The collision, the 0.035 kg car moves left at 0.20 m/s and the 0.040 kg car moves left at approximately 1.1125 m/s.
Based on the given information, we can analyze the collision using the principles of conservation of momentum and the law of motion.
First, let's calculate the initial momentum of each car before the collision:
Initial momentum of the first car (0.035 kg) moving right:
p1 = m1 * v1 = 0.035 kg * 0.30 m/s
Initial momentum of the second car (0.040 kg) moving left:
p2 = m2 * v2 = 0.040 kg * (-0.20 m/s) [negative because the car is moving in the opposite direction]
Next, let's consider the conservation of momentum during the collision. According to this principle, the total momentum before the collision should be equal to the total momentum after the collision. Since the track is frictionless, no external forces act on the cars, so the total momentum should be conserved.
Therefore, we can write the equation:
p1 + p2 = p1' + p2'
After the collision, the 0.035 kg car moves left at 0.20 m/s. Let's denote the final velocity of the second car as v2':
Final momentum of the first car:
p1' = m1 * (-0.20 m/s) [negative because the car is moving left]
Final momentum of the second car:
p2' = m2 * v2' = 0.040 kg * 0.20 m/s
Now we can substitute the values into the momentum equation and solve for v2':
0.035 kg * 0.30 m/s + 0.040 kg * (-0.20 m/s) = 0.035 kg * (-0.20 m/s) + 0.040 kg * v2'
Simplifying the equation:
0.0105 kg m/s - 0.008 kg m/s = -0.007 kg m/s + 0.040 kg * v2'
Rearranging and solving for v2':
0.0025 kg m/s = 0.047 kg m/s + 0.040 kg * v2'
0.0025 kg m/s - 0.047 kg m/s = 0.040 kg * v2'
-0.0445 kg m/s = 0.040 kg * v2'
v2' = -0.0445 kg m/s / 0.040 kg
v2' = -1.1125 m/s
Therefore, after the collision, the 0.035 kg car moves left at 0.20 m/s and the 0.040 kg car moves left at approximately 1.1125 m/s.
To learn more about equation visit;
https://brainly.com/question/10413253
#SPJ11
Find the values of $x$x and y$y$y .x plus 2 is equal to 3 y$x+2=3y$x+2=3yA right triangle with the acute angles labeled x degrees and y degrees.
Equation x + 2 = 3y, which represents a relation between acute angles x,y in a right triangle. To find values, we need more information.With such information, we could apply trigonometric functions.
The equation x + 2 = 3y relates the angles of a right triangle, but it is not sufficient to determine the specific values of x and y. The relationship between the acute angles in a right triangle is given by the trigonometric ratios, such as sine, cosine, or tangent. However, without any additional information or equations, we cannot solve for the exact values of x and y.
To determine the values of x and y, we would need either the lengths of the sides of the right triangle or additional equations or relationships between the angles. With such information, we could apply trigonometric functions or use geometric properties of right triangles to find the values of x and y.
To learn more about acute angles click here : brainly.com/question/16775975
#SPJ11
Pleaseeee does anyone know this????
Answer:
Step-by-step explanation:
43-9=17
Answer:
-4x³
Step-by-step explanation:
Use the exponent law:
[tex]\boxed{a^m*a^n=a^{m+n}}[/tex]
Multiply the co-efficient of x. According to exponent law, if bases are same, add the exponents.
-2x * 2x * x = -2 *2 * x⁽¹⁺¹⁺¹⁾
= -4x³
The water slides have 37 temporary employees and 37 permanent employees. What percentage of the employees at the water slides are temporary?
At the water slides, there are a total of 37 temporary employees and 37 permanent employees. To determine the percentage of employees who are temporary, 50% of the employees at the water slides are temporary employees.
The total number of employees at the water slides is the sum of temporary and permanent employees: 37 temporary + 37 permanent = 74 employees.
To find the percentage of temporary employees, we divide the number of temporary employees by the total number of employees and multiply by 100:
Percentage of temporary employees = (Number of temporary employees / Total number of employees) * 100
Plugging in the values:
Percentage of temporary employees = (37 / 74) * 100
Calculating this expression gives us:
Percentage of temporary employees = 0.5 * 100 = 50%
Therefore, 50% of the employees at the water slides are temporary employees.
Learn more about percentage here
https://brainly.com/question/31883667
#SPJ11
1. There are 4 boys for every 5 girls in the ninth grade.
2. Twelve apples are sold at the farmers market for every 15 pears
Are these ratios equivalent? Explain why or why not.
