To find the mean, we sum up all the weights and then divide by the number of cats, which is 8.
Sum of the weights = 13 + 13 + 6 + 14 + 5 + 12 + 16 + 14 = 93
Mean weight = 93/8 ≈ 11.6 pounds
To find the median, we list the weights in increasing order:
5, 6, 12, 13, 13, 14, 14, 16
Since there are 8 weights, the middle two weights are 13 and 14. Therefore, the median weight is the average of these two numbers.
Median weight = (13 + 14)/2 = 27/2 = 13.5 pounds
Therefore, the mean weight is approximately 11.6 pounds and the median weight is 13.5 pounds.
Each of the 8 cats in a pet store was weighed (in pounds).
13, 13, 6, 14, 5, 12, 16, 14
Find the mean and median weights of these cats.
If necessary, round your answers to the nearest tenth.
38 answers
Answer the questions below. Write your answers in simplest form.
(a) A square has an area of 49cm^2. What is the length of each side?
(b) A square has the perimeter of 20m. What is the length of each side?
(a) A square has an area of 49cm^2. What is the length of each side?
(b) A square has the perimeter of 20m. What is the length of each side?
(a) To find the length of each side of a square with an area of 49cm^2, we need to find the square root of the area.
√49 = 7
Therefore, the length of each side is 7cm.
(b) To find the length of each side of a square with a perimeter of 20m, we divide the perimeter by 4 (since all sides of a square are equal).
20 / 4 = 5
Therefore, the length of each side is 5m.
√49 = 7
Therefore, the length of each side is 7cm.
(b) To find the length of each side of a square with a perimeter of 20m, we divide the perimeter by 4 (since all sides of a square are equal).
20 / 4 = 5
Therefore, the length of each side is 5m.
Two parallel lines are cut by a transversal as shown below. Suppose m angle 4 = 76 degrees
Find m angle 6 and m angle 7
Find m angle 6 and m angle 7
As the image is not provided, I cannot see the specific positions of angles 4, 6, and 7. However, I can provide you with the general relationships between angles formed by parallel lines cut by a transversal.
When two parallel lines are cut by a transversal, the corresponding angles are equal. If angle 4 is 76 degrees, then angle 6, which is the corresponding angle to angle 4, must also be 76 degrees.
Additionally, the alternate interior angles are congruent. So, if angle 4 is 76 degrees, then angle 7, which is the alternate interior angle to angle 4, must also be 76 degrees.
Therefore, m angle 6 = m angle 7 = 76 degrees.
When two parallel lines are cut by a transversal, the corresponding angles are equal. If angle 4 is 76 degrees, then angle 6, which is the corresponding angle to angle 4, must also be 76 degrees.
Additionally, the alternate interior angles are congruent. So, if angle 4 is 76 degrees, then angle 7, which is the alternate interior angle to angle 4, must also be 76 degrees.
Therefore, m angle 6 = m angle 7 = 76 degrees.
What does it mean when angles are corresponding
When angles are corresponding, it means that they are in the same relative position at different intersections created by a transversal line crossing two parallel lines.
Specifically, when two parallel lines are intersected by a transversal line, corresponding angles are formed on the same side of the transversal and in the same relative position at each intersection. That is, if there is a pair of corresponding angles at one intersection, then there will be another pair of corresponding angles at a different intersection.
Corresponding angles are congruent, meaning that they have the same measure or angle size. This property is a result of the parallel lines and transversal creating equal angles at each intersection.
Specifically, when two parallel lines are intersected by a transversal line, corresponding angles are formed on the same side of the transversal and in the same relative position at each intersection. That is, if there is a pair of corresponding angles at one intersection, then there will be another pair of corresponding angles at a different intersection.
Corresponding angles are congruent, meaning that they have the same measure or angle size. This property is a result of the parallel lines and transversal creating equal angles at each intersection.
Do all the angles from the previous problem equal 76 degrees?
Apologies for the confusion. In the previous problem, we only know that angle 4 is 76 degrees. Without more information or a diagram, we cannot determine the exact measures for angles 6 and 7.
If you can provide more details or a diagram, I would be happy to help you determine the measures of angles 6 and 7.
If you can provide more details or a diagram, I would be happy to help you determine the measures of angles 6 and 7.
Solve for y.
2(3y+8)=70
Simplify your answer as much as possible.
2(3y+8)=70
Simplify your answer as much as possible.
To solve for y in the equation 2(3y+8) = 70, we will use the distributive property to eliminate the parentheses and then solve for y.
