1. It is not unusual for Joe to roll a four twice in six attempts because a die has 6 sides, so the probability of rolling a four is 1/6 (one in six).
2. If Joe rolled a four three times in six attempts, it would still not be considered unusual because when the probability of rolling a four three times is slightly lower than rolling it twice, it is still not considered a very low probability or unusual occurrence.
It is not unusual for Joe to roll a four twice in six attempts. Here's why:
1. A die has 6 sides, so the probability of rolling a four is 1/6 (one in six).
2. When rolling the die six times, the probability of rolling a four twice can be calculated using the binomial probability
formula:[tex]P(X=k) = (nCk) * (p^k) * (q^(n-k)),[/tex]
where n is the number of trials,
k is the number of successful outcomes,
p is the probability of success, and q is the probability of failure (1-p).
3. In this case, n=6, k=2, p=1/6, and q=5/6.
So, [tex]P(X=2) = (6C2) * (1/6)^2 * (5/6)^4[/tex] ≈ 0.2009 or 20.09%.
4. Since 20.09% is not a low probability, it is not unusual for Joe to roll a four twice in six attempts.
If Joe rolled a four three times in six attempts, it would still not be considered unusual. Here's why:
1. Using the same binomial probability formula as before, we now have k=3.
2. [tex]P(X=3) = (6C3) * (1/6)^3 * (5/6)^3[/tex] ≈ 0.1550 or 15.50%.
3. While the probability of rolling a four three times is slightly lower than rolling it twice, it is still not considered a very low probability or unusual occurrence.
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))
Which operation should be completed first to find the value of the expression
below?
6-3
12+ 30 (6-3) + 1
12+ 30
306
3+1
Don
Answer:
(6-3)
Step-by-step explanation:
The weight of a puppy is modeled by 2x - y=-2, where x represents the puppy's age in
weeks and y represents its weight in pounds. Which graph models the puppy's growth?
Answer:
Graph H
Step-by-step explanation:
intercept (0,2)
Hey, we're doing IXLs in pre-alg rn
After solving the given equation 1/4b - 2 = -1/2b + 4, the resultant value of b is 8/3 respectively.
What are equations?An equation is a mathematical expression with two equal sides and an equal sign.
4 + 6 = 10 is an illustration of an equation.
On the left side of the equal sign, you can see 4 + 6, and on the right, you can see 10.
A formula exists in every equation.
Some equations do not have formulae.
Equations are designed to be solved for a variable.
We look over formulas.
So, we have the equation:
1/4b - 2 = -1/2b + 4
Now, solve the equation for b as follows:
1/4b - 2 = -1/2b + 4
1/4b = -1/2b + 6
1/4b + 2/1b = 6
1+8/4b = 6
9/4b = 6
b = 6 * 4/9
b = 2 * 4/3
b = 8/3
Therefore, after solving the given equation 1/4b - 2 = -1/2b + 4, the resultant value of b is 8/3 respectively.
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simplify completely
sin(90°-x)co(180°-X)+tanX×cos(-x)sin180°+x)
Therefore , the solution of the given problem of trigonometry comes out to be -1 is the simplified formula.
What is a trigonometry?Some claim that the fusion of various fields contributed to the development of astrophysics. With the aid of precise mathematical methods, many metric issues can be resolved or the output of a computation can be determined. The scientific investigation of all six fundamental geometric calculations is known as trigonometry. They are known by a number of names and abbreviations, such as sine, variance, angle, and others. (csc).
Here,
Let's first use trigonometric identities to separately simplify each term:
=> cos(x - 90°) equals sin(x)
=> cos(x - 180°) = -cos(x)
=> tan(x) = cos(x) / sin(x)(x)
=> x(cos(-)) = x(x)
=> (180° + x) sin = -sin(x)
When we replace the equation with these simplifications, we get:
=> cos(x) * sin(180° plus x) * cos(x) * (-cos(x)) + (sin(x) / cos(x))
=> sin(180° plus x) * sin(-cos2(x))
=> -cos²(x) - sin(x)*sin(180° + x) (using the equation sin(x)*sin(x)) = -sin^2(x))
Using the identity sin2(x) +cos2(x) = 1, we get = -1.
Consequently, -1 is the simplified formula.