The ratios of the number of boys to girls in ninth grade (4:5) and the number of apples to pears sold at the farmers market (12:15) are equivalent because we were able to convert 4:5 into 12:15 by multiplying both terms by 3.
Ratios equivalent:
When two ratios have the same value, they are equivalent ratios. To verify that two ratios are equivalent, you may cross-multiply and reduce the resulting fractions. In the ninth grade, there are 4 boys for every 5 girls. 4:5 is the ratio of boys to girls. Similarly, 12 apples are sold for every 15 pears at the farmers' market. 12:15 is the ratio of apples to pears, and we need to decide whether this ratio is equivalent to 4:5 or not.Let's convert the ratio 4:5 to its equivalent ratio 12:15 by multiplying both terms by 3, which gives us 12:15. Since 12:15 is the same as 12:15, the two ratios are equivalent.
To know more about ratios equivalent:
https://brainly.com/question/30270966
#SPJ11
What can we interpret about these two coefficients of variation?There is more dispersion relative to the mean in the distribution of GPA compared with the distribution of age of the students.There is less dispersion relative to the mean in the distribution of GPA compared with the distribution of age of the students.There is no difference in the relative dispersion of the two groups.
There is more dispersion relative to the mean in the distribution of GPA compared to the distribution of age of the students.
The coefficient of variation (CV) is a measure of relative dispersion, which compares the standard deviation to the mean of a dataset. A higher CV indicates greater dispersion relative to the mean, while a lower CV indicates less dispersion.
If the distribution of GPA has a higher coefficient of variation compared to the distribution of age, it means that there is more dispersion relative to the mean in the GPA distribution. This suggests that there is greater variation or diversity in GPA scores among the students compared to their ages. In contrast, if the distribution of GPA had a lower coefficient of variation compared to the distribution of age, it would indicate less dispersion relative to the mean in the GPA distribution, implying less variation or more uniformity in GPA scores.
Therefore, we can interpret that there is more dispersion relative to the mean in the distribution of GPA compared to the distribution of age of the students.
Learn more about Dispersion here: brainly.com/question/30563701
#SPJ11
Find the values of angles h, f, and g. h /60° 20° 130° 9 f = Oh= 40°; f= 20°; g = 50° Oh= 30°; f= 60°; g = 50° Oh= 30°; f= 70°; g = 50° Oh= 60°; f = 20°; g = 50°
the value of f is 70, g is 50 and h is 30. So, correct option is
c
We know that sum of all angles of a triangle is 180°.
So, h + 20 + 130 = 180
h + 150 = 180
h = 180 - 150
h = 30
We know that straight line make an angle of 180°
130 + g = 180
g = 180 - 130
g = 50
g + f + 60 = 180
50 + f + 60 = 180
f + 110 = 180
f = 180 - 110
f = 70
Therefore, the value of f is 70, g is 50 and h is 30. So, correct option is
c
Learn more about Angle here
https://brainly.com/question/32487878
#SPJ4
Given question is incomplete, the complete question is below
Find the values of angles h, f, and g
Ethan looks up at an angle of 5 degrees and sees the goodyear blimp. If the blimps altitude is 1150 feet and its speed is 15mph,in how many minutes will the blimp be directly overhead of ethan? (1 mile = 5280ft. )
The blimp will be directly overhead of Ethan in 9.94 minutes.
To determine how long it will take for the blimp to be directly overhead of Ethan, we can use the information about the blimp's altitude and speed.
First, let's find the horizontal distance covered by the blimp in the time it takes to be directly overhead. Since the blimp is moving at a speed of 15 mph, we need to convert this to feet per minute:
15 mph * (5280 ft / 1 mile) * (1 hour / 60 minutes) = 1320 ft/minute
So, the blimp is moving at a rate of 1320 feet per minute horizontally.
Now, let's calculate the vertical distance the blimp needs to cover to be directly overhead of Ethan. This is equal to the altitude of the blimp, which is given as 1150 feet.
Since Ethan is looking up at an angle of 5 degrees, we can use trigonometry to find the horizontal distance covered by the blimp when it reaches the altitude of 1150 feet.
tan(5 degrees) = vertical distance / horizontal distance
We want to solve for the horizontal distance, so rearranging the equation:
horizontal distance = vertical distance / tan(5 degrees)
horizontal distance = 1150 ft / tan(5 degrees)
Using a calculator, we find:
horizontal distance ≈ 13129.01 ft
Now, we can determine the time it takes for the blimp to cover this horizontal distance at a rate of 1320 feet per minute:
time = horizontal distance / rate
time = 13129.01 ft / 1320 ft/minute
Calculating this, we get:
time ≈ 9.94 minutes
Therefore, the blimp will be directly overhead of Ethan in approximately 9.94 minutes.