First, distribute the 2 to both terms inside the parentheses:
6y + 16 = 70
Next, subtract 16 from both sides to isolate the variable terms:
6y = 70 - 16
6y = 54
Finally, divide both sides of the equation by 6 to solve for y:
y = 54/6
y = 9
Therefore, the solution to the equation 2(3y+8) = 70 is y = 9.
First, distribute the 2 to both terms inside the parentheses:
6y + 16 = 70
Next, subtract 16 from both sides to isolate the variable terms:
6y = 70 - 16
6y = 54
Finally, divide both sides of the equation by 6 to solve for y:
y = 54/6
y = 9
Therefore, the solution to the equation 2(3y+8) = 70 is y = 9.
Approximate 95 (to the square root) as a decimal to the hundredths place. Note that your answer must be within a hundredth of the actual value.
To approximate the square root of 95 as a decimal to the hundredths place, we can use a calculator or estimation method.
Using a calculator, the square root of 95 is approximately 9.747
Rounding to the hundredths place, we get 9.75.
Therefore, the approximation of the square root of 95 to the hundredths place is 9.75.
Using a calculator, the square root of 95 is approximately 9.747
Rounding to the hundredths place, we get 9.75.
Therefore, the approximation of the square root of 95 to the hundredths place is 9.75.
I have a problem where I have to find x which is an amount of degrees for the angle of a triangle and I’m only given the left corner angle which is 92 degrees and a line that goes past the triangle labeled 142 degrees. How do I solve this problem?
To solve this problem, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
Let's denote the left corner angle of the triangle as x. We are also given a line that goes past the triangle, which forms a straight line with the left corner angle. This line forms a straight angle, which measures 180 degrees.
From this information, we can set up the equation:
x + 92 + 180 = 180
x + 92 + 180 = 360 (since the sum of the angles in a triangle is 180 degrees)
Next, we can simplify the equation:
x + 272 = 360
Now, we can isolate the variable x by subtracting 272 from both sides of the equation:
x = 360 - 272
x = 88
Therefore, the angle of the triangle opposite the left corner angle (which is 92 degrees) is 88 degrees.
Let's denote the left corner angle of the triangle as x. We are also given a line that goes past the triangle, which forms a straight line with the left corner angle. This line forms a straight angle, which measures 180 degrees.
From this information, we can set up the equation:
x + 92 + 180 = 180
x + 92 + 180 = 360 (since the sum of the angles in a triangle is 180 degrees)
Next, we can simplify the equation:
x + 272 = 360
Now, we can isolate the variable x by subtracting 272 from both sides of the equation:
x = 360 - 272
x = 88
Therefore, the angle of the triangle opposite the left corner angle (which is 92 degrees) is 88 degrees.
I have a problem where I have to find x which is an amount of degrees for the angle of a triangle and I’m only given the left corner angle which is 92 degrees and a line that goes past the right corner of the triangle triangle labeled 142 degrees. How do I solve this problem?
To solve this problem, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
Let's denote the left corner angle of the triangle as 92 degrees. We are also given a line that goes past the right corner of the triangle, forming a straight angle. Since a straight angle measures 180 degrees, the sum of the right corner angle and the angle we need to find (x) must equal 180 degrees.
Therefore, we can set up the equation:
92 + x + 142 = 180
Now, we can simplify the equation:
234 + x = 180
Next, we can isolate the variable x by subtracting 234 from both sides of the equation:
x = 180 - 234
x = -54
Therefore, the angle of the triangle opposite the left corner angle (which is 92 degrees) is -54 degrees. However, since angles in a triangle cannot be negative, we can conclude that there must be an error in the problem or the given information. Please double-check the problem, as angles in triangles are always positive.
Let's denote the left corner angle of the triangle as 92 degrees. We are also given a line that goes past the right corner of the triangle, forming a straight angle. Since a straight angle measures 180 degrees, the sum of the right corner angle and the angle we need to find (x) must equal 180 degrees.
Therefore, we can set up the equation:
92 + x + 142 = 180
Now, we can simplify the equation:
234 + x = 180
Next, we can isolate the variable x by subtracting 234 from both sides of the equation:
x = 180 - 234
x = -54
Therefore, the angle of the triangle opposite the left corner angle (which is 92 degrees) is -54 degrees. However, since angles in a triangle cannot be negative, we can conclude that there must be an error in the problem or the given information. Please double-check the problem, as angles in triangles are always positive.
I have a problem where I have to find x which is an amount of degrees for the left top corner angle of a triangle and I’m only given the left corner angle which is 92 degrees and a line that goes past the triangle labeled 142 degrees. How do I solve this problem?
