Answers
The solutions to the circle equations in the attached figure are: (5) (x + 2)² + (y - 1)² = 20, (6) x² + y² = 9, (7) (x + 3)² + (y - 1)² = -9 and (8) (x - 4)² + (y - 3)² = -16
Finding the Solution to Equation of CircleEquation of a Circle in the Cartesian coordinate system (x, y) is given by:
(x - h)² + (y - k)² = r²
where
(h, k) = coordinates of the center of the circle
r = radius.
The expression (x - h)² + (y - k)² represents the squared distance between any point (x, y) on the circle and the center point (h, k). By setting this expression equal to the square of the radius, r², we ensure that all points on the circle are equidistant from the center.
You can also expand the equation to get the standard form:
x² - 2hx + h² + y² - 2ky + k² = r².
Using the information above, let us solve the circle equations:
5) y² + 4x - 20 - 2y = -x²
First we need to find the coordinates (h, k) of the circle
x² + 4x + y² - 2y = 20
-2h = 4 => h = -2
-2k = -2 => k = 1
(h,k) = (-2, 1)
Rewrite the equation in a standard circle format
Recall: (x - h)² + (y - k)² = r²
(x - (-2))² + (y - (1))² = 20
(x + 2)² + (y - 1)² = 20
Therefore the solution to the circle equation is: (x + 2)² + (y - 1)² = 20 and the curve is attached.
6) -9 = -y² - x²
First we need to find the coordinates (h, k) of the circle
x² + y² = 9
-2h = 0 => h = 0
-2k = 0 => k = 0
(h, k) = (0, 0)
Rewrite the equation in a standard circle format
Recall: (x - h)² + (y - k)² = r²
(x - (0))² + (y - (0))² = 9
x² + y² = 9
Therefore the solution to the circle equation is: x² + y² = 9 and the curve is attached.
7) 9 = 2y - y² - 6x - x²
First we need to find the coordinates (h, k) of the circle
x² + 6x + y² - 2y = -9
-2h = 6 => h = -3
-2k = -2 => k = 1
(h, k) = (-3, 1)
Rewrite the equation in a standard circle format
Recall: (x - h)² + (y - k)² = r²
(x - (-3))² + (y - (1))² = -9
(x + 3)² + (y - 1)² = -9
Therefore the solution to the circle equation is: (x + 3)² + (y - 1)² = -9 and the curve is attached
8) 16 + x² + y² - 8x - 6y = 0
First we need to find the coordinates (h, k) of the circle
x² - 8x + y² - 6y = -16
-2h = -8 => h = 4
-2k = -6 => k = 3
(h,k) = (4, 3)
Rewrite the equation in a standard circle format
Recall: (x - h)² + (y - k)² = r²
(x - (4))² + (y - (3))² = -16
(x - 4)² + (y - 3)² = -16
Therefore the solution to the circle equation is: (x - 4)² + (y - 3)² = -16 and the curve is attached.
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Related Questions
The table shows the mass of four packages. What is the total mass of the packages?
Answers
The total mass of the four packages is given as follows:
37.67 kg.
How to obtain the total mass of the four packages?The total mass of the four packages is obtained adding the masses of each package given on the table for this problem.
From the table given in this problem, the mass for each package is given as follows:
Package 1: 3.94 kg.Package 2: 14.81 kg.Package 3: 11.27 kg.Package 4: 7.65 kg.Hence, adding these amounts, the total mass of the package is obtained as follows:
3.94 + 14.81 + 11.27 + 7.65 = 37.67 kg.