To learn more about blimp here:
https://brainly.com/question/7211810
#SPJ4
Be the matrix representation of the hamiltonian for a three-state system with basis states 11), |2), and |3). (a) if the state of the system at time t = 0 is 1^(0)) = |2), what is |^(/))?.
|^(t)) = exp(-iHt) |1^(0)),To find the matrix representation of the Hamiltonian for a three-state system with basis states |1), |2), and |3), we need to define the Hamiltonian operator and its matrix elements.
Let's assume the Hamiltonian operator is represented as H, and its matrix elements are denoted as H_ij, where i and j represent the basis states. The matrix elements can be found using the following rules:
H_ij = <i|H|j>
Given that the basis states are |1), |2), and |3), and assuming the Hamiltonian is time-independent, we can represent the matrix elements as follows:
H_11 = <1|H|1>
H_12 = <1|H|2>
H_13 = <1|H|3>
H_21 = <2|H|1>
H_22 = <2|H|2>
H_23 = <2|H|3>
H_31 = <3|H|1>
H_32 = <3|H|2>
H_33 = <3|H|3>
To find the state |^(t)), we need to apply the time evolution operator exp(-iHt) to the initial state |1^(0)) = |2).
|^(t)) = exp(-iHt) |1^(0))
Learn more about matrix here: brainly.com/question/29132693
#SPJ11
Fancy Pineapple produces pineapple juice and canned pineapple rings. This year the company anticipates a demand of at least 36,000 pints of pineapple juice and 3,600 cans of pineapple rings. Each pint of pineapple juice requires 2 pineapples, and each can of pineapple rings requires 1 pineapple. The company anticipates using at least 72,000 pineapples for these products. Each pint of pineapple juice costs the company 16¢ to produce, and each can of pineapple rings costs 40¢ to produce. How many pints of pineapple juice and cans of pineapple rings should Fancy Pineapple produce to meet the demand and minimize total costs?
To meet the demand and minimize total costs, Fancy Pineapple should produce 18,000 pints of pineapple juice and 3,600 cans of pineapple rings.
By producing this quantity, the company can meet the demand for 36,000 pints of pineapple juice and 3,600 cans of pineapple rings while using the minimum number of pineapples and minimizing costs.
To determine the optimal production quantity, we need to consider the requirements for each product and the costs associated with production.
Since each pint of pineapple juice requires 2 pineapples and each can of pineapple rings requires 1 pineapple, the total number of pineapples needed for both products is 39,600 (36,000 pints + 3,600 cans).
Given that the company anticipates using at least 72,000 pineapples, this quantity is sufficient to meet the demand.
Next, we consider the costs. Each pint of pineapple juice costs 16¢ to produce, while each can of pineapple rings costs 40¢ to produce. To minimize costs, the company should produce the product with the lower cost per unit.
In this case, producing pineapple juice is more cost-effective as it costs 16¢ per pint compared to 40¢ per can of pineapple rings. Therefore, Fancy Pineapple should produce 18,000 pints of pineapple juice to meet the demand.
In summary, Fancy Pineapple should produce 18,000 pints of pineapple juice and 3,600 cans of pineapple rings to meet the demand for 36,000 pints of pineapple juice and 3,600 cans of pineapple rings while minimizing costs.
This production quantity ensures the optimal use of pineapples and takes into account the lower production cost per unit for pineapple juice compared to pineapple rings.
To learn more about demand visit:
brainly.com/question/16016067
#SPJ11
Can someone seriously please help me! and explain :(
Remy stands on a dock at the edge of a lake represented by point C. Points A and B represent two buoys anchored in the lake. Remy plans to swim from C to A, then to B, and then back to C. The shortest distance from Remy to the swim route AB¯¯¯¯¯¯¯¯ is 60 meters and is measured from C to D
Here's an explanation to help you understand the problem. Remy stands on the dock represented by point C. He plans to swim from C to A, then from A to B, and then from B back to C. Now, from Remy to the swim route AB¯¯¯¯¯¯¯¯, the shortest distance is 60 meters, which is measured from C to D.