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when a study sample shows representativeness, what can be concluded about the study? group of answer choices the study results show evidence of sampling bias the study used strict inclusion and exclusion criteria to limit the sample size the study is most likely not generalizable because the sample was obtained using specific inclusion criteria. the study is most likely generalizable, with results that can be applied to the target population
When a study sample is representative of the target population, it allows for the results to be generalizable, meaning they can be applied to the broader population.
This is an important aspect of research, as it ensures the study's findings are relevant and useful beyond the specific sample studied.
When a study sample shows representativeness, it means that the sample accurately reflects the characteristics of the target population.
In this case, the study is most likely generalizable, with results that can be applied to the target population.
To achieve representativeness, researchers often use random sampling techniques, which help minimize the potential for sampling bias.
Sampling bias occurs when certain groups within the target population are over- or under-represented in the sample, which can lead to inaccurate conclusions.
In contrast, if a study used strict inclusion and exclusion criteria to limit the sample size or relied on specific inclusion criteria, it could result in a sample that is not representative of the target population.
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Very confused on this question, unsure of the answer
Answer:
a = 9 , b = 5 , c = 25
Step-by-step explanation:
using the Cosine rule in the triangle
a² = b² + c² - 2bc cosA
where a is the side opposite ∠ A and b, c the sides adjacent to ∠ A
here
a = y , b = x + 5 , c = 3x and A = Θ , then
y² = (x + 5)² + (3x)² - [ 2(x + 5) × 3x × cosΘ ]
y² = x² + 10x + 25 + 9x² - [ 6x(x + 5) × [tex]\frac{1}{6}[/tex] ]
y² = 10x² + 10x + 25 - x(x + 5)
y² = 10x² + 10x + 25 - x² - 5x
y² = 9x² + 5x + 25 ← in the form y² = ax² + bx + c
with a = 9 , b = 5 , c = 25
students arrive at the administrative services office at an average of one every 14 minutes, and their requests take, on average, 8 minutes to be processed. the service counter is staffed by only one clerk, judy gumshoes, who works eight hours per day. assume poisson arrivals and exponential service times. a. what is the utilization rate? b. the average number of students in line. c. the average time of waiting in line.
A. The Utilization rate is 0.5714 or 57.14%, B. The average number of students in line is 0.9 students and C. The average time of waiting in line was 4.57 minutes.
The utilization rate refers to the proportion of time Judy Gumshoes spends processing student requests.
To calculate this rate, divide the average service time by the average time between arrivals. In this case, the average service time is 8 minutes, and students arrive every 14 minutes on average.
a) Utilization rate: 8 minutes / 14 minutes = 0.5714 or 57.14%
b) To determine the average number of students in line,
we can use the formula L = λW, where L represents the average number of students in the system, λ is the arrival rate (1 student per 14 minutes), and W is the average time a student spends in the system (waiting and being served). Since we know the utilization rate,
we can calculate the average waiting time (Wq) using the formula,
Wq = (U^2) / (1 - U), where U is the utilization rate.
In this case, Wq = (0.5714^2) / (1 - 0.5714) = 0.3265 or 32.65% of 14 minutes = 4.57 minutes.
W = Wq + service time
= 4.57 minutes + 8 minutes
= 12.57 minutes.
Finally, L = λW = (1 student / 14 minutes) * 12.57 minutes
= 0.9 students.
c) The average time of waiting in line is the same as the average waiting time in the system (Wq), which we calculated as 4.57 minutes.
In summary, the utilization rate of the service counter is 57.14%, the average number of students in line is 0.9, and the average waiting time in line is 4.57 minutes.
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PLEASE HELP!! 50 POINTS!! if you just take the points without actually helping you will be forever cursed within my mind and never forgiven.
Christopher borrows 7,500$ to build a garage. He agrees to pay 475$ a month for 24 months but pays off the loan after 18 months.
Part A: Determine the amount of unearned interest.
Part B: Determine the amount needed to repay the loan using the Rule of 78.
Part C: Show your work to support your answers to Part A and Part B.
To solve the problem, we can use the formula for the future value of an annuity:
FV = PMT * ( (1 + r)^n - 1 ) / r
where:
- PMT is the periodic payment
- r is the periodic interest rate
- n is the number of periods
In this case,
- PMT = $475 (the monthly payment)
- r = the monthly interest rate
- n = 24 (the number of months in the agreement)
We first need to calculate the monthly interest rate. We can find this by dividing the yearly interest rate by 12 months:
r = 18% / 12 months = 0.015
Now we can calculate the future value (FV) of the annuity using the above formula:
FV = $475 * ( (1 + 0.015)^24 - 1 ) / 0.015 = $13,237.19
This is the amount that Christopher would owe after 24 months if he made monthly payments of $475.