To solve this problem, we can use the fact that the sum of the angles in a triangle is always 180 degrees.
Let's denote the left top corner angle of the triangle as x. We are also given a line that goes past the triangle and forms a straight angle with the left corner angle. A straight angle measures 180 degrees.
Since the left top corner angle and the left corner angle are adjacent and form a straight angle, their sum must equal 180 degrees. So we can set up the equation:
x + 92 = 180
Next, we can solve for x by subtracting 92 from both sides of the equation:
x = 180 - 92
x = 88
Therefore, the left top corner angle of the triangle is 88 degrees.
Let's denote the left top corner angle of the triangle as x. We are also given a line that goes past the triangle and forms a straight angle with the left corner angle. A straight angle measures 180 degrees.
Since the left top corner angle and the left corner angle are adjacent and form a straight angle, their sum must equal 180 degrees. So we can set up the equation:
x + 92 = 180
Next, we can solve for x by subtracting 92 from both sides of the equation:
x = 180 - 92
x = 88
Therefore, the left top corner angle of the triangle is 88 degrees.
How do I find the area of a 2d rectangle and a 2d triangle
To find the area of a 2D rectangle, you multiply the length of one of its sides (length or width) by the length of the other side:
Area of a rectangle = length × width
For example, if a rectangle has a length of 5 units and a width of 3 units, the area would be:
Area = 5 units × 3 units = 15 square units
To find the area of a 2D triangle, you multiply the base of the triangle by the height and divide the result by 2:
Area of a triangle = (base × height) / 2
For example, if a triangle has a base length of 6 units and a height of 4 units, the area would be:
Area = (6 units × 4 units) / 2 = 12 square units
So, the area of the rectangle is 15 square units, and the area of the triangle is 12 square units.
Area of a rectangle = length × width
For example, if a rectangle has a length of 5 units and a width of 3 units, the area would be:
Area = 5 units × 3 units = 15 square units
To find the area of a 2D triangle, you multiply the base of the triangle by the height and divide the result by 2:
Area of a triangle = (base × height) / 2
For example, if a triangle has a base length of 6 units and a height of 4 units, the area would be:
Area = (6 units × 4 units) / 2 = 12 square units
So, the area of the rectangle is 15 square units, and the area of the triangle is 12 square units.
Calculate.
(3x10^9)(1.3x10^8)
(3x10^9)(1.3x10^8)
To calculate the product of (3x10^9)(1.3x10^8), we can multiply the numerical parts together separately from the exponential parts.
(3x10^9)(1.3x10^8) = (3)(1.3) x (10^9)(10^8)
The numerical part gives us:
(3)(1.3) = 3.9
The exponential part gives us:
(10^9)(10^8) = 10^(9+8) = 10^17
Putting it all together, we have:
(3x10^9)(1.3x10^8) = 3.9 x 10^17
Therefore, the product is 3.9 x 10^17.
(3x10^9)(1.3x10^8) = (3)(1.3) x (10^9)(10^8)
The numerical part gives us:
(3)(1.3) = 3.9
The exponential part gives us:
(10^9)(10^8) = 10^(9+8) = 10^17
Putting it all together, we have:
(3x10^9)(1.3x10^8) = 3.9 x 10^17
Therefore, the product is 3.9 x 10^17.
Calculate.
(3x10^9)(1.3x10^8)
Write your answer in scientific notation.
(3x10^9)(1.3x10^8)
Write your answer in scientific notation.
To multiply numbers in scientific notation, we can multiply the coefficients and add the exponents.
The coefficient multiplication gives us: (3)(1.3) = 3.9
The exponent addition gives us: 10^(9 + 8) = 10^17
Putting it all together, we get:
(3x10^9)(1.3x10^8) = 3.9x10^17
Therefore, the answer is 3.9x10^17.
The coefficient multiplication gives us: (3)(1.3) = 3.9
The exponent addition gives us: 10^(9 + 8) = 10^17
Putting it all together, we get:
(3x10^9)(1.3x10^8) = 3.9x10^17
Therefore, the answer is 3.9x10^17.
For each set of three lengths, determine if they can be the side lengths of a triangle or not.
1) 5.3, 11.6, 17.6 Yes / no
2) 8, 14,17 Yes / no
3) 8, 6, 6 Yes / no
4) 8, 17, 6 Yes / no
1) 5.3, 11.6, 17.6 Yes / no
2) 8, 14,17 Yes / no
3) 8, 6, 6 Yes / no
4) 8, 17, 6 Yes / no
To determine if a set of three lengths can be the side lengths of a triangle, we need to check if the sum of the two smaller lengths is greater than the longest length.
