Step-by-step explanation:
x²+ y² -12x - 18y +17 = 0 means : (x²-12x+36)-36+(y²-18y+81)-81-27 =0
(x-6)²+(y-9)² =12²....standard form when the center is (-6 , 9) and radius 12
Answer:
The center is at (1, 6) and the radius is 1.
Step-by-step explanation:
x^2 + y^2 - 2x - 12y +36 = 0
Convert to standard form:
x^2 - 2x + y^2 - 12y = -36
(x - 1)^2 - 1 + (y - 6)^2 - 36 = -36
(x - 1)^2 + (y - 6)^2 = -36 + 36 + 1
(x - 1)^2 + (y - 6)^2 = 1
The center is at (1, 6) and the radius is 1.
What is the volume of the following rectangular prism?
Answer:
44/3
Step-by-step explanation:
V=L*W*H
WH=22/3
V=2*(22/3)
3. Find the minimum number of students needed to guarantee that five of them belong to the same class (Freshman, Sophomore, Junior, Senior)
Answer:
100
Step-by-step explanation:
well you can put 5 students in each class guaranteed 5 times over so it would make sense because 5 for each class 9th-12th 5 times over again and again will eventually give you the answer of 100 5•20
If we take 5 students are in each class.
Then let minimum number of students be x
ATQ
1/20()x = 5
x = 5 × 20
x = 100
Answer: 100 people
Must click thanks and mark brainliest
What are the zeros of f(x) = x^2 - x - 12?
A. x= -4 and x= 3
B. x=-3 and x = 4
C. x=-2 and x = 6
D. x=-6 and x = 2
Answer:
B. x = -3 and x = 4
General Formulas and Concepts:
Algebra I
Terms/CoefficientsFactoringSolving quadraticsStep-by-step explanation:
Step 1: Define
Identify
f(x) = x² - x - 12
Step 2: Solve for x
Factor: (x - 4)(x + 3) = 0Solve: x = 4, -3A contributor for the local newspaper is writing an article for the weekly fitness section. To prepare for the story, she conducts a study to compare the exercise habits of people who exercise in the morning to the exercise habits of people who work out in the afternoon or evening. She selects three different health centers from which to draw her samples. The 57 people she sampled who work out in the morning have a mean of 5.2 hours of exercise each week. The 70 people surveyed who exercise in the afternoon or evening have a mean of 4.5 hours of exercise each week. Assume that the weekly exercise times have a population standard deviation of 0.6 hours for people who exercise in the morning and 0.4 hours for people who exercise in the afternoon or evening. Let Population 1 be people who exercise in the morning and Population 2 be people who exercise in the afternoon or evening.
Step 1 of 2: Construct a 95% confidence interval for the true difference between the mean amounts of time spent exercising each week by people who work out in the morning and those who work out in the afternoon or evening at the three health centers. Round the endpoints of the interval to one decimal place, if necessary.
Answer:
The 95% confidence interval for the true difference between the mean amounts of time spent exercising each week by people who work out in the morning and those who work out in the afternoon or evening at the three health centers is (0.5, 0.9).
Step-by-step explanation:
Before building the confidence intervals, we need to understand the central limit theorem and subtraction of normal variables.
Central Limit Theorem
The Central Limit Theorem establishes that, for a normally distributed random variable X, with mean [tex]\mu[/tex] and standard deviation [tex]\sigma[/tex], the sampling distribution of the sample means with size n can be approximated to a normal distribution with mean [tex]\mu[/tex] and standard deviation [tex]s = \frac{\sigma}{\sqrt{n}}[/tex].
For a skewed variable, the Central Limit Theorem can also be applied, as long as n is at least 30.
Subtraction between normal variables:
When two normal variables are subtracted, the mean is the difference of the means, while the standard deviation is the square root of the sum of the variances.
