To find the force, F, needed to move a piano given the amount of work applied, W, and distance moved, d, we can use the equation W = Fd.
Rearranging the equation, we can solve for F by dividing both sides of the equation by d.
The equation W = Fd represents the relationship between work (W), force (F), and distance (d).
In this case, we are given the values of W and d and need to find F.
To isolate F, we can rearrange the equation as F = W/d.
By dividing the work (W) by the distance (d), we obtain the force (F) required to move the piano. The unit of force is typically measured in newtons (N), work in joules (J), and distance in meters (m).
It's important to note that this equation assumes a linear motion, where the force applied remains constant throughout the displacement of the piano. In practical situations, however, additional factors such as friction and the piano's weight distribution may affect the force required to move it.
Learn more about equations:
https://brainly.com/question/32634451
#SPJ11
The two-way table shows poll results for the number of athletes and nonathletes who take the stairs or the elevator at work. Of the people polled, how many take the elevator? Enter your answer in the box. People Stairs Elevator Athletes 10 3 Nonathletes 7 16.
The total number of people who take the elevator is 19.
Based on the given two-way table, the number of people who take the elevator is found in the "Elevator" column, which includes both athletes and non-athletes.
Looking at the "Elevator" column, we can see that the number of athletes who take the elevator is 3, and the number of non-athletes who take the elevator is 16.
To find the total number of people who take the elevator, we add the number of athletes and non-athletes who take the elevator:
3 (athletes) + 16 (non-athletes) = 19
To learn more about elevator visit;
https://brainly.com/question/2076153
#SPJ11
How do I know if the cost in dollars and the amount of something is proportional
To know if the cost in dollars and the amount of something is proportional, you need to find the unit rate for both. Here are the steps to find out Step 1: Write the given cost and amount as a ratio. For example, if the cost of 2 pounds of apples is $4.
Simplify the ratio by dividing both the cost and the amount by a common factor. For example, if you divide both the cost and the amount by 2: $$\frac{\$4}{2 \text{ pounds}} = \frac{\$2}{1 \text{ pound}}$$ Step 3: Compare the unit rates for both the cost and the amount.
If they are equal, then they are proportional. If they are not equal, then they are not proportional. For example, if the cost of 1 pound of apples is $2, write it as: $$\frac{\$2}{1 \text{ pound}}$$Then compare the unit rates: $$\frac{\$2}{1 \text{ pound}} \neq \frac{\$2}{1 \text{ pound}}$$ Since the unit rates are not equal, the cost and the amount are not proportional.
To know more about proportional visit :
https://brainly.com/question/31548894
#SPJ11
Michael and Layla stand 21. 2 meters apart. From Michael’s position, the angle of elevation to the top of the Eiffel Tower is 40°. From Layla’s position, the angle of elevation to the top of the Eiffel Tower is 38. 5°. How many meters high is the Eiffel Tower? Round your answer to the nearest meter
The height of the Eiffel Tower is approximately 290 meters. Michael and Layla are standing 21.2 meters apart, and from their respective positions, The height of the Eiffel Tower is approximately 290 meters.
To explain further, let's consider the triangle formed by the base of the Eiffel Tower, Michael's position, and the top of the tower. In this triangle, the angle of elevation from Michael's position is 40°, and the opposite side is the height of the tower. Similarly, in the triangle formed by the base of the tower, Layla's position, and the top of the tower, the angle of elevation from Layla's position is 38.5°, and the opposite side is also the height of the tower.
Using trigonometric ratios, we can set up the following equations:
For Michael's triangle:
tan(40°) = height of the tower / 21.2
For Layla's triangle:
tan(38.5°) = height of the tower / 21.2
By solving these equations, we find that the height of the Eiffel Tower is approximately 290 meters.
Learn more about triangle here:
https://brainly.com/question/2773823
#SPJ11
Grantsville's governor received 3 times as many votes as Cary's governor. Cary's governor received 790 votes. How many people voted altogether?