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Suppose a random sample of size 48 is selected from a population
Answers
The caluclated values are:
1.241.30 1.30 How to solve for the valuesN = 500:
SEM = 9 * √[(500 - 48) / (500 - 1)] / √(48)
= 1.24 (rounded to 2 decimals)
N = 5000:
SEM = 9 * √t[(5000 - 48) / (5000 - 1)] / √(48)
= 1.30 (rounded to 2 decimals)
N = 50000:
SEM = 9 * √[(50000 - 48) / (50000 - 1)] / √(48)
= 1.30 (rounded to 2 decimals)
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Pls help me and find out which 2 I got wrong I need it for my corrections pls help I don’t know which 2 I got wrong
Answers
The value of ascending order of numbers are,
⇒ (- 1/2)², 30%, 5/8, 5⁰ , |2|
We have to given that,
All the numbers are,
⇒ 5⁰
⇒ |2|
⇒ (- 1/2)²
⇒ 5/8
⇒ 30%
Now, We can simplify each as,
⇒ 5⁰
⇒ 1
⇒ |2|
⇒ 2
⇒ (- 1/2)²
⇒ 1/4
⇒ 0.25
⇒ 5/8
⇒ 0.625
⇒ 30%
⇒ 30/100
⇒ 0.3
Hence, Ascending order is,
0.25, 0.3, 0.625, 1 , 2
Or,
⇒ (- 1/2)², 30%, 5/8, 5⁰ , |2|
Thus, The value of ascending order of numbers are,
⇒ (- 1/2)², 30%, 5/8, 5⁰ , |2|
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a survey of families who took a summer vaction found that 3/4 of them traveled by car if 10,860 families in one city take a summer vaction how many would be expected to not travel by car?
Answers
Answer:
2715
Step-by-step explanation:
10860/4 = 2715
if im wrong smite me
i need help with this problem
Answers
The value of x is 40 degree.
We have,
Far Arc = 130 degree
Near Arc = 50 degree
According to "Angle-Arc Theorem." It states that the angle formed by the intersection of two tangents, two secants, or one tangent and one secant outside a circle is equal to half the difference of the intercepted arcs.
In other words, The angle formed outside of the circle is always equal to the the far arc minus the near arc divided by 2.
Using Angle = (Far Arc - Near Arc) /2
So, x= (130- 50)/2
x = 80/2
x= 40
Thus, the value of x is 40 degree.
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please help! thank uu ~ :)
Answers
Answer:
d. Certain
Andres will always roll a number greater than or equal to 1 since 1 is the lowest number on the die. Therefore, the probability of rolling a number greater than or equal to 1 is certain.
50 Points! Multiple choice algebra question. Photo attached. Thank you!
Answers
Answer:
C
Step-by-step explanation:
using the sine ratio in the right triangle
sin P = [tex]\frac{opposite}{hypotenuse}[/tex] = [tex]\frac{QR}{PQ}[/tex] = [tex]\frac{12}{13}[/tex] , then
∠ P = [tex]sin^{-1}[/tex] ( [tex]\frac{12}{13}[/tex] ) ≈ 67° ( to the nearest degree )
nathan makes $10 an hour delivering pizzas and $5 an hour babysitting his sister. he wants to make atleast $40, and his mom said he has to work for less than six hours a week. put this into a system of inequalities equation
Answers
Step-by-step explanation:
Let's denote the number of hours Nathan works delivering pizzas as "x" and the number of hours he works babysitting as "y." We can set up the following system of inequalities:
Nathan's total earnings should be at least $40:
10x + 5y ≥ 40
Nathan's total working hours should be less than six hours a week:
x + y < 6
These two inequalities represent the given conditions that Nathan wants to make at least $40 and work for less than six hours a week.
8. A car traveling down the highway moves at a speed of 68 mph going 15
degrees South of East. How far is the car moving in the Southern and
Eastern direction?
Answers
Answer:
The car is moving 15 degrees South of East. This means that it is moving in a direction that is 75 degrees from the positive x-axis.
The velocity vector of the car can be broken down into its components in the x and y directions as follows:
vx = v * cos(theta) = 68 * cos(75) = 17.3 mph
vy = v * sin(theta) = 68 * sin(75) = 66.3 mph
where
v = 68 mph (magnitude of velocity)
theta = 75 degrees (angle of velocity vector with respect to the positive x-axis)
Therefore, the car is moving 17.3 mph in the Eastern direction and 66.3 mph in the Southern direction.
Fine the coordinates of the hole
Answers
The coordinates of the hole of the rational function are (-3, -3).
How to find the coordinates of the hole?Here we have the following rational function:
[tex]f(x) = \frac{x^2 + 3x}{x + 3}[/tex]
The hole is when the denominator becomes zero, that is at x = -3
Now, we can rewrite the numerator as:
x² + 3x = x*(x + 3)
Then we can rewrite the function as:
[tex]f(x) = \frac{x^2 + 3x}{x + 3} = \frac{x*(x + 3)}{x + 3} = x[/tex]
Evaluating that in x = -3 we get f(x) = -3, then the coordinates of the hole aer (-3, -3).
