in common since the student both works and plays volleyball on Tuesdays and Thursdays. Thus, the events are not mutually exclusive.
Please help. I’ll mark you as brainliest if correct!
Answer:
When x = -1/4 and when x = -15/4
Step-by-step explanation:
The x intercept will be when f(x)=0, so
0 = 4|x+2| -7
7 = 4|x+2|
|x+2|=7/4 here you have to cases
case 1
x+2=7/4
x=7/4-2
x=-1/4 = -0.25
case 2
x+2 = -7/4
x = -2-7/4
x = -15/4 = -3.75
An HP laser printer is advertised to print text documents at a speed of 18 ppm (pages per minute). The manufacturer tells you that the printing speed is actually a Normal random variable with a mean of 17.35 ppm and a standard deviation of 3.25 ppm. Suppose that you draw a random sample of 10 printers.
Required:
a. Using the information about the distribution of the printing speeds given by the manufacturer, find the probability that the mean printing speed of the sample is greater than 17.55 ppm.
b. Use normal approximation to find the probability that more than 48.6% of the sampled printers operate at the advertised speed (i.e. the printing speed is equal to or greater than 18 ppm)
Answer:
a) The probability that the mean printing speed of the sample is greater than 17.55 ppm = 0.4247
b) The probability that more than 48.6% of the sampled printers operate at the advertised speed = 0.4197
Step-by-step explanation:
The central limit theorem explains that for an independent random sample, the mean of the sampling distribution is approximately equal to the population mean and the standard deviation of the distribution of sample is given as
σₓ = (σ/√n)
where σ = population standard deviation
n = sample size
So,
Mean of the distribution of samples = population mean
μₓ = μ = 17.35 ppm
σₓ = (σ/√n) = (3.25/√10) = 1.028 ppm
a) The probability that the mean printing speed of the sample is greater than 17.55 ppm.
P(x > 17 55)
We first normalize 17.55 ppm
The standardized score for any value is the value minus the mean then divided by the standard deviation.
z = (x - μ)/σ = (17.55 - 17.35)/1.028 = 0.19
To determine the required probability
P(x > 17.55) = P(z > 0.19)
We'll use data from the normal probability table for these probabilities
P(x > 17.55) = P(z > 0.19) = 1 - P(z ≤ 0.19)
= 1 - 0.57535 = 0.42465 = 0.4247
b) The probability that more than 48.6% of the sampled printers operate at the advertised speed
We first find the probability that one randomly selected printer operates at the advertised speed.
Mean = 17.35 ppm
Standard deviation = 3.25 ppm
Advertised speed = 18 ppm
Required probability = P(x ≥ 18)
We standardize 18 ppm
z = (x - μ)/σ = (18 - 17.35)/3.25 = 0.20
To determine the required probability
P(x ≥ 18) = P(z ≥ 0.20)
We'll use data from the normal probability table for these probabilities
P(x ≥ 18) = P(z ≥ 0.20) = 1 - P(z < 0.20)
= 1 - 0.57926 = 0.42074
48.6% of the sample = 48.6% × 10 = 4.86
Greater than 4.86 printers out of 10 includes 5 upwards.
Probability that one printer operates at advertised speed = 0.42074
Probability that one printer does not operate at advertised speed = 1 - 0.42074 = 0.57926
probability that more than 48.6% of the sampled printers operate at the advertised speed will be obtained using binomial distribution formula since a binomial experiment is one in which the probability of success doesn't change with every run or number of trials. It usually consists of a number of runs/trials with only two possible outcomes, a success or a failure. The outcome of each trial/run of a binomial experiment is independent of one another.
Binomial distribution function is represented by
P(X = x) = ⁿCₓ pˣ qⁿ⁻ˣ
n = total number of sample spaces = 10
x = Number of successes required = greater than 4.86, that is, 5, 6, 7, 8, 9 and 10
p = probability of success = 0.42074
q = probability of failure = 0.57926
P(X > 4.86) = P(X ≥ 5) = P(X=5) + P(X=6) + P(X=7) + P(X=8) + P(X=9) + P(X=10) = 0.4196798909 = 0.4197
Hope this Helps!!!
For the given central angle, determine the distance traveled along the unit circle from the point (1, 0). 210 degrees a. 3.67 units c. 1.83 units b. 1.17 units clockwise d. 7.33 units
Answer:
3.67 units
Step-by-step explanation:
The central angle is at the point (0,0).
Then it's at the point (1,0)
Then it moved 210 degrees.
Let's bear in mind that we start moving the degree from it's current position.
So moving 210 degrees is moving 180 degrees plus 30 degrees.
Moving 180 degrees I like transforming linearly.
Now the location is at (-1,0)
But the distance covered will be
= 2πr*210/360
r = 1
= 2*3.142*1*(210/360)
= 6.144*0.5833333
= 3.67 units
A girl threw a marble 15 m vertically up in the air which later fell and settled at the bottom of a lake 7 m deep. Find the total distance travelled by the marble while falling down?