The total number of people who voted altogether is 3160.
if cary's governor received 790 votes and grantsville's governor received three times as many votes, we can calculate the total number of votes cast by adding the votes received by both governors.
let's denote the number of votes received by grantsville's governor as g. since grantsville's governor received three times as many votes as cary's governor, we can express this as:
g = 3 * 790
calculating this:
g = 2370
so, grantsville's governor received 2370 votes.
to find the total number of votes, we add the votes received by both governors:
total votes = votes for cary's governor + votes for grantsville's governor
total votes = 790 + 2370
total votes = 3160
Learn more about denote here:
https://brainly.com/question/28911152
#SPJ11
Calculator A What is m/CDJ? (4x) (3x - 8) M Enter your answer in the box.
The expression m/CDJ is equal to (4x)(3x - 8). To simplify the expression m/CDJ, we need to substitute the value of CDJ with its equivalent expression. Based on the given information, CDJ is equal to (3x - 8).
To further simplify the expression, we multiply the numerator m by the factor in the denominator, which is (4x). This gives us (4x)m/(3x - 8). Therefore, m/CDJ can be rewritten as m/(3x - 8). So, the simplified expression for m/CDJ is (4x)(3x - 8). The result is a product of the two factors, 4x and (3x - 8), and it represents the value of m/CDJ.
Learn more about product here: brainly.com/question/26260956
#SPJ11
What number comes next in the sequence of 6 1 8 4 2 7
The next number in the sequence 6, 1, 8, 4, 2, 7 is 3.
To determine the pattern and find the next number in the sequence, we need to observe the given numbers and look for any consistent rule or pattern. Let's examine the given sequence:
6, 1, 8, 4, 2, 7
Upon closer inspection, we can identify a pattern where each number seems to be related to its position in the sequence. Specifically, the first number (6) corresponds to the 1st position, the second number (1) corresponds to the 2nd position, the third number (8) corresponds to the 3rd position, and so on.
By applying this pattern, we can determine that the next number should correspond to the 6th position. Since the sequence follows a repeating pattern with a length of 6, we can cycle back to the beginning. Therefore, the number in the 6th position is 3.
Hence, the next number in the sequence is 3.
To learn more about sequence click here: brainly.com/question/23857849
#SPJ11
Is this statement true or false? p = 2 is a solution to p−5<20 plsssss help it a unit teast t or f
The statement is true. The value p = 2 is a solution to the inequality p - 5 < 20.
To determine if a given value is a solution to an inequality, we substitute that value into the inequality and check if it holds true. In this case, we substitute p = 2 into the inequality p - 5 < 20:
2 - 5 < 20
-3 < 20
Since -3 is indeed less than 20, the inequality holds true when p = 2. Therefore, p = 2 is a valid solution to the inequality p - 5 < 20.
It is important to note that there may be other values of p that also satisfy the inequality. However, the question specifically asks if p = 2 is a solution, and based on the substitution and evaluation, it is true that p = 2 satisfies the inequality.
Learn more about inequality here :
https://brainly.com/question/20383699
#SPJ11
Rosa and Gina launched their rockets at the same time. Gina's rocket flew x seconds. Rosa's rocket flew 2.5 seconds
longer than 1.5 times the number of seconds Gina's rocket flew. Which expression describes how long Rosa's rocket
flew?
To describe how long Rosa's rocket flew, we can use the given information that Rosa's rocket flew 2.5 seconds longer than 1.5 times the number of seconds Gina's rocket flew.
Let's denote the number of seconds Gina's rocket flew as x. According to the information given, Rosa's rocket flew 1.5 times the number of seconds Gina's rocket flew, which is 1.5x. Additionally, Rosa's rocket flew 2.5 seconds longer than that.
Therefore, the expression that describes how long Rosa's rocket flew is:
1.5x + 2.5
So Rosa's rocket flew for 1.5x + 2.5 seconds.
Learn more about rocket problem here:
https://brainly.com/question/29203675
#SPJ11
A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t2 40t 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0. 2 s and 2. 7 s. Which solution can be eliminated and why? The solution –0. 2 s can be eliminated because time cannot be a negative value. The solution –0. 2 s can be eliminated because the pass was not thrown backward. The solution 2. 7 s can be eliminated because the pass was thrown backward. The solution 2. 7 s can be eliminated because a ball cannot be in the air for that long due to gravity.
Based on the fact that time values cannot be negative, the value which can be eliminated is -0.2s. Hence, the correct option is A.
The time values given are -0.2s and 2.7s. Time values cannot be negative. Hence, 2.7s is a more reasonable solution for the value of Time in this scenario.