However, Christopher pays off the loan after 18 months. To find out how much he owes at this point, we can calculate the future value after 18 months:
FV = $475 * ( (1 + 0.015)^18 - 1 ) / 0.015 = $10,198.66
So, after 18 months, Christopher owes approximately $10,198.66.
Can 2x divided by 3y be simplified
Answer:
No, you cannot simplify it.
Step-by-step explanation:
Because 2 and 3 are one of the lowest numbers that cannot be simplified.
The box plot represents the number of tickets sold for a school dance.
A horizontal line labeled Number of Tickets sold that starts at 8, with tick marks every one unit up to 30. The graph is titled Tickets Sold for A Dance. The box extends from 17 to 21 on the number line. A line in the box is at 19. The lines outside the box end at 10 and 27.
Which of the following is the appropriate measure of variability for the data, and what is its value?
The IQR is the best measure of variability, and it equals 17.
The range is the best measure of variability, and it equals 4.
The IQR is the best measure of variability, and it equals 4.
The range is the best measure of variability, and it equals 17
The IQR is the best measure of variability for this data set, and its value is 4.
What is median?
Median is a measure of central tendency that represents the middle value in a dataset when the values are arranged in order of magnitude.
The correct answer is:
The IQR is the best measure of variability, and it equals 4.
The box plot shows the median (represented by the line in the box), the interquartile range (IQR) (represented by the length of the box), and the range (represented by the lines outside the box).
The IQR is the range between the first quartile (Q1) and the third quartile (Q3) of the data set, which contains the middle 50% of the data. In this case, the box extends from 17 to 21, indicating that Q1 is 17 and Q3 is 21. Therefore, the IQR is the difference between Q3 and Q1, which is 21-17=4.
The range is the difference between the maximum and minimum values in the data set, which is 27-10=17. However, the range can be affected by outliers and is not as robust as the IQR.
Therefore, the IQR is the best measure of variability for this data set, and its value is 4.
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Naomi's bedroom is 6 meters long and 4 meters wide. Starting at the far left corner, Naomi walks down the length, across the width, and then diagonally back to the far left corner. How far does Naomi walk? If necessary, round to the nearest tenth.
Naomi walks a total of 6 + 4 + 7.2 ≈ 17.2 meters.
How to calculate?
Naomi walks the length of the room, which is 6 meters, then across the width, which is 4 meters.
Using the Pythagorean theorem, the length of the diagonal can be found:
diagonal = √(6²2 + 4²2)
diagonal = √(36 + 16)
diagonal = √52
diagonal ≈ 7.2 meters
Therefore, Naomi walks a total of 6 + 4 + 7.2 ≈ 17.2 meters.
The Pythagorean theorem is a fundamental concept in mathematics that states that in a right triangle, the square of the length of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the lengths of the other two sides.
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HELPPPPP DUE SOON!!!!
The distance between the points H (-9, 1), and K (-1, 8) in the coordinate plane, obtained using the distance formula is; Distance: 10.63
What is the distance formula?The distance formula is a formula that is used to find the distance between two points on the coordinate plane.
The specified points are; H = (-9, 1), and K = (-1, 8)
The distance formula can be used to calculate the distance between the points as follows;
The distance formula is; d = √((x₂ - x₁)² + (y₂ - y₁)²)
Where; (x₁, y₁) and (x₂, y₂) are the coordinates of the two points.
When, (x₁, y₁) = (-9, 1), and (x₂, y₂) = (-1, 8), we get;
d = √((-1 - (-9))² + (8 - 1)²) = √(8² + 7²) =
√(8² + 7²) = √(64 + 49) = √(113) ≈ 10.63 (rounded to the nearest hundredth)
The distance between the points is about 10.63 units
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help with this problem
Answer:
PQ = 165.60m
Step-by-step explanation:
Since triangles are similar
PQ/70 + 210 = 124.2/210
PQ = 124.2 (70 + 210)/210 = 165.60m
Review the information on FICO score calculations to answer the question:
Category Percentage
Payment History 35%
Amount Owed 30%
Length of Credit History 15%
New Credit and Inquiries 10%
Credit Mix 10%
A borrower has a credit score of 725. How many points come from amount owed and length of credit history?