In the morning:
Sample of 57, mean of 5.2, standard deviation of 0.6, so:
[tex]\mu_1 = 5.2[/tex]
[tex]s_1 = \frac{0.6}{\sqrt{57}} = 0.0795[/tex]
In the afternoon/evening:
Sample of 70, mean of 4.5, standard deviation of 0.4, so:
[tex]\mu_2 = 4.5[/tex]
[tex]s_2 = \frac{0.2}{\sqrt{70}} = 0.0239[/tex]
Distribution of the difference:
[tex]\mu = \mu_1 - \mu_2 = 5.2 - 4.5 = 0.7[/tex]
[tex]s = \sqrt{s_1^2+s_2^2} = \sqrt{0.0795^2 + 0.0239^2} = 0.083[/tex]
Confidence interval:
The confidence interval is:
[tex]\mu \pm zs[/tex]
In which
z is the z-score that has a p-value of [tex]1 - \frac{\alpha}{2}[/tex].
95% confidence level
So [tex]\alpha = 0.05[/tex], z is the value of Z that has a p-value of [tex]1 - \frac{0.05}{2} = 0.975[/tex], so [tex]Z = 1.96[/tex].
The lower bound of the interval is:
[tex]\mu - zs = 0.7 - 1.96*0.083 = 0.5[/tex]
The upper bound of the interval is:
[tex]\mu + zs = 0.7 + 1.96*0.083 = 0.9[/tex]
The 95% confidence interval for the true difference between the mean amounts of time spent exercising each week by people who work out in the morning and those who work out in the afternoon or evening at the three health centers is (0.5, 0.9).
There are 16 more people in front of Kollam on a line than behind him. There are five times as many people in front of him as behind him. How many people are on the line?
Answer:
There are 21 people in the line (including Kollam himself).
The graph of the piecewise function f(x) is shown.
What is the range of f(x)?
6
5
O {x1-2 sx<4)
O {x1-2
Oy1-5
O {1-5 sys-1)
3+
2+
1
-7 -6 -5 -4 -3
-
1
3
4
5
8
The range is virtually the answer to the question,
"In which interval can find all y-values of the function".
So you look at the y-axis and see that your function begins with [tex]y=-5[/tex] (including -5 because of the dot on the graph) and ends at including [tex]y=-1[/tex].
So the interval notation is,
[tex]y\in[-5,-1][/tex]
But you are asked to specify the set notation of the interval, to do so first rewrite the interval using inequality operators, say we find some y in between (and including) -5 and -1,
[tex]-5\leq y\leq-1[/tex]
To specify that this is a set use curly bracelets and a bar,
[tex]\{y\mid-5\leq y\leq-1\}[/tex].
The y before bar is a step function and everything followed after the vertical bar is the range of the step function.
Hope this helps.
Using it's concept, it is found that the range of f(x) is given by:
{y|-5 <= -y <= -1}
What is the range of a function?The range of a function is the set that contains all possible output values. In a graph, it is given by the values of y, that is, the values of the vertical axis.
In the function described by this graph, the vertical axis assumes values between -1 and -5, inclusive, hence the range is given by:
{y|-5 <= -y <= -1}
More can be learned about the range of a function at https://brainly.com/question/24374080
f(x)=3(x+5)+4/xwhat is f (a+2) solve this problem with showing the work
write your answer in simplest radical form
Answer:
[tex]s=6\sqrt{3}[/tex]
Step-by-step explanation:
In any 30-60-90 triangles, the sides are in ratio [tex]x:x\sqrt{3}:2x[/tex], where [tex]x[/tex] is the side opposite to the 30 degree angle and [tex]2x[/tex] is the hypotenuse of the triangle.
In the given diagram, the hypotenuse is marked as 12 miles. Therefore, the side opposite to the 30 degree angle must be [tex]12 \div 2=6[/tex] miles. The final leg, [tex]s[/tex], must then represent the [tex]x\sqrt{3}[/tex] part of our ratio, hence [tex]\implies \boxed{6\sqrt{3}}[/tex]
For a standard normal distribution, find:
P(z > c) = 0.058
Find c.