Also, passes Can be thrown in any direction around the field. Hence, passes could be thrown forward or backward as the case may be.
Therefore, the solution which could be eliminated is -0.2 seconds.
Learn more on motion equation :https://brainly.com/question/27899272
#SPJ4
2.1.5. Mr Mathebula says that more than 60% of the learners achieved above 25 out of 50. Verify whether his statement is correct. Clearly show your calculations. 2.2. (4)
Mr Mathebula says that more than 60% of the learners achieved above 25 out of 50. To verify Mr. Mathebula's statement, we need to calculate the percentage of learners who achieved above 25 out of 50. In this case, 60.1% is not greater than 60%, so Mr. Mathebula's statement would be incorrect.
To verify Mr. Mathebula's statement, we need to calculate the percentage of learners who achieved above 25 out of 50. Let's assume there are a total of 'n' learners in the class.
First, we need to determine the number of learners who scored above 25. Let's denote this as 'x'. Since the statement mentions that more than 60% of the learners achieved above 25, we can assume 'x' to be any number greater than 0.6n.
Now, let's calculate the percentage of learners who achieved above 25 out of 50:
Percentage = (x / n) * 100
Since we want to verify whether Mr. Mathebula's statement is correct, we need to determine if the calculated percentage is greater than 60%.
If we assume that 'x' is the lowest possible value of 0.6n + 1 (to satisfy the "more than 60%" condition), the percentage becomes:
Percentage = ((0.6n + 1) / n) * 100
Simplifying this expression:
Percentage = (0.6 + 1/n) * 100
Now, let's substitute some values for 'n' to see if the percentage is greater than 60%:
If we consider 'n' to be 100, the percentage becomes:
Percentage = (0.6 + 1/100) * 100 = 60.6%
Since 60.6% is greater than 60%, Mr. Mathebula's statement holds true for this scenario.
However, if we consider 'n' to be 1000, the percentage becomes:
Percentage = (0.6 + 1/1000) * 100 = 60.1%
For more such information on: percentage
https://brainly.com/question/24877689
#SPJ8
The runs scored by 10 players in a cricket match are :
26,33,47,108,0,6,73,85,54,18. Find the median of the data.
To find the median of the given data, we need to arrange the data in ascending or descending order.
Then, the median is the middle value of the arranged data.For the given runs scored by 10 players in a cricket match, the arranged data in ascending order is 0, 6, 18, 26, 33, 47, 54, 73, 85, 108.The number of observations is even, so the median is the average of two middle values.The middle values are 33 and 47.The median is, Median = (33 + 47)/2 = 80/2 = 40.Hence, the median of the given data is 40.
Considering the definition of median, the median is 40.
Definition of medianThe median is the middle value of all the data in order from least to greatest. That is, the median divides the entire ordered data set into two equal parts.
The calculation of the median depends on whether the total number of data is even or odd:
If the total number of data items is odd, the median will be the value that is right in the middle of the data.If the total number of data is even, the median will be the mean of the two data that are in the center, that is, the arithmetic mean or average of the two central values of the ordered data.Median of the data in this caseIn this case, the data is:
26,33,47,108,0,6,73,85,54,18
Sorting the data from smallest to largest:
0, 6, 18, 26, 33, 47, 54, 73, 85, 108
The total number of data is even (10 numbers). So the median is calculated as the arithmetic mean or average of the two central values of the ordered data:
Median= (33 +47)÷2
Solving:
Median= 40
Finally, the median is 40.
Learn more about median:
https://brainly.com/question/30759854
#SPJ4
Write down the coordinates of the points where the line 10x ------ 8y = 40 cuts the x- and y-axes
Answer:
Step-by-step explanation:
To find the coordinates of the points where the line 10x - 8y = 40 intersects the x- and y-axes, we can set one of the variables to zero and solve for the other variable.
For the x-intercept (where the line intersects the x-axis), we set y = 0 and solve for x:
10x - 8(0) = 40
10x = 40
x = 40/10
x = 4
Therefore, the x-intercept is (4, 0).
For the y-intercept (where the line intersects the y-axis), we set x = 0 and solve for y:
10(0) - 8y = 40
-8y = 40
y = 40/-8
y = -5
Therefore, the y-intercept is (0, -5).