1) The lengths are 5.3, 11.6, and 17.6. We need to check if 5.3 + 11.6 > 17.6.
Calculating: 5.3 + 11.6 = 16.9 which is less than 17.6.
Therefore, the lengths 5.3, 11.6, and 17.6 cannot be the side lengths of a triangle. The answer is "No".
2) The lengths are 8, 14, and 17. We need to check if 8 + 14 > 17.
Calculating: 8 + 14 = 22 which is greater than 17.
Therefore, the lengths 8, 14, and 17 can be the side lengths of a triangle. The answer is "Yes".
3) The lengths are 8, 6, and 6. We need to check if 6 + 6 > 8.
Calculating: 6 + 6 = 12 which is greater than 8.
Therefore, the lengths 8, 6, and 6 can be the side lengths of a triangle. The answer is "Yes".
4) The lengths are 8, 17, and 6. We need to check if 6 + 8 > 17.
Calculating: 6 + 8 = 14 which is less than 17.
Therefore, the lengths 8, 17, and 6 cannot be the side lengths of a triangle. The answer is "No".
1) The lengths are 5.3, 11.6, and 17.6. We need to check if 5.3 + 11.6 > 17.6.
Calculating: 5.3 + 11.6 = 16.9 which is less than 17.6.
Therefore, the lengths 5.3, 11.6, and 17.6 cannot be the side lengths of a triangle. The answer is "No".
2) The lengths are 8, 14, and 17. We need to check if 8 + 14 > 17.
Calculating: 8 + 14 = 22 which is greater than 17.
Therefore, the lengths 8, 14, and 17 can be the side lengths of a triangle. The answer is "Yes".
3) The lengths are 8, 6, and 6. We need to check if 6 + 6 > 8.
Calculating: 6 + 6 = 12 which is greater than 8.
Therefore, the lengths 8, 6, and 6 can be the side lengths of a triangle. The answer is "Yes".
4) The lengths are 8, 17, and 6. We need to check if 6 + 8 > 17.
Calculating: 6 + 8 = 14 which is less than 17.
Therefore, the lengths 8, 17, and 6 cannot be the side lengths of a triangle. The answer is "No".
Rewrite using a single positive exponent.
9^5/9^3
9^5/9^3
When dividing two numbers with the same base but different exponents, we subtract the exponent in the denominator from the exponent in the numerator.
Therefore, we can rewrite 9^5/9^3 as 9^(5-3):
9^5 ÷ 9^3 = 9^(5-3) = 9^2
Therefore, 9^5/9^3 can be written as 9^2.
Therefore, we can rewrite 9^5/9^3 as 9^(5-3):
9^5 ÷ 9^3 = 9^(5-3) = 9^2
Therefore, 9^5/9^3 can be written as 9^2.
How do I reflect a point over the x-axis and then reflect that point over the y-axis
To reflect a point over the x-axis, we simply change the sign of the y-coordinate while keeping the x-coordinate the same.
Let's say we have a point with coordinates (a, b).
When we reflect this point over the x-axis, we change the sign of the y-coordinate, so the new coordinates become (a, -b).
To reflect this new point over the y-axis, we change the sign of the x-coordinate, while the y-coordinate remains the same.
Therefore, the coordinates of the final reflected point would be (-a, -b).
To summarize the process:
- Reflect the original point over the x-axis: (a, b) → (a, -b)
- Reflect the new point over the y-axis: (a, -b) → (-a, -b)
Let's say we have a point with coordinates (a, b).
When we reflect this point over the x-axis, we change the sign of the y-coordinate, so the new coordinates become (a, -b).
To reflect this new point over the y-axis, we change the sign of the x-coordinate, while the y-coordinate remains the same.
Therefore, the coordinates of the final reflected point would be (-a, -b).
To summarize the process:
- Reflect the original point over the x-axis: (a, b) → (a, -b)
- Reflect the new point over the y-axis: (a, -b) → (-a, -b)
Which are the each quartile labels for graphing charts e.g quartile II
When it comes to graphing charts and data, the quartile labels are commonly referred to as Q1, Q2, Q3, and Q4. Also known as the first quartile, second quartile, third quartile, and fourth quartile, respectively.
More specifically:
- Q1 represents the lower quartile or the 25th percentile.
- Q2 represents the median or the 50th percentile.
- Q3 represents the upper quartile or the 75th percentile.
- Q4 represents the maximum or the highest value in the dataset.
These quartile labels are often used in box plots or box-and-whisker plots to show the distribution of data and provide information about the range and spread of the values.
More specifically:
- Q1 represents the lower quartile or the 25th percentile.
- Q2 represents the median or the 50th percentile.
- Q3 represents the upper quartile or the 75th percentile.
- Q4 represents the maximum or the highest value in the dataset.
These quartile labels are often used in box plots or box-and-whisker plots to show the distribution of data and provide information about the range and spread of the values.
In a chart that holds points and line segments ect what are each of the four boxes called
In a chart that holds points, line segments, and other elements, the four boxes typically correspond to the four quadrants of a coordinate plane. Each quadrant is named depending on the signs of the x and y coordinates within that quadrant.
1. The first quadrant, located in the upper right, is where both the x and y coordinates are positive.
2. The second quadrant, located in the upper left, is where the x coordinate is negative and the y coordinate is positive.
3. The third quadrant, located in the lower left, is where both the x and y coordinates are negative.
4. The fourth quadrant, located in the lower right, is where the x coordinate is positive and the y coordinate is negative.
These quadrants are labeled as follows:
1. First Quadrant (or Q1)
2. Second Quadrant (or Q2)
3. Third Quadrant (or Q3)
4. Fourth Quadrant (or Q4)
These labels are used to identify the specific region of the coordinate plane where the points, line segments, or other elements are plotted.
1. The first quadrant, located in the upper right, is where both the x and y coordinates are positive.
2. The second quadrant, located in the upper left, is where the x coordinate is negative and the y coordinate is positive.
3. The third quadrant, located in the lower left, is where both the x and y coordinates are negative.
4. The fourth quadrant, located in the lower right, is where the x coordinate is positive and the y coordinate is negative.
These quadrants are labeled as follows:
1. First Quadrant (or Q1)
2. Second Quadrant (or Q2)
3. Third Quadrant (or Q3)
4. Fourth Quadrant (or Q4)
These labels are used to identify the specific region of the coordinate plane where the points, line segments, or other elements are plotted.
Keeping in mind of this: 1. The first quadrant, located in the upper right, is where both the x and y coordinates are positive.
2. The second quadrant, located in the upper left, is where the x coordinate is negative and the y coordinate is positive.
3. The third quadrant, located in the lower left, is where both the x and y coordinates are negative.
4. The fourth quadrant, located in the lower right, is where the x coordinate is positive and the y coordinate is negative.
How do I reflect a point in the fourth quadrant over the x-axis and then reflect that point over the y-axis
2. The second quadrant, located in the upper left, is where the x coordinate is negative and the y coordinate is positive.
3. The third quadrant, located in the lower left, is where both the x and y coordinates are negative.
4. The fourth quadrant, located in the lower right, is where the x coordinate is positive and the y coordinate is negative.
How do I reflect a point in the fourth quadrant over the x-axis and then reflect that point over the y-axis
If we have a point located in the fourth quadrant and we want to reflect it over the x-axis, we keep the x-coordinate the same and change the sign of the y-coordinate.
For example, let's say we have a point (3, -4) in the fourth quadrant.
To reflect this point over the x-axis, we keep the x-coordinate as 3 and change the sign of the y-coordinate to positive:
Reflected over x-axis: (3, -4) → (3, 4)
Now, if we want to reflect this newly obtained point (3, 4) over the y-axis, we change the sign of the x-coordinate while keeping the y-coordinate the same.
Reflected over y-axis: (3, 4) → (-3, 4)
Therefore, the final reflected point, after reflecting a point in the fourth quadrant over the x-axis and then reflecting it over the y-axis, would be (-3, 4).
For example, let's say we have a point (3, -4) in the fourth quadrant.
To reflect this point over the x-axis, we keep the x-coordinate as 3 and change the sign of the y-coordinate to positive:
Reflected over x-axis: (3, -4) → (3, 4)
Now, if we want to reflect this newly obtained point (3, 4) over the y-axis, we change the sign of the x-coordinate while keeping the y-coordinate the same.
Reflected over y-axis: (3, 4) → (-3, 4)
Therefore, the final reflected point, after reflecting a point in the fourth quadrant over the x-axis and then reflecting it over the y-axis, would be (-3, 4).
Be able to take her dream vacation, Isabel decides to stay for two years. She opens a savings account with $500. The account pays simple interest Addyson annual rate of 3%. She doesn’t make any more deposits. Answer the following questions. If necessary refer to the list of financial formulas.
A. How much total interest will Isabelle earn?
B. What will the total amount in the account be (including interest)?
A. How much total interest will Isabelle earn?
B. What will the total amount in the account be (including interest)?