Answer:
1.572
Step-by-step explanation:
For a standard normal distribution,
P(z > c) = 0.058
To obtain C ; we find the Zscore corresponding to the proportion given, which is to the right of the distribution ;
Using technology or table,
Zscore equivalent to P(Z > c) = 0.058 is 1.572
Hence, c = 1.572
An economics instructor would like to test the theory that spraying lavender essential oil in a room while studying will improve test scores. One group of participants studies in a room that releases 2 ounces of lavender every 3 to 4 hours. The second group studies in a room that does not release any essential oils. Both groups study the same amount of time leading up to all course exams. The instructor records the number of points each group gets on a total of 4 exams during a 5 week summer course. What is the dependent variable?
a. Number of ounces of lavender sprayed every 3 to 4 hours.
b. The number of weeks of the course.
c. If students are allowed to use open notes.
d. The average exam scores for each group.
Answer:
d. The average exam scores for each group.
Step-by-step explanation:
The dependent variable, also called the measured or predicted variable is the variable which is being tested or measured in an experiment. It is the variable with which an experiment is being conducted. The outcome of the dependent variable however, relies on another variable called the independent variable.changes in the independent variable affects the outcome of the dependent variable. In the scenario above, the dependent variable is the average exam scores obtained which depends on how the amount of lavender sprayed brings an effect. Ounces of lavender sprayed is the independent variable.
(b) Express the prime number 43 as the difference of two squares? 43 =
8 A test rocket is fired and follows a path described by y = 0.1x(200 – x). The height is y metres above
ground and x is the horizontal distance in metres.
How far does the rocket travel horizontally?
b How high does the rocket reach mid-flight?
Answer:
a) The rocket travels 200 meters horizontally.
b) The height of the rocket mid-flight is of 1000 meters.
Step-by-step explanation:
Height of the rocket:
The height of the rocket, in meters, after an horizontal distance of x, is given by:
[tex]y = 0.1x(200 - x)[/tex]
a) How far does the rocket travel horizontally?
This is x when [tex]y = 0[/tex]. So
[tex]0.1x(200 - x) = 0[/tex]
Then
[tex]0.1x = 0[/tex]
[tex]x = 0[/tex]
And
[tex]200 - x = 0[/tex]
[tex]x = 200[/tex]
So
The rocket travels 200 meters horizontally.
b How high does the rocket reach mid-flight?
This it the height y when x = 0, so:
[tex]y = 20*100 - 0.1*100^2 = 1000[/tex]
The height of the rocket mid-flight is of 1000 meters.
17 Geometry question: Use an algebraic equation to find the measurement of each angle that is represented in terms of X
Answer:
2x + 30° = 40°
4x + 30° = 50°
Step-by-step explanation:
2x + 30° and 4x + 30° are complementary angles.
Complementary angles sum up to give 90°.
Therefore,
2x + 30° + 4x + 30° = 90°
Add like terms
6x + 60 = 90
6x = 90 - 60
6x = 30
6x/6 = 30/6
x = 5
✔️2x + 30°
Plug in the value of x
2(5) + 30
10 + 30
= 40°
✔️4x + 30°
4(5) + 30°
20 + 30
= 50°
Find the value of k if y-' is a factor of y³ + 4y² + ky - 6
Answer:
1
step by step explanation
hope this helps :)
Select the statement that best justifies the conclusion based on the given information.
a. Definition of bisector.
b. Definition of midpoint.
c. If two lines intersect, then their intersection is exactly one point.
d. Through any two different points, exactly one line exists.
9514 1404 393
Answer:
a. Definition of bisector.
Step-by-step explanation:
Line l is a line through the midpoint M. We can conclude it is a bisector, because, by definition, a bisector is a line through the midpoint.
The conclusion is justified by the definition of a bisector.
Complete the problems. (From Example 2)
1. How much compound interest will $50,000 have earned in 10 years at 6.4% annual interest compounded
quarterly?