In summary, the coordinates of the points where the line 10x - 8y = 40 intersects the x- and y-axes are:
x-intercept: (4, 0)
y-intercept: (0, -5)
know more about coordinates: brainly.com/question/15300200
#SPJ11
How do you advise school leavers on stress management techniques to deal with the psychologist impact of unemployment
To advise school leavers on stress management techniques to deal with the psychological impact of unemployment, it is essential to encourage self-care practices, maintain a positive mindset, seek support from others, develop new skills, and explore alternative opportunities.
1. Self-care practices: Emphasize the importance of self-care activities such as exercise, proper sleep, healthy eating, and engaging in hobbies or activities that bring joy and relaxation. These practices help reduce stress and promote overall well-being.
2. Positive mindset: Encourage school leavers to maintain a positive outlook by focusing on their strengths, setting realistic goals, and maintaining a sense of optimism. Remind them that unemployment is a temporary phase and that opportunities will arise in the future.
3. Seek support: Encourage school leavers to reach out to family, friends, or mentors for emotional support and guidance. Sharing their concerns and feelings with others can help alleviate stress and provide valuable perspectives.
4. Develop new skills: Suggest utilizing the free time to learn new skills or enhance existing ones. This could involve taking online courses, volunteering, or participating in community projects. Skill development increases confidence and expands future job prospects.
5. Explore alternative opportunities: Encourage school leavers to explore alternative paths such as entrepreneurship, freelancing, internships, or part-time work. Encouraging them to think creatively and consider different options can help them find fulfilling opportunities.
By adopting these stress management techniques, school leavers can proactively cope with the psychological impact of unemployment, maintain a positive mindset, and continue developing themselves for future opportunities.
To learn more about taking online courses click here: brainly.com/question/16732793
#SPJ11
Reread pages 240-242. Which of Carol's thoughts and actions show she is naturally curious?
The story called Mr. Linden's Library
In the story "Mr. Linden's Library," Carol's curiosity is evident as she eagerly explores the library, wonders about its contents, and immerses herself in books, showcasing her natural thirst for knowledge.
In the story "Mr. Linden's Library," Carol exhibits several thoughts and actions that demonstrate her natural curiosity. On pages 240-242, the following instances highlight her inquisitive nature:
1. Carol's initial interest: When Carol first hears about Mr. Linden's library, she becomes immediately curious and eager to explore it. Her excitement indicates her natural curiosity and desire for new knowledge.
2. Wondering about the library's contents: As Carol enters the library, she starts imagining what books might be present. She wonders about the possibilities and what mysteries the library might hold. This demonstrates her inquisitive mind, always seeking answers and new experiences.
3. Actively exploring the library: While inside, Carol actively explores the library, examining different shelves and titles. She is genuinely interested in the books and artifacts, indicating her natural curiosity and desire to discover and learn.
4. Delving into books: Carol dives into a book on Greek mythology and loses track of time, immersing herself in the fascinating stories. This action showcases her curiosity-driven passion for learning and her willingness to explore different subjects.
Overall, Carol's immediate interest, wondering about the library's contents, active exploration, and delving into books exemplify her natural curiosity throughout the mentioned pages of the story.
To learn more about initial interest click here
brainly.com/question/32406448
#SPJ11
Anthony surveys a group of students at his school about whether they play a sport. This table shows the results broken down by gender. Are being a girl and playing sports independent events? Why or why not?
The table provided displays the results of Anthony's survey on whether students at his school play a sport, categorized by gender. The question at hand is whether being a girl and playing sports are independent events.
In order to determine if being a girl and playing sports are independent events, we need to understand the concept of independence in probability. Two events are considered independent if the occurrence of one event does not affect the probability of the other event happening.
Looking at the table, we can analyze the data for girls and boys separately. If the proportion of girls playing sports is consistent regardless of the total number of girls surveyed, then being a girl and playing sports can be considered independent events. However, if the proportion of girls playing sports varies depending on the total number of girls surveyed, then being a girl and playing sports are not independent events.
To determine the independence, we would need additional information about the total number of girls surveyed and the proportion of girls playing sports across different sample sizes. Without that information, we cannot definitively conclude whether being a girl and playing sports are independent events based solely on the provided table.