Answer:
22 m
Step-by-step explanation:
Total distance travelled by marble while falling down = height above surface of lake + depth of lake = 15 + 7 = 22 m
Identify the lower class limits, upper class limits, class width, class midpoints, and class boundaries for the given frequency distribution. Also identify the number of individuals included in the summary.
Age (yr) when award was won:
20-24
25-29
30-34
35-39
40-44
45-49
50-54
Frequency:
29
36
15
3
6
2
2
Answer:
Lower class Limit: 20,25,30,35,40,45,50
Upper class limit: 24,29,34,39,44,49,54
Class width: 4
Class Midpoints : 22,27,32,37,42,47,52
Class Boundries : 19.5,24.5,29.5,34,5,39.5,44.5,49.5,54.5
Total Individuals: 93
Step-by-step explanation:
Lower class limit is the lowest value of a class e.g in the first class, the lowest value is 20. Similarly find lower class limit of othere classes.
Upper class limit is the highest value of a class e.g in the first class, the highest value is 24. Similarly find upper class limit of othere classes.
Class width is the difference between highest and lowest value of a class e.g 24-20=4
Class Midpoints can be found by adding lowest and highest value of a class and dividing it by 2 e.g (20+24)/2 = 22
Class boundaries are the halfway point which seperates the classes e.g for first classes, clasee boundry is (19.5,24.5)
Total individuals are founf by adding all the frequencies.
Please help me with this problem I'm lost
Answer:
24
Step-by-step explanation:
Multiple (4)(2)= 8
-3(8) =24
ANSWER QUICK!!! Need 2 people to answer with the same answer to make sure! in the fridge there are 7 apples and 5 oranges. which of the following does NOT represent a ratio in the fridge? 7:5 5:7 5:12 7:12 6:7
You have two numbers to work with 7 and 5.
To keep the ratios the same using different numbers they would have to increase or decrease by the same multiple.
The answers would be 5:12, 7:12 and 6:7 do not represent a ratio in the fridge.
Select the correct answer. Meg deposited a $3,000 bonus check in a new savings account. The account has an interest rate of 3% for 5 years. The interest is compounded daily. How much money did Meg have at the end of the account term? (Round your answer to the nearest dollar.)
Answer:
$3,485.48
Step-by-step explanation:
For computing the money required at the end of the account term we need to apply the Future value formula i.e be to shown in the attachment below:
Given that,
Present value = $3,000
Rate of interest = 3% ÷ 365 days = 0.00821917
NPER = 5 years × 365 days = 1,825
PMT = $0
The formula is shown below:
= FV(Rate;NPER;PMT;PV;type)
So, after applying the above formula
the amount of future value is $3,485.48
Can anyone help me with the answer please
Answer:
Graph D
Step-by-step explanation:
First, look at the x-intercepts (where the graph touches the x-axis): x= -1 and x= 3
This rules out Graph B and C which have x-intercepts at x= -3 and x= -1
Next, look at the y-intercept (where the graph touches the y-axis): y= -3
This rules out Graph A which has a y-intercept at y= 3
A parabola has a focus of (6,–6) and a directrix of y = –2. Which of the following could be the equation of the parabola?
Answer:
[tex]-8(y+4) =(x-6)^{2}[/tex]
Step-by-step explanation:
The standard form of a parabola is given by the following equation:
[tex](x-h)^{2} =4p(y-k)[/tex]
Where the focus is given by:
[tex]F(h,k+p)[/tex]
The vertex is:
[tex]V=(h,k)[/tex]
And the directrix is:
[tex]y-k+p=0[/tex]
Now, using the previous equations and the information provided by the problem, let's find the equation of the parabola.
If the focus is (-6,6):
[tex]F=(h,k+p)=(6,-6)[/tex]
Hence:
[tex]h=6\\\\k+p=-6\hspace{10}(1)[/tex]
And if the directrix is [tex]y=-2[/tex] :
[tex]-2-k+p=0\\\\k-p=-2\hspace{10}(2)[/tex]
Using (1) and (2) we can build a 2x2 system of equations:
[tex]k+p=-6\hspace{10}(1)\\k-p=-2\hspace{10}(2)[/tex]
Using elimination method:
(1)+(2)
[tex]k+p+k-p=-6+(-2)\\\\2k=-8\\\\k=-\frac{8}{2}=-4\hspace{10}(3)[/tex]
Replacing (3) into (1):
[tex]-4+p=-6\\\\p=-6+4\\\\p=-2[/tex]
Therefore:
[tex](x-6)^{2} =4(-2)(y-(-4)) \\\\(x-6)^{2} =-8(y+4)[/tex]
So, the correct answer is:
Option 3
Five thousand tickets are sold at $1 each for a charity raffle. Tickets are to be drawn at random and monetary prizes awarded as follows: 1 prize of $ 500 500, 3 prizes of $ 200 200, 5 prizes of $ 10 10, and 20 prizes of $5. What is the expected value of this raffle if you buy 1 ticket?
Answer:
-$0.75
Step-by-step explanation:
For calculation of expected value first we need to find out the probability distribution for this raffle which is shown below:-
Amount Probability
500 - 1 = $499 1 ÷ 5,000
200 - 1 = $199 3 ÷ 5,000
10 - 1 = $9 5 ÷ 5,000
5 - 1 = $4 20 ÷ 5,000
-$1 5,000 - 29 ÷ 5,000 = 4,971 ÷ 5,000
Now, the expected value of raffle will be
[tex]= \$499 \times (\frac{1}{5,000}) + \$199 \times (\frac{3}{5,000}) + \$9 \times (\frac{5}{5,000}) + \$4 \times (\frac{20}{5,000}) - \$1 \times (\frac{4,971}{5,000})[/tex]
= 0.0998 + 0.1194 + 0.009 + 0.016 - 0.9942
= -$0.75
The expected value of this raffle per ticket is $ 0.25.
Given that five thousand tickets are sold at $ 1 each for a charity raffle, and tickets are to be drawn at random and monetary prizes awarded as follows: 1 prize of $ 500, 3 prizes of $ 200, 5 prizes of $ 10, and 20 prizes of $ 5, to determine what is the expected value of this raffle if you buy 1 ticket, the following calculation must be performed:
(500 + 3 x 200 + 5 x 10 + 20 x 5) / 5000 = X (500 + 600 + 50 + 100) / 5000 = X 1250/5000 = X 0.25 = X
Therefore, the expected value of this raffle per ticket is $ 0.25.
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What is the answer ?
Answer:
[tex]f = \frac{1}{ {d}^{2} } [/tex]
If p(x) = 2x2 - 4x and q(x) = x - 3, what is (pºq)(x)?
Answer:
Step-by-step explanation:
p(x)=2x^2
q(x)=x-3
(p•q)(x)=2(x-3)^2
2(x^2-6x+9)
2x^2-12x+18
A service club is organizing a concert to raise funds for a retirement home. The club determines that the revenue from the concert can
be represented by R(x) = 0.0027x3 - 125, where x is the number of tickets sold. The cost to put on the concert is represented by the
function C(X) = 21x + 11,305.
Which of the following functions describes the funds raised, F(x), as a function of the number of tickets sold?
FX) = 0.0027x3 - 21x - 11,430
FAX) = 0.0027x3 + 21x - 11,180
FX) = 0.0027x3 - 21x - 11,180
F(X) = 0.0027x3+
+ 21-11,430
Answer:
maybe is a
Step-by-step explanation:
Answer:
F(x) = 0.0027x^3 - 21X - 11,430
Step-by-step explanation:
What is the product?
(45+2)(5s2+ 10s+3)
Answer:
your answer is 127596 because you would take (45+2) first then you would take (55^2+10s+3) then you multiply them
Step-by-step explanation:
The image point using the translation (x,) + (x+4,y-1)
for the point (3,3) is
Answer: (7, 2)
Step-by-step explanation:
(x, y) → (x + 4, y - 1)
(3, 3) → (3 + 4, 3 - 1)
= (7, 2)
Please help. I’ll mark you as brainliest if correct!!!!
Answer:
a= 2/5
b= -3/5
Step-by-step explanation:
We need to multiply the numerator and denominator by -i (conjugate) to cancel out i in the denominator
[tex]\frac{(3+2i)(-i)}{5i(-i)}[/tex]
This simplifies to:
[tex]\frac{-3i+-2i^{2} }{-5i^{2} }[/tex]
This further simplifies to:
[tex]\frac{-3i +2}{5}[/tex]
Can be rewritten as:
[tex]\frac{2}{5} +-\frac{3}{5} i[/tex]
a = 2/5
b = -3/5
If a⊕ b= 1/a + 1/b , for what decimal value of a is a⊕ 0.2=10?
Answer:
0.2
Step-by-step explanation:
1/0.2 = 5
10-5 = 5
1/a = 5
a = 1/5
a = 0.2
Answer:1/5 or 0.2
Step-by-step explanation:
1/a+1/0.2=10
1/a+1/2/10=10
1/a=10/2=10
1/a+5=10
1/a=10-5
1/a=5
a=1/5 or 0.2
On the map, Seattle, Portland, and Boise form a triangle whose sides are shown in the figure below. If the actual distance from Seattle to Boise is 400 miles, find the distance from Seattle to Portland.
Answer:
150 miles
Step-by-step explanation:
If the distance between Seattle and Boise is 400 miles and the image illustrates 4", then there must be a proportionate between the two values. Therefore, if the distance between Seattle and Portland is 1.5", then the real distance must be 150 miles.