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Problema 1
En una calculadora se tecleó 35 X 100, pero se
cometió un error ya que se quería multiplicar
por 50. ¿Cómo se corrige sin borrar lo que ya
está?
Answers
The way to correct the entry on the calculator without deleting what is already there is by multiplying by 2.
Why would this correct the entry ?Consider the scenario at hand, where an inadvertent error was committed during a calculator operation. The initial intention was to multiply by 100, yet the input mistakenly resulted in a multiplication by 50.
Seeing as this is multiplication, and the number that was to be multiplied is larger than the number given, you can find the quotient of the larger number from the smaller number to be :
= 100 / 50
= 2
Then multiply the entry by 2 as this would then lead to the correct result of 3, 500.
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The data set below represents the number of books checked out at the library each day. 21, 12, 15, 17, 6, 3, 19 Choose the correct answer from each drop-down menu to complete the statements. The range is books checked out. The median is books checked out.
Answers
The median and the range for the data-set are given as follows:
Median of 15 books checked out.Range of 18 books checked out.How to obtain the median and the range of a data-set?The median of a data-set is the middle value of a data-set, the value of which 50% of the measures are less than and 50% of the measures are greater than. Hence, the median also represents the 50th percentile of a data-set.
The ordered data-set is given as follows:
3, 6, 12, 15, 17, 19, 21.
The middle value is of 15, hence it represents the median of the data-set.
The range of a data-set is defined as the difference between the largest and the smallest value in the data-set, hence:
21 - 3 = 18.
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2. Janice polled her friends on social media and asked them to rate four flavors of ice cream (C= (1 point)
chocolate, V = vanilla, S = strawberry, P=pistachio). The preference schedule created from
their replies is shown. In order to be the majority winner, how many votes would an ice cream
need to accumulate?
number of votes 3 5 7 9
1st
2nd
3rd
4th
SSCV
CVVC
VPSS
PCPP
O An ice cream would need more than 12 votes from anywhere in the preference schedule.
O An ice cream would need 12 votes from anywhere in the preference schedule.
O An ice cream would need more than 12 votes from the first-place line in the preference schedule.
O An ice cream would need 12 votes from the first-place line in the preference schedule.
Answers
The correct statement would be: An ice cream would need more than 9 votes from the first-place line in the preference schedule.
To determine the number of votes an ice cream would need to accumulate in order to be the majority winner, we should analyze the preference schedule provided.
Looking at the preference schedule, we can see that there are four ice cream flavors:
Chocolate (C), vanilla (V), strawberry (S), and pistachio (P).
Each row represents the rankings given by Janice's friends.
To be the majority winner, an ice cream flavor would need to accumulate more votes than any other flavor.
In this case, we can determine the highest number of votes an ice cream flavor can receive by considering the first-place line in the preference schedule.
From the first-place line, we can see that the maximum number of votes any flavor has received is 9.
Therefore, an ice cream flavor would need more than 9 votes from the first-place line to be the majority winner.
Based on the given options, the correct statement would be: An ice cream would need more than 9 votes from the first-place line in the preference schedule.
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Help me find x in this circle
Answers
The value of x in the circle is 180° - 85° = 95°. The Cyclic Quadrilateral Theorem states that the sum of any opposite angle pair within a cyclic quadrilateral is additional,
Given
Angle = 85°
Required to find the opposite angle to 85° which is x
x = 180° - 85°
x= 95°
Thus, the quadrilateral is inscribed in a circle. Due to the shape being a quadrilateral, it is presumed that the angle in the middle is supplementary and adds up to 180° 180° 180°. The opposing angles in a quadrilateral are presumed to be equal since angles in the same segment are equal.
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Help me pleaseee
create a rubric or criteria for grading that you assign to students
Answers
When creating a rubric or criteria for grading students, it is important to establish clear expectations and criteria that align with the learning objectives of the assignment or task. Here is a suggested rubric format:
1. Content Knowledge: Assess the depth and accuracy of the student's understanding of the subject matter.
2. Organization and Structure: Evaluate the clarity and logical flow of the student's work, including the use of headings, subheadings, and transitions.
3. Research and Evidence: Consider the quality and relevance of sources used, as well as the integration of evidence to support arguments or claims.
4. Critical Thinking: Assess the student's ability to analyze, evaluate, and synthesize information, demonstrating higher-order thinking skills.
5. Writing Mechanics: Evaluate the student's grammar, spelling, punctuation, and overall writing style.
6. Creativity and Originality: Acknowledge unique or innovative ideas, approaches, or perspectives.
7. Presentation (if applicable): Assess the student's ability to effectively present their work, including visual aids, organization, and delivery.
Each criterion should have specific descriptors or levels of achievement (e.g., Excellent, Good, Fair, Poor) that clearly communicate expectations. It is also helpful to assign weights to each criterion to reflect their relative importance.
Providing detailed feedback and examples can further enhance the usefulness of the rubric for students' understanding and improvement.
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Solve this quiestion
Answers
The chord in this circle is RS while the radius of the circle is QT. If the diameter of the circle is 28 cm, then the radius will be 14 cm.
What is the chord of a circle?The chord of a circle refers to the line that connects two parts of the circle. In the diagram provided, points RS represent the chord of the circle. Also, the diameter of a circle are the points that run between two segemnts of the circle's center.
In this circle these are points GP. The radius is gotten by dividing the diameter by 2, so the radius of the given diameter is 28/2 = 14.
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Please answer this question
Answers
Answer:
$40.00 is the answer
Step-by-step explanation:
also can you mark me as a brainlist if you get a chance
Answer: $40.00
Step-by-step explanation:
12 is 30% of 40
6 12 15 60 65
What is the next number in the sequence?
Answers
Answer:
123
Step-by-step explanation:
Add 6 to the first number to get the second number.
Add 3 to the second number to get the third number.
Multiply the third number by 4 to get the fourth number.
Add 5 to the fourth number to get the fifth number.
Using this pattern, we can find the next number in the sequence by following the same rule:
Multiply the fifth number by 2 and then subtract 7 to get the next number.
So, the next number in the sequence is:
65 x 2 - 7 = 123
II. Record in a university shows that 60% of students here get a job within 2 months after graduation. Past records indicate that for students in the school who get a job within 2 months after graduation, 70% gets scholarship at least one time during university. For those who can not get a job within 2 months, 25% get at least one university scholarship. Randomly select 1 student. Answer the following question:
a. What is the probability that the selected student does not get a scholarship, given that he cannot
get a job within 2 months after graduation?
b. What is the probability that the selected student gets no university scholarship?
Answers
To answer the given questions, let's use conditional probability based on the information provided:
a. To find the probability that the selected student does not get a scholarship, given that they cannot get a job within 2 months after graduation, we can use Bayes' theorem. Let's denote the events as follows:
A: Not getting a scholarship
B: Not getting a job within 2 months after graduation
We want to find P(A|B), which is the probability of not getting a scholarship given that the student cannot get a job within 2 months. According to the given information, 25% of students who cannot get a job within 2 months get at least one university scholarship.
Using Bayes' theorem:
P(A|B) = (P(B|A) * P(A)) / P(B)
P(B|A) is the probability of not getting a job within 2 months given that the student does not get a scholarship. Since this information is not provided, we cannot determine this probability.
b. To find the probability that the selected student gets no university scholarship, we can use the law of total probability. Let's denote the events as follows:
A: Not getting a scholarship
B: Getting a job within 2 months after graduation
C: Not getting a job within 2 months after graduation
We want to find P(A), the probability of not getting a university scholarship. According to the given information, 60% of students get a job within 2 months after graduation, and among those students, 70% get at least one university scholarship. For students who cannot get a job within 2 months, 25% get at least one university scholarship.
Using the law of total probability:
P(A) = P(A|B) * P(B) + P(A|C) * P(C)
We don't have the values for P(A|B) or P(B) and P(A|C) or P(C), so we cannot calculate the exact probability of not getting a university scholarship.
Therefore, without additional information or values for conditional probabilities, we cannot provide specific numerical answers to these questions.
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Six packs of cola are on sale for $1.50. If a customer buys a 24 pack
Answers
First, we need to figure out how many sets of six packs are in a 24 pack.
24 ÷ 6 = 4
There are 4 sets of six packs in a 24 pack.
Next, we multiply the cost of one set of six packs by 4.
$1.50 x 4 = $6
Therefore, it would cost $6 for a customer to buy a 24 pack of cola on sale.
A line passes through the points (−1, −2) and (3, 3). Find its x- and y-intercepts.
Answers
3/5 and -3/4 are the x and y-intercept of the line respectively
Determining the equation of a line'Given the coordinate points (−1, −2) and (3, 3), we need to determine the x and y-intercept
The equation of a line in slope intercept form is y = mx + b where:
m is the slope
b is the intercept
For the slope:
slope = 3-(-2)/3-(-1)
Slope = 5/4
For the y- intercept
3 = 5/4(3) + b
3 = 15/4 + b
b = 3 - 15/4
b = -3/4
Hence the equation of the line is. y = 5/4 x - 3/4
For the x-intercept
The x-intercept is the point where y = 0
0 = 5/4 x - 3/4
5/4 x = 3/4
5x = 3
x = 3/5
Hence the x- and y-intercepts of the line are 3/5 and -3/4 respectively.
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Use the data to answer questions 1-8.
8-iron, distance to hole (vards) 20 12 12 8 6 11 7 7 10 12 8 10 11 20
1) Organize the data from least to greatest.
6,7,7,8,8,10,10,11,11,12,12,12,20,20
2) Use the data to create a histogram.
Frequency
5 10 15 20 25 30
Distance to Hole (yds)
3) What is the mean (average) of the data? Round your answer to the nearest tenth.
4) Make a box plot of the data.
5 10 15 20 25 30
Distance to Hole (yds)
5) What is the median of the data?
6) What is the First Quartile(Q1)?
7) What is the Third Quartile(Q3)?
CODIO
Can somebody help with the whole thing?? All besides number 1
Answers
3) To find the mean (average) of the data, add up all the values and divide by the total number of values. Using the data provided, the sum of all the values is 141, and there are 14 values. Therefore, the mean is 141/14 = 10.1 (rounded to the nearest tenth).
4) To create a box plot of the data, we need to determine the minimum, maximum, median, first quartile (Q1), and third quartile (Q3).
Minimum: 6
Maximum: 20
Median: The median is the middle value when the data is arranged in ascending order. In this case, we have an even number of values, so we take the average of the two middle values. The two middle values are 10 and 11, so the median is (10 + 11)/2 = 10.5.
Q1 (First Quartile): The first quartile is the median of the lower half of the data. Since we have 14 values, the lower half consists of the first 7 values when arranged in ascending order. The values are 6, 7, 7, 8, 8, 10, and 10. The median of these values is (7 + 8)/2 = 7.5.
Q3 (Third Quartile): The third quartile is the median of the upper half of the data. Again, we have 14 values, so the upper half consists of the last 7 values when arranged in ascending order. The values are 10, 11, 11, 12, 12, 12, and 20. The median of these values is (11 + 12)/2 = 11.5.
Now, we can construct the box plot:
| (6) |
|_______|________|
(7.5) (10.1) (11.5)
The line in the middle represents the median (10.1), the left boundary represents Q1 (7.5), and the right boundary represents Q3 (11.5). The whiskers extend from the box to the minimum (6) and maximum (20) values.
5) The median of the data is 10.5.
6) The First Quartile (Q1) is 7.5.
7) The Third Quartile (Q3) is 11.5.
I hope this helps! Let me know if you have any further questions.
In AOPQ, 0 = 180 cm, p = 280 cm and ZQ=84°. Find the area of AOPQ, to the
nearest square centimeter.
Answers
The area of the triangle is 25061.6 cm²
What is area of triangle?A triangle is a closed, 2-dimensional shape with 3 sides, 3 angles, and 3 vertices. A triangle is also a polygon.
The area of a triangle is expressed as;
A = 1/2bh where b is the base a d h is the height. This formula only works for right angled triangle.