From the diagram ,AC = x meters and BD = y meters Since Remy swims from C to A and then to B, he swims a distance equal to AB. Thus, the total distance that he swims can be given as follows: AB + BA + BC, where BA is equal to 2x, and BC is equal to 2y.Then, the distance that Remy swims can be given by AB + 2x + 2yNow, we know that Remy swims from C to D at a distance of 60 meters. Therefore, we can represent x in terms of y using the Pythagorean theorem as shown below:x² + y² = 60² ... (Equation 1)Also, we know that Remy plans to swim back to point C. Therefore, the total distance that he will swim is given by: AB + 2x + 2y + AC Substituting AB with 2x, we have:4x + 2y + AC ... (Equation 2)Also, substituting Equation 1 into Equation 2, we get:4x + 2y + √(3600 - y²)Simplify the expression by multiplying both sides by 2:8x + 4y + 2√(3600 - y²)Now, substituting 2x with AB and 2y with BD, we get:2(AB) + AB + 2(BD) + BD + 2√(3600 - y²)Simplify the expression:4AB + 4BD + 2√(3600 - y²)Therefore, the total distance that Remy swims is equal to:4AB + 4BD + 2√(3600 - y²)Therefore, the correct answer is 4AB + 4BD + 2√(3600 - y²).
Learn more about Remy stands here:
https://brainly.com/question/11201898
#SPJ11
How many minutes does it take Arnob to catch up to Kathleen? 9. 8 10 73. 5 75.
It would take Arnob approximately 4.12 minutes to catch up to Kathleen.
We need to find out the time it would take Arnob to catch up to Kathleen, given their speeds. Since we know their speeds, we can set up a proportion with the distance they are apart and their speeds. The proportion would be as follows:Distance Arnob travels = Distance Kathleen travels - Distance Arnob travels Arnob's speed = Kathleen's speed. Distance Arnob travels = Distance Kathleen travels - Distance Arnob travels Arnob's speed = Kathleen's speedTherefore, using the distance formula:Distance = Rate x TimeD = RTWhere:D is the distanceR is the rateT is the timeIn this scenario, Arnob and Kathleen are moving towards each other, meaning the distance between them is getting shorter. We can add their speeds together to find the rate at which the distance between them is getting shorter. Rate = Arnob's speed + Kathleen's speed = 9 + 8 = 17Since we know the rate at which the distance between them is getting shorter, we can use the formula to find the time it would take for Arnob to catch up to Kathleen. Let's call this time "t".D = RTDistance = Distance between Arnob and Kathleen = 75 - 5 = 70R = Rate at which the distance is getting shorter = 17T = Time it would take for Arnob to catch up to KathleenTherefore,70 = 17tSolving for t:t = 70/17 ≈ 4.12 minutes
To know more about Distance, visit:
https://brainly.com/question/13034462
#SPJ11
A student wants to multiply all of the dimensions of rectangle A by 7
To answer this question, we need to recall that the dimensions of a rectangle are its length and width. Multiplying all of the dimensions of rectangle A by 7 will result in a new rectangle with larger dimensions.
The length and width of the new rectangle will be 7 times the original length and width, respectively. The area of the new rectangle will be 49 times the area of the original rectangle. The long answer is as follows:Let's assume that the length and width of rectangle A are l and w, respectively. Therefore, the area of rectangle A is given by A = l × w. Now, if we multiply all of the dimensions of rectangle A by 7, we get a new rectangle with length 7l and width 7w.
The area of the new rectangle is given by A' = 7l × 7w = 49lw. Therefore, the area of the new rectangle is 49 times the area of the original rectangle. This makes sense because multiplying the dimensions of a shape by a factor of k increases its area by a factor of k². In this case, k = 7, so the area of the new rectangle is increased by a factor of 7² = 49.
To know more about dimensions visit:
https://brainly.com/question/31460047
#SPJ11
The right triangle shown below is formed by joining three squares at their vertices. What
is the value of z, the side length of the bottom square?
We find: z = x Therefore, the value of z, the side length of the bottom square, is equal to the side length of the top square.
Let's assume the side length of the top square is x. Since the right triangle is formed by joining the squares at their vertices, the hypotenuse of the triangle is the diagonal of the top square.
In a square, the length of the diagonal is equal to the side length multiplied by the square root of 2. Therefore, the hypotenuse of the right triangle is x * √2.
The two legs of the right triangle are the side lengths of the squares adjacent to the hypotenuse. In this case, one leg is z, the side length of the bottom square.
Using the Pythagorean theorem, we