Answer:
Compound interest is $7,037,339.2
Step-by-step explanation:
[tex]{ \boxed{ \bf{A=P(1+ \frac{r}{100} ) {}^{n} }}}[/tex]
substitute:
[tex]{ \sf{ = 50000(1 + \frac{6.4}{100}) {}^{10} }} \\ \\ = { \sf{50000(1.64) {}^{10} }} \\ \\ { = \sf{7037339.2}}[/tex]
A bag of M&M's has 6 red, 5 green, 4 blue, and 8 yellow M&M's. What is the probability of randomly picking: (give answer as a reduced fraction) 1) a yellow? w 2) a blue or green? 3) an orange?
Answer:
P( yellow) = 8/23
P( blue or green) = 9/23
P(orange) = 0
Step-by-step explanation:
6 red, 5 green, 4 blue, and 8 yellow M&M's = 23 total
P( yellow) = yellow / total = 8/23
P( blue or green) = (blue+green) / total = (5+4)/23 = 9/23
P(orange) = orange/ total = 0/23
Answer:
there are 23 m&m's.
Step-by-step explanation:
Probability of getting red is 6/23
Probability of getting green is 5/23
Probability of getting blue is 4/23
Probability of getting yellow is 8/23
Orange = red + yellow = 6+8/23
Probability of getting Orange = 14/23
A)15.8 inches
B) 17.8 inches
C)16.2 inches
D)14.8 inches
Answer:
B
Step-by-step explanation:
Use pythagorean theorem
4^2+5^2=AC^2, AC= 6.4
7^2+9^2=CB^2, CB=11.4
When is the Declaration of Independence?
Answer:
July 4th, 1776.
Step-by-step explanation:
By issuing the Declaration of Independence, adopted by the Continental Congress on July 4, 1776, the 13 American colonies severed their political connections to Great Britain. The Declaration summarized the colonists' motivations for seeking independence.
a. 1.5
b. 2.3
c. 2.4
d. 1.9
Answer:
2.3
Step-by-step explanation:
.5 - .3 = .2
.8 - .5 = .3
1.2 - .8 = .4
1.7 - 1.2 = .5
We should add .6 next
1.7+.6 = 2.3
plz help asap
Peter, Jan, and Maxim are classmates. Their total score for the last test was 269. Peter's score was higher than Jan's score and higher than Maxim's score. What could be Peter's least possible score?
Answer:
91
Step-by-step explanation:
269 / 3 = about 90
Peter score = 90
others could be 90,81
+1 to peter
=91
4. find possible value for m if
X=-3 and (3m-x)2=81
Answer:
m = 12.5
Step-by-step explanation:
x = - 3
(3m - x) 2= 81
(3m - (-3)) 2= 81
(3m + 3) 2= 81
6m + 6 = 81
- 6 - 6
6m = 75
[tex]\frac{6m}{6}[/tex] = [tex]\frac{75}{6}[/tex]
m = 12.5
hope this helps! if you have an questions, pls let me know!
In my town, it's rainy one third of the days. Given that it is rainy, there will be heavy traffic with probability 1/2, and given that it is not rainy, there will be heavy traffic with probability 1/4. If it's rainy and there is heavy traffic, I arrive late for work with probability 1/2. On the other hand, the probability of being late is reduced to 1/8 if it is not rainy and there is no heavy traffic. In other situations (rainy and no traffic, not rainy and traffic) the probability of being late is 0.25. You pick a random day.
a. What is the probability that it’s not raining and there is heavy traffic and I am not late?
b. What is the probability that I am late?
c. Given that I arrived late at work, what is the probability that it rained that day?
Answer:
a) 0.125 = 12.5% probability that it’s not raining and there is heavy traffic and I am not late.
b) 0.2292 = 22.92% probability that I am late.
c) 0.5454 = 54.54% probability that it rained that day.
Step-by-step explanation:
Conditional Probability
We use the conditional probability formula to solve this question. It is
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)}[/tex]
In which
P(B|A) is the probability of event B happening, given that A happened.
[tex]P(A \cap B)[/tex] is the probability of both A and B happening.
P(A) is the probability of A happening.
Question a:
2/3 probability of not raining.
If not raining, 1/4 probability of heavy traffic.
1 - 0.25 = 0.75 = 3/4 probability of not late.