Learn more about probability here: https://brainly.com/question/31828911
#SPJ11
7. A rocket launched into the air reaches a height of 720 feet after 5 seconds. After 10 seconds, the rocket
lands. Let the x-axis be the ground and the y-axis be at the starting point of the rocket.
a.
Write an equation modeling the path of the rocket, where h is the height of the rocket and t is the
time in seconds after the rocket is launched.
I
H(t)=
b.
What was the height of the rocket 7 seconds after it was launched?
C.
How many seconds is the rocket in the air?
A rocket launched into the air reaches a height of 720 feet after 5 seconds. After 10 seconds, the rocket lands. Let the x-axis be the ground and the y-axis be at the starting point of the rocket. Equation modeling the path of the rocket where h is the height of the rocket and t is the time in seconds after the rocket is launched is:
a. H(t) = -16t² + vt + h
Where: H(t) = Height of rocket at time t (in feet)
h = Initial height (in feet) = 0
v = Initial velocity (in feet/sec) = 0
Gravity = 32 ft/s²
(Since the rocket is going upward)So the equation for the path of the rocket is:
H(t) = -16t² + 0t + 0
H(t) = -16t²b.
The height of the rocket 7 seconds after it was launched can be determined by using the formula derived above:
H(t) = -16t² + 0t + 0
H(7) = -16(7)²
= -784
b. The height of the rocket after 7 seconds of launch is 784 feet.
c. Time duration the rocket is in the air is given by the formula:
H(t) = -16t² + 0t + 0
We can determine the time at which the rocket lands by equating the height of the rocket to 0:
H(t) = -16t² + 0t + 0
= 0
To know more about Equation visit:
https://brainly.com/question/29657992
#SPJ11
A quarterback throws an incomplete pass. The height of the football at time t is modeled by the equation h(t) = –16t2 40t 7. Rounded to the nearest tenth, the solutions to the equation when h(t) = 0 feet are –0. 2 s and 2. 7 s. Which solution can be eliminated and why? The solution –0. 2 s can be eliminated because time cannot be a negative value. The solution –0. 2 s can be eliminated because the pass was not thrown backward. The solution 2. 7 s can be eliminated because the pass was thrown backward. The solution 2. 7 s can be eliminated because a ball cannot be in the air for that long due to gravity.
The solution that can be eliminated is -0.2 s. The reason for eliminating this solution cannot be a negative value in this context. The height of football at t is modeled by quadratic equation h(t) = -16t^2 + 40t + 7,
When solving the equation h(t) = 0 to find the times when the height of the football is zero, we obtain two solutions: -0.2 s and 2.7 s (rounded to the nearest tenth). We need to determine which solution is valid and which one should be eliminated.
In this case, the solution -0.2 s can be eliminated because time cannot be negative. Time represents the duration after the ball is thrown, and it cannot go back in time before the throw occurred. Therefore, -0.2 s does not make sense in the context of this problem.
On the other hand, 2.7 s is a valid solution as it represents the time when the football reaches a height of zero during its trajectory. This solution indicates that after approximately 2.7 seconds, the football has landed or reached its lowest point in its flight path.Thus, the solution -0.2 s can be eliminated because time cannot be negative in this situation.
To learn more about quadratic equation click here : brainly.com/question/30098550
#SPJ11
A catapult launches a pumpkin from the base of a hill. The hill
follows an incline with the height in meters, y, in terms of
horizontal distance in meters, x, given by the equation
y= 0.8x. The height of the pumpkin, as it is launched uphill,
is given by the function h(x) = -0.3.02 + 3.8x
What is the height, in meters, where the pumpkin lands on the
hill? Round to the nearest whole number if necessary.
The height where the pumpkin lands on the hill is approximately 13 meters.
The height where the pumpkin lands on the hill, we need to determine the point where the height of the hill (y) equals the height of the pumpkin (h(x)).
1. Equate the two height functions: Setting the equations y = 0.8x and h(x) = -0.3x^2 + 3.8x equal to each other allows us to find the x-value where the heights are equal.
0.8x = -0.3x^2 + 3.8x
2. Simplify the equation: Rearrange the equation to form a quadratic equation.
0 = -0.3x^2 + 3x - 3.8x
0 = -0.3x^2 - 0.8x
3. Solve for x: To find the x-value where the heights are equal, solve the quadratic equation. The solutions will give the points where the pumpkin lands on the hill.