290
322.65
363
326.25
From the given percentage values, 326.25 points come from amount owed and length of credit history.
What is percentage?
Percentage is a method of representing a value as a fraction of 100. This is frequently used to make comparisons, demonstrate ratios, or determine a fraction of a whole.
The borrower's credit score is 725, and we need to find out how many points come from amount owed and length of credit history.
From the information given, we know that these two categories make up a total of 45% of the score calculation (30% for amount owed and 15% for length of credit history).
We can set up a proportion:
(30% + 15%) / 100% = x / 725
Simplifying the left side:
45% / 100% = 0.45
0.45 = x / 725
Multiplying both sides by 725:
x = 0.45 * 725
x = 326.25
Therefore, 326.25 points come from amount owed and length of credit history.
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44% of c is 72. find the value of c
Answer: 163.6363...
Step-by-step explanation:
44% of c is 72, so then [tex]0.44*c=72\\[/tex].
Divide both sides by 0.44 to solve for c, and you get c=163.6363...
Tip: if you are ever trying to figure out what a number is a percentage of, like in this problem, just divide the number by the percent in decimal form.
Draw the image of triangle△ABC under a dilation whose center is C and scale factor is 2
The original triangle ABC is down below.
PLEASE HELP
The resulting triangle would have twice the area and all sides would be twice as long as the original triangle, but the angles would remain the same.
What is triangle?A triangle is a geometric shape that consists of three straight line segments or sides that are connected at three points called vertices. Triangles are two-dimensional and are the simplest polygon that can exist in Euclidean space. Triangles can be classified according to the size and shape of their sides and angles. Triangles are used in many different areas of mathematics, science, and engineering. They are also common in everyday life, for example in construction, architecture, and design.
Here,
To dilate a triangle with a center point C and a scale factor of 2, you would first draw a ray from C through each vertex of the triangle. Then, you would measure the distance from C to each vertex of the original triangle and multiply it by the scale factor (2 in this case) to find the distance from C to each corresponding vertex of the dilated triangle. Finally, you would draw lines connecting the dilated vertices to form the dilated triangle.
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dustin has 3 cups of buttermilk.does he have enough to make four batches of muffins.explain(he needs 3/4 cup butter milk to make 1 batch)
Answer:
Step-by-step explanation:
The math used shows how much cups it would take to make 4 batches, 3 cups. Therefor yes, he does have exactly enough to make 4 batches of muffins.
Three numbers whose sum is 26 are in GP.If 5,9 and 5 are added to them respectively, then the three numbers are in AP. Find the numbers.
The three numbers are:
(-1 + √(97))/2, (-1 ± √(97))/2, (-1 ± 7√(97))/2
What is an arithmatic progression?
An arithmetic progression is a sequence of numbers in which each term after the first is obtained by adding a fixed constant to the preceding term. The fixed constant is called the common difference, denoted by d.
Let the three numbers in the GP be a/r, a, and ar, where a is the middle term.
Then we have:
a/r + a + ar = 26 (sum of GP)
(a/r + 5) + (a + 9) + (ar + 5) = 3(a + 4) (sum of AP)
Simplifying the second equation, we get:
a(r - 1) = 3
Substituting this into the first equation, we get:
a/r + a + ar = 26
1/r + 1 + r = 26/a
r^2 + r - 26/a = 0
Solving for r using the quadratic formula, we get:
r = (-1 ± √(1 + 104/a))/2
Since r > 0 (because the terms are in GP), we take the positive root:
r = (-1 + √(1 + 104/a))/2
Substituting this into the equation a(r - 1) = 3, we get:
a(-1 + √(1 + 104/a))/2 - a = 3
-a + a √(1 + 104/a) - 2 = 0
a √(1 + 104/a) = -a + 2
a² (1 + 104/a) = a² - 4a + 4
104a = 4a² - 4a + 4
a² - a + 1 = 26
(a - 1/2)² + 3/4 = 26
(a - 1/2)² = 97/4
a - 1/2 = ±√(97)/2
a = (1 ± √(97))/2
Since the terms are in GP, we can use the value of a to find the other two terms:
a/r = (1 ± √(97))/(2(-1 + √(1 + 104/a))/2) = (-1 ± √(97))/2
ar = (1 ± √(97))/(2(-1 - √(1 + 104/a))/2) = (-1 ± 7√(97))/2
Therefore, the three numbers are:
(-1 + √(97))/2, (-1 ± √(97))/2, (-1 ± 7√(97))/2
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PLEASE HELP WILL MARK BRAINLIEST
20 points
write an explicit formula for each sequence
1,4,7,10….