So
[tex]p = \frac{2}{3} \times \frac{1}{4} \times \frac{3}{4} = \frac{2}{16} = 0.125[/tex]
0.125 = 12.5% probability that it’s not raining and there is heavy traffic and I am not late.
b. What is the probability that I am late?
0.5 of (1/3)*(1/2) = 1/6(rainy and heavy traffic).
0.25 of (1/3)*(1/2) = 1/6(rainy and no traffic).
1/8 = 0.125 of (2/3)*(3/4) = 1/2(not rainy and no traffic).
0.25 of (2/3)*(1/4) = 1/6(not rainy and traffic). So
[tex]P(A) = 0.5\frac{1}{6} + 0.25\frac{1}{6} + 0.125\frac{3}{6} + 0.25\frac{1}{6} = \frac{0.5 + 0.25 + 3*0.125 + 0.25}{6} = 0.2292[/tex]
0.2292 = 22.92% probability that I am late.
c. Given that I arrived late at work, what is the probability that it rained that day?
Event A: Late
Event B: Rained
0.2292 = 22.92% probability that I am late.
This means that [tex]P(A) = 0.2292[/tex]
Probability of late and rain:
0.5 of 1/6(rain and heavy traffic).
0.25 of 1/6(rain and no traffic). So
[tex]P(A \cap B) = 0.5\frac{1}{6} + 0.25\frac{1}{6} = \frac{0.5 + 0.25}{6} = \frac{0.75}{6} = 0.125[/tex]
Probability:
[tex]P(B|A) = \frac{P(A \cap B)}{P(A)} = \frac{0.125}{0.2292} = 0.5454[/tex]
0.5454 = 54.54% probability that it rained that day.
Which table represents a linear function?
Answer:
the the 3rd one Is the one
What are the solutions of this quadratic equation?
4x2 + 3 = 4x + 2
Answer:
A. x = 1/2
General Formulas and Concepts:
Pre-Algebra
Equality PropertiesAlgebra I
Terms/CoefficientsFactoringStandard Form: ax² + bx + c = 0Solving quadraticsStep-by-step explanation:
Step 1: Define
Identify
4x² + 3 = 4x + 2
Step 2: Solve for x
[Equality Property] Rewrite in standard form: 4x² - 4x + 1 = 0Factor: (2x - 1)² = 0Solve: x = 1/2can yall answer it in the box like the numbers
Answer:
Hi!
Step-by-step explanation:
1234567890987654211234567890......
Step-by-step explanation:
12345678890098764321
What is the order of rotational symmetry for the figure?
A. 2
B. 3
C. 1
D. 4 or more
The order of rotational symmetry for the figure will be 2. The correct option is A.
What is rotational symmetry?A shape exhibits rotational symmetry when it retains its appearance following a little amount of rotation by a partial turn. The number of different orientations in which an object appears exactly the same for each rotation is known as the degree of rotational symmetry.
The number of full rotations a shape may undergo while maintaining its appearance is its order of rotational symmetry. The triangle never seems the same after being rotated a complete 360 degrees, with the exception of when it is returned to its original starting position.
Therefore, the order of rotational symmetry for the figure will be 2. The correct option is A.
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Using the following information to answer the questions.
- A survey asked 75 people if they wanted a later school day start time.
- 45 people were students, and the rest were teachers.
- 50 people voted yes for the later start
- 30 students voted yes for the later start
Use this information to complete the frequency table.
Use the completed table from Part a. What percentage of the people surveyed were teachers?
Use the completed table from Part a. What percentage of the people surveyed were teachers who wanted a later start time?
What does the number in the bolded cell represent?
Answer:
Hi! I'll provide the answers in the explanation.
Step-by-step explanation:
a) The table is in the attachment.
b) The percentage is 40%. Looking at the table, we can see that the total of teachers who voted is 30. You'll be able to find the percentage if you divide 30/75, since 75 is the total people who took the survey.
c) The percentage is 40%. For this situation, we have to divide the total of the people who voted for NO by the teachers who voted NO. So it'll be 20/50, which is 0.4. We can simplify that and the solution is 40%.
d) It represents the students who took the survey voted NO for a later start.
Hope this helps! :D
Answer:
5. Use the following information to answer the questions.
A survey asked 75 people if they wanted a later school day start time.
45 people were students, and the rest were teachers.
50 people voted yes for the later start.
30 students voted yes for the later start.
a) Use this information to complete the frequency table. (5 points: 1 point for each cell that was not given above)
Vote YES for later start
Vote NO for later start
Total
Students
30
15
45
Teachers
20
10
30
Total
50
25
75
b) Use the completed table from Part a. What percentage of the people surveyed were teachers? (2 points)
40%
c) Use the completed table from Part a. What percentage of the people surveyed were teachers who wanted a later start time? (2 points)
40%
d) What does the number in the bolded cell represent? (1 point)
The number of students that said no to a later start.
Step-by-step explanation:
A p E x
the probability of a thunderstorm on memorial day 0.72 and the probability of a thunderstorm on independance day is 0.14. assuming that these two events are independent, what is the probability of thunderstorms on both memorial day and independence day
Answer:
0.1008 = 10.08% probability of thunderstorms on both memorial day and independence day.
Step-by-step explanation:
Probability of independent events:
If two events are independent, the probability of both happening is the multiplication of the probabilities of each happening, that is:
[tex]P(A \cap B) = P(A)P(B)[/tex]
In this question:
Event A: Thunderstorm on memorial day.
Event B: Thunderstorm on memorial day
The probability of a thunderstorm on memorial day 0.72
This means that [tex]P(A) = 0.72[/tex]
The probability of a thunderstorm on independance day is 0.14.
This means that [tex]P(B) = 0.14[/tex]
What is the probability of thunderstorms on both memorial day and independence day?
[tex]P(A \cap B) = P(A)P(B) = 0.72*0.14 = 0.1008[/tex]
0.1008 = 10.08% probability of thunderstorms on both memorial day and independence day.
Probabilities are used to determine the chances of events
The probability of thunderstorm on both days is 0.1008
Represent the event that there is thunderstorm on Memorial Day with A, and the event that there is thunderstorm on Independence Day with B
So, we have:
P(A) = 0.72
P(B) = 0.14
The probability of thunderstorm on both days is then calculated as;
P(Both) = P(A) * P(B) - P(A or B)
Given that the events are independent, the equation becomes
P(Both) = P(A) * P(B)
So, we have:
P(Both) = 0.72 * 0.14
Multiply
P(Both) = 0.1008
Hence, the probability of thunderstorm on both days is 0.1008
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Trevor is studying a polynomial function f(x). Three given roots of f(x) are -7, 2i, and 7. Trevor concludes that f(x) must
be polynomial with degree 3. Which statement is true?
Answer:
B Trevor isn't correct because -2i must also be a root
Step-by-step explanation:
A Trevor is correct.
B Trevor is not correct because –2i must also be a root.
C Trevor is not correct there cannot be an odd number of roots.
D Trevor is not correct because there cannot be both rational and complex roots.
statements^^^^^^
The statement that f(x) must be a polynomial with degree 3 is not necessarily true based on the given roots.
What is a function?A function has an input and an output.
A function can be one-to-one or onto one.
It simply indicated the relationships between the input and the output.
Example:
f(x) = 2x + 1
f(1) = 2 + 1 = 3
f(2) = 2 x 2 + 1 = 4 + 1 = 5
The outputs of the functions are 3 and 5
The inputs of the function are 1 and 2.
We have,
Since one of the roots is complex (2i), it follows that the coefficients of f(x) must be complex as well, and therefore f(x) must be a polynomial with complex coefficients.
However, it is possible for f(x) to have a higher degree than 3.
For example,
The polynomial (x + 7)(x - 2i)(x + 2i)(x - 7) has degree 4 and has the given roots of -7, 2i, and 7. Therefore, f(x) could be a polynomial with degree 4 or higher.
Thus,
The statement that f(x) must be a polynomial with degree 3 is not necessarily true based on the given roots.
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