Using a quadratic solver or factoring, we find that x = 0 and x ≈ 13.33.
4. Determine the height: Substituting the x-value into either the hill equation or the pumpkin equation gives us the height.
Using the hill equation, y = 0.8(13.33) ≈ 10.67.
Therefore, the height where the pumpkin lands on the hill is approximately 13 meters (rounded to the nearest whole number).
Learn more about function : brainly.com/question/28278690
#SPJ11
Interpret the following exponential function: y = 6 (1. 07) Superscript x What is the growth/decay factor? What is the y-intercept? a. Decay factor is 6; y-intercept is 1. 07 b. Decay factor is 1. 07; y-intercept is 6 c. Growth factor is 6; y-intercept is 1. 07 d. Growth factor is 1. 07; y-intercept is 6.
The growth/decay factor of the given exponential function y = 6(1.07)^x is 1.07, and the y-intercept is 6.
In the exponential function y = 6(1.07)^x, the base of the exponential term is 1.07. Since the base is greater than 1, it represents a growth factor. This means that as x increases, the value of y will grow exponentially.
The coefficient 6 represents the initial value or y-intercept of the function. When x is equal to 0, the exponential term becomes 1, and multiplying it by 6 gives us the y-intercept of 6. This means that when x is 0, the value of y is 6.
Therefore, the correct answer is:
d. Growth factor is 1.07; y-intercept is 6.
Learn more about growth factor here:
https://brainly.com/question/12052909
#SPJ11
If PQ has endpoints(5,-8)and (-5,8) what is the slope of PQ?
The slope of line PQ, which has endpoints (5, -8) and (-5, 8), can be determined by finding the ratio of the change in y-coordinates to the change in x-coordinates.
The slope represents the rate at which the line rises or falls as we move from one endpoint to the other. The slope formula is given by:
Slope = (change in y-coordinates) / (change in x-coordinates)
To calculate the slope of PQ, we subtract the y-coordinate of one endpoint from the y-coordinate of the other endpoint and divide it by the difference of the corresponding x-coordinates. In this case, the calculation would be as follows:
Slope = (8 - (-8)) / (-5 - 5) = 16 / -10 = -8 / 5
Therefore, the slope of line PQ is -8/5. This means that as we move from the point (5, -8) to (-5, 8), the line rises 8 units for every 5 units it moves to the left.
To learn more about endpoint click here: brainly.com/question/29164764
#SPJ11
Phylea has a bag with 30 fireballs and 24 Dreldy ranchers for a party she wants to repackage the candy into smaller bags in once each bag to have the same number of fireballs and Jolly ranchers
Phylea can repackage the candy into smaller bags, each containing 6 fireballs and 6 Jolly Ranchers.
To repackage the candy into smaller bags with an equal number of fireballs and Jolly Ranchers, we need to find the greatest common divisor (GCD) of 30 and 24. The GCD represents the largest number that divides both 30 and 24 evenly.
The prime factorization of 30 is 2 * 3 * 5, and the prime factorization of 24 is 2 * 2 * 2 * 3. To find the GCD, we take the common factors with the lowest exponent: 2 * 3 = 6.
To learn more about prime factorization visit;
https://brainly.com/question/29763746
#SPJ11
The Bronx Zoo has a number of 4-legged mammals and 2-legged birds. Maggie visited the zoo and counted 200 animals that were either mammals or birds. Among these animals she counted a total of 522 legs. Write an algebraic equation that can be used to solve for the number of birds, and then solve the equation.
The number of birds at the Bronx Zoo is 139. There are 139 birds at the Bronx Zoo, based on the information provided by Maggie's animal count and leg count.
Let's use algebraic equations to solve for the number of birds at the Bronx Zoo.
Let's assume that the number of mammals is represented by the variable "m" and the number of birds is represented by the variable "b."
From the given information, we know that the total number of animals counted, whether mammals or birds, is 200. This can be expressed as:
m + b = 200 (Equation 1)
Additionally, we know that the total number of legs counted is 522. Mammals have 4 legs each, while birds have 2 legs each. Therefore, the total number of legs can be calculated as:
4m + 2b = 522 (Equation 2)
To solve this system of equations, we can use substitution or elimination method.
Let's solve using the elimination method:
Multiply Equation 1 by 2 to make the coefficients of "b" in both equations the same:
2m + 2b = 400 (Equation 3)
Now subtract Equation 3 from Equation 2:
4m + 2b - (2m + 2b) = 522 - 400
Simplifying:
2m = 122
Divide both sides by 2:
m = 61
Now substitute the value of "m" back into Equation 1 to solve for "b":
61 + b = 200
Subtract 61 from both sides:
b = 200 - 61
b = 139
Therefore, the number of birds at the Bronx Zoo is 139.
By solving the given algebraic equation, we determined that there are 139 birds at the Bronx Zoo, based on the information provided by Maggie's animal count and leg count.
Learn more about Bronx Zoo here
https://brainly.com/question/16620380
#SPJ11
1. two rectangles have a scale factor 4/3 If the perimeter of the smaller rectangle is 120 what is the perimeter of the larger rectangle 2.two rectangles have a scale factor 4/3 If the perimeter of the smaller rectangle is 45 what is the perimeter of the larger rectangle
3.two hexagons have an area ratio of 36:49 Find the ratio of their perimeters.
The perimeter of the larger rectangle is 160. The ratio of the perimeters of the two hexagons is 36/7.
To find the perimeter of the larger rectangle, we can use the concept that the perimeter scales with the scale factor.
If the scale factor of 4/3 is applied to the smaller rectangle, it means that the corresponding sides of the larger rectangle are 4/3 times longer than the sides of the smaller rectangle. Since the perimeter is the sum of all the sides, we can multiply the perimeter of the smaller rectangle by the scale factor to find the perimeter of the larger rectangle.
Given that the perimeter of the smaller rectangle is 120, we can calculate the perimeter of the larger rectangle as follows:
Perimeter of the larger rectangle = Scale factor * Perimeter of the smaller rectangle
Perimeter of the larger rectangle = (4/3) * 120
Perimeter of the larger rectangle = 160
Therefore, the perimeter of the larger rectangle is 160.
Using the same logic as in the previous question, we can find the perimeter of the larger rectangle when the perimeter of the smaller rectangle is 45.
Perimeter of the larger rectangle = Scale factor * Perimeter of the smaller rectangle
Perimeter of the larger rectangle = (4/3) * 45
Perimeter of the larger rectangle = 60
Therefore, the perimeter of the larger rectangle is 60.
The ratio of the areas of the two hexagons is given as 36:49. Since the area of a hexagon is proportional to the square of its side length, we can take the square root of the area ratio to find the ratio of their side lengths.
√(Area ratio) = √(36/49) = 6/7
The ratio of their side lengths is 6/7. Since the perimeter of a regular hexagon is equal to six times the length of its side, we can multiply the ratio of the side lengths by 6 to find the ratio of their perimeters.
Ratio of perimeters = 6 * (6/7) = 36/7
Therefore, the ratio of the perimeters of the two hexagons is 36/7.
Learn more about perimeter here
https://brainly.com/question/19819849
#SPJ11
The dimensions of a rectangle are given in base two, The width is 10 base two cm and the length is 11 base two cm. Find the perimeter
The perimeter of the rectangle is 10 cm.
To find the perimeter of the rectangle, we need to convert the base two dimensions to base ten and then use the formula for calculating the perimeter.
The width of the rectangle is 10 base two cm. In base ten, this is equivalent to 2 cm (since 10 base two is equal to 2 in base ten).
The length of the rectangle is 11 base two cm. In base ten, this is equivalent to 3 cm (since 11 base two is equal to 3 in base ten).
Now, we can calculate the perimeter using the formula:
Perimeter = 2 * (Width + Length)
Perimeter = 2 * (2 cm + 3 cm)
Perimeter = 2 * 5 cm
Perimeter = 10 cm
Therefore, the perimeter of the rectangle is 10 cm.
learn more about "perimeter ":- https://brainly.com/question/397857
#SPJ11
The teacher realizes that a mistake was made and the student whose score was recorded as 49%
If the student's score was recorded as 49%, the solution to the mistake would be to correct the score to its accurate value.
To correct the mistake, the teacher needs to determine the actual score of the student. If the recorded score is 49%, it means the student received 49% of the total possible marks. The teacher should review the student's work and re-evaluate their performance to obtain the correct score. Once the correct score is determined, it should be recorded accurately in the student's records. This ensures that the student's academic progress is assessed and reported correctly.
To learn more about Calculation Of Score
brainly.com/question/30759870
#SPJ11
If f(x) = x2, g(x) = 5x, and h(x) = x + 4, find each value.[f ◦ (h ◦ g)](2)
To solve the given function: f(x) = x², g(x) = 5x, and h(x) = x + 4 for [f ◦ (h ◦ g)](2), we have to calculate for the following steps:
To find [h ◦ g](x), we substitute g(x) into h(x) as follows:
h(g(x)) = g(x) + 4
Substitute g(x) with 5x, we get:
h(g(x)) = 5x + 4
Therefore, [h ◦ g](x) = 5x + 4
To find [f ◦ (h ◦ g)](x), we substitute [h ◦ g](x) into f(x) as follows:
f(h(g(x))) = [h(g(x))]²
Substitute [h ◦ g](x) with 5x + 4, we get:
f(h(g(x))) = [5x + 4]²= (5x + 4)(5x + 4)= 25x² + 40x + 16
Therefore, [f ◦ (h ◦ g)](x) = 25x² + 40x + 16
The final step is to find [f ◦ (h ◦ g)](2). Substitute x = 2, we get:
[f ◦ (h ◦ g)](2)= 25(2)² + 40(2) + 16= 100 + 80 + 16= 196
Hence, we have found that [f ◦ (h ◦ g)](2) = 196.
To know more about function visit:
brainly.com/question/30721594
#SPJ11
Andrew needs to order a pool top covering for his above ground circular swimming pool. The swimming pool is 20 feet across. how large of a pool top does he need to order? round to the nearest tenth
Answer:
π(10²) = 100π = about 314.2 ft²
At the Stanford Used Car Dealership, a salesperson is paid a commission of 5% of the sale price for every car he or she sells. If a salesperson sells a car for $13,500, how much would he or she be paid as a commission?
Cost of commission he or she be paid is, $675
We have,
At the Stanford Used Car Dealership, a salesperson is paid a commission of 5% of the sale price for every car he or she sells.
Here, Cost of a car = $13,500
Hence, Cost of commission he or she be paid is,
5% of $13,500
5/100 x $13,500
5 x $135
$675
Therefore, Cost of commission he or she be paid is, $675
Learn more about the percent visit:
https://brainly.com/question/24877689
#SPJ4
Express the area of a square with side length 3xy2 as a monomial
The area of a square with side length 3xy^2 can be expressed as a monomial, which is 9x^2y^4.
The area of a square is calculated by multiplying the length of its side by itself. Given a side length of 3xy^2, we can express the area as a monomial by simplifying the expression. First, we square the side length: (3xy^2)^2. Applying the exponent to each term within the parentheses, we get 9x^2y^4. This monomial represents the area of the square with a side length of 3xy^2. It indicates that the area is the product of the coefficient, 9, and the variables raised to their respective exponents, x^2 and y^4. Therefore, the monomial expression for the area of the square is 9x^2y^4.
Learn more about simplifying algebraic expressions here: brainly.com/question/30200858
#SPJ11
Which pair of fractions is equivalent to 5/6 and 3/5
[tex]To find out which pair of fractions is equivalent to 5/6 and 3/5, we need to convert them to fractions with a common denominator.[/tex]
The common denominator of 6 and 5 is 30. Thus, we need to convert both fractions into 30th fractions. 5/6=25/30, and 3/5=18/30. Therefore, the pair of fractions that is equivalent to 5/6 and 3/5 is 25/30 and 18/30.Explanation:Given fractions are 5/6 and 3/5To make a pair of equivalent fractions, we need to find out a common denominator.Now, let's try to find out the LCM of 6 and 5.LCM of 6 and 5 is 30Thus,We need to convert fractions with a common denominator of 30.5/6 = 25/303/5 = 18/30Therefore, the pair of equivalent fractions is 25/30 and 18/30.
To know more about the word equivalent fractions visits :
https://brainly.in/question/27965723
#SPJ11