SHOW WORK PLS
Answer:
aₙ = 3n - 2
Step-by-step explanation:
The given sequence is an arithmetic sequence with the first term a₁ = 1 and the common difference d = 3.
The explicit formula for an arithmetic sequence is:
aₙ = a₁ + (n - 1)d
where aₙ represents the nth term in the sequence.
Substituting the values we have:
aₙ = 1 + (n - 1)3
Simplifying the equation we get:
aₙ = 3n - 2
Therefore, the explicit formula for the given sequence 1, 4, 7, 10, ... is aₙ = 3n - 2.
6x^2-12x-18 factor the polynomial
Answer:
6x² - 12x - 18
the factors are -18 and 6
6x² - 18x + 6x - 18
6x(x - 3) + 6 (x - 3)
(6x + 6) or (x - 3)
the factors are:
(6x + 6) or (x - 3)
please help with this question?!!
Answer: SHawn
Step-by-step explanation:
Are these right? If not, can you tell the right answers so I can change them please?
Answer:
O=0
T=-5
c = 0
R = -2
6 = 8
2 = 8
11=-3
Step-by-step explanation: Sorry for the late answer It took me a bit to solve all the problems but I hope this helps you!!
Question 1 (Multiple Choice Worth 2 points)
(Multiplying Linear Expressions MC)
Simplify ---
O
45
m²
8.
45
8
45
2
m²-m
35
2
-m² + m
35
8
45
2
·m² + m
35
Answer:
[tex] - \frac{2}{5} m( - \frac{4}{9} m - \frac{1}{7} ) = [/tex]
[tex] \frac{8}{45} {m}^{2} + \frac{2}{35} [/tex]
the edges of a cube increase at a rate of 2 centimeters per second. how fast is the volume changing when the length of each cube edge is 50 centimeters ?
The required volume of the cube is increasing at a rate of 15,000 cubic centimeters per second when the length of each edge is 50 centimeters and the edges are increasing at a rate of 2 centimeters per second.
Let us consider V be the volume of the cube,
And s be the length of one edge of the cube.
Volume of a cube is equal to,
V = s^3
To find how fast the volume is changing with respect to time,
Use the chain rule of differentiation,
dV/dt = dV/ds × ds/dt
where dV/dt is the rate of change of volume with respect to time,
dV/ds is the rate of change of volume with respect to the length of one edge of the cube,
And ds/dt is the rate of change of the length of one edge of the cube with respect to time.
ds/dt = 2 cm/s,
find dV/dt when s = 50 cm.
First, find dV/ds,
dV/ds = 3s^2
Then, we can plug in s = 50 cm,
dV/ds = 3(50)^2
= 7500 cm^2
Finally, we can plug in the values we have to find dV/dt,
dV/dt = (dV/ds) × (ds/dt)
= 7500 cm^2/s × 2 cm/s
= 15,000 cm^3/s
Therefore, the volume of the cube is increasing at a rate of 15,000 cubic centimeters per second .
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a classmate walks into class and states that he has an extra ticket to a festival on friday night. he asks everyone in the class to put their name on a piece of paper and put it in a basket. he plans to draw from the basket to choose the person who will attend the festival with him. if there are 22 other people in class that night, what is your chance of being chosen to attend the festival? round your answer to four decimal places, if necessary.
Your chance of being chosen to attend the festival is approximately: Probability = 1 / 23 ≈ 0.0435 or 4.35% when rounded to four decimal places.
To determine your chance of being chosen to attend the festival, you need to find the probability of your name being
drawn from the basket.
There are 22 other people in class, and each person, including you, will have their name on a piece of paper.
Total number of names in the basket = 22 (other people) + 1 (you) = 23
Since each person has an equal chance of being chosen, the probability of your name being drawn is:
Probability = (Number of favorable outcomes) / (Total number of outcomes)
Probability = 1 (your name) / 23 (total names)
So, your chance of being chosen to attend the festival is approximately:
Probability = 1 / 23 ≈ 0.0435 or 4.35% when rounded to four decimal places.
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One card each is drawn from four different standard decks of cards. Find the total number of outcomes
Since there are 52 cards in a standard deck, there are 52 possible outcomes for the first draw from the first deck. Similarly, there are 52 possible outcomes for the first draw from the second, third, and fourth decks. Therefore, the total number of outcomes for the first draw is 52 + 52 + 52 + 52 = 208.