Another formula for area of triangle is 1/2 absinC
a = 180cm
b = 280cm
C = 84°
A = 1/2 × 180 × 280 × sin84
A = 50123.9/2
A = 25061.6 cm²
Therefore the area of triangle OPQ is 25061.6 cm².
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Do you know Squidward? According to a survey by Nickelodeon TV, 82% of children under 13 in Germany recognized a picture of the cartoon character SpongeBob SquarePants. Assume that among those children, 83% also recognized SpongeBob's cranky neighbor Squidward Tentacles. What is the probability that a German child recognized both SpongeBob and Squidward? Write your answer as a fraction or a decimal, rounded to four decimal places.
Answers
P(A and B) = P(A) * P(B | A)
where A and B are events, P(A) is the probability of event A, and P(B | A) is the probability of event B given that event A has occurred.
Let A be the event that a child recognized SpongeBob, and let B be the event that a child recognized Squidward. Then:
P(A) = 0.82 (given)
P(B | A) = 0.83 (given)
So the probability that a German child recognized both SpongeBob and Squidward is:
P(A and B) = P(A) * P(B | A) = 0.82 * 0.83 = 0.6806
Rounding to four decimal places, the probability is 0.6806, or approximately 0.681 as a decimal or 681/1000 as a fraction. Therefore, the probability that a German child recognized both SpongeBob and Squidward is about 0.681.
Luna has 8 pints of juice. Michael has 2% times as many
pints of juice as Luna.a) How many pints of juice does Michael have?b) How many more pints of juice does Michael have than
Luna?Give your answers as whole numbers or as fractions in their simplest form.
Answers
b) Michael has 8 - 0.16 = 7.84 less pints of juice than Luna. Alternatively, Michael has 0.16 more pints of juice than Luna.
Answer: 0.16
Step-by-step explanation:
A plug is removed from a trough to drain the water. The volume, in gallons, in the trough after it has been unplugged can be modeled by the expression 10x2 − 11x + 3, where x is the time in minutes. Choose the appropriate form of the expression that would reveal the time, in minutes, when the trough is empty. (1 point)
10(0)2 − 11(0) + 3
(5x − 3)(2x − 1)
10(x − 3)2 − 1
10(x − 1)2 − 3
Answers
When A plug is removed from a trough to drain the water, The appropriate form of the expression is 10(x - 1)² - 3. Option D
How to determine the appropriate form of expressionThe appropriate form of the expression that would reveal the time, in minutes, when the trough is empty is: 10(x - 1)² - 3.
This expression represents the volume of the trough after the plug is removed, with x representing the time in minutes. When the volume of the trough is equal to zero, it means the trough is empty.
Therefore, setting the expression equal to zero and solving for x will give us the time when the trough is empty.
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Estimate 94.44 + 65.392 by first rounding each number to the nearest whole number.
Answers
5-9 rounds up to the next whole number
94.44 rounds to 94
65.392 rounds to 65
94+65=159
ANSWER: 159
A 25-year-old woman burns 550t cal/hr while walking on her treadmill. How many calories are
burned after walking for 3 hours?
Answers
Answer:
1650 calories
Step-by-step explanation:
You want to know how many calories are burned in 3 hours of walking if 550 calories are burned each hour of walking.
TotalThe total number of calories burned is the product of the number burned per hour and the number of hours:
(550 cal/h)·(3 h) = 550·3 cal = 1650 cal
The woman burned 1650 calories after walking 3 hours.
__
Additional comment
As with most rate problems, the quantity is the product of the rate and the time.
<95141404393>
Factor the polynomial.
2x²10x + 12 =
Answers
Answer: 2(x+3)(x+2)
Step-by-step explanation:
68 65 62 72 70 79 66 72 68 63 70 68 MeanMedianMode(s)Range
Answers
The mean, median, mode and range of the data are 68.58, 68, 68 and 17 respectively.
What are measures of central tendency?A measure of central tendency is a single value that attempts to describe a set of data by identifying the central position within that set of data.
1. The mean of the data is;
mean = 62 + 63 + 65 + 66 + 68 + 68 + 68 + 70 + 70 + 72 + 72 + 79 / 12
mean = 68.58
2. The median of the data = 68
3. The mode of the data = 68
4. The range of the data = 17
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