For the second draw, there are only 51 possible outcomes for each deck, since one card has already been drawn. Therefore, the total number of outcomes for the second draw is 51 + 51 + 51 + 51 = 204.
For the third draw, there are only 50 possible outcomes for each deck, since two cards have already been drawn. Therefore, the total number of outcomes for the third draw is 50 + 50 + 50 + 50 = 200.
For the fourth draw, there are only 49 possible outcomes for each deck, since three cards have already been drawn. Therefore, the total number of outcomes for the fourth draw is 49 + 49 + 49 + 49 = 196.
The total number of outcomes for drawing one card each from four different standard decks of cards is the product of the outcomes for each draw: 208 x 204 x 200 x 196 = 338,401,792.
suppose that 5% of teachers at a university attended a conference. if 4000 teachers are enrolled at the university, about how many teachers attended the conference?
Answer: 200 teachers attended the conference
Step-by-step explanation:
To answer this question, we will find 5% of 4,000. A percent divided by 100 becomes a decimal, and "of" means multiplication in mathematics.
5% / 100 = 0.05
4,000 * 0.05 = 200 teachers attended the conference
The answer is 200
If 5% of teachers at a university attended a conference and 4000 teachers are enrolled at the university, about 200 teachers attended the conference. What is the problem asking for? The problem is asking us to calculate how many teachers attended a conference given that 5% of the total number of teachers at a university attended the conference and that the university has 4000 teachers .What is the formula for percentage? The formula for percentage is given by:(Part/Whole)*100Let T be the total number of teachers at the university, and let x be the number of teachers that attended the conference. We know that 5% of teachers at a university attended a conference, therefore:(5/100)*T = x,. Given that there are 4000 teachers in the university, we can substitute this value into the equation: (5/100)*4000 = x. Simplifying the equation, we get: x = 0.05 * 4000x = 200.
Therefore, about 200 teachers attended the conference.
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Solve for z in the proportion.
60
90
Z =
22
Z + 17
Submit
The equation is not a proportion, and the value of z in the equation is 17
Calculating the value of z in the equationGiven that
2Z = Z + 17
To solve for z in the proportion:
2z = z + 17
We can start by simplifying the equation by subtracting z from both sides:
2z - z = 17
Simplifying further, we get:
z = 17
Therefore, the solution to the proportion is z = 17.
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The standard form of a circle is (x-5)^2+(y-5)^2=16. Convert the standard form into general form.
Therefore, the general form of the circle is:
[tex]x^2 + y^2 - 10x-10y+34=0[/tex].
What is circle?A circle is a geometric shape that is defined as the set of all points in a plane that are at a fixed distance (called the radius) from a given point (called the center). The distance from the center to any point on the circle is always the same. Circles are often represented using the symbol "O" or "⚪" and are important in mathematics, geometry, and physics. They have many properties, such as circumference (the distance around the circle), area (the space inside the circle), and diameter (the distance across the circle through the center). Circles are used in various fields, including architecture, engineering, and art.
To convert the standard form of a circle to the general form, we expand and simplify the equation as follows:
[tex](x - 5)^2 + (y - 5)^2 = 16[/tex]
[tex]x^2 - 10x + 25 + y^2 - 10y + 25 = 16[/tex] (using the identity [tex](a - b)^2 = a^2 - 2ab + b^2)[/tex]
[tex]x^2 + y^2 - 10x-10y+34=0[/tex]
Therefore, the general form of the circle is:
[tex]x^2 + y^2 - 10x-10y+34=0[/tex]
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Problem 5.2 A cone has volume V, radius r, and a height of 12 cm. Another cone has the same height and 3 times the radius of the original cone. Write an expression for its volume. | Submit
Answer: The volume of a cone is given by the formula V = (1/3)πr^2h, where r is the radius and h is the height.
For the original cone with radius r and height 12 cm, we have:
V = (1/3)πr^2h
V = (1/3)πr^2(12)
V = 4πr^2
For the second cone with 3 times the radius of the original cone and the same height of 12 cm, we have:
V' = (1/3)π(3r)^2h
V' = (1/3)π9r^2(12)
V' = 36πr^2
Therefore, the expression for the volume of the second cone is 36πr^2.
Step-by-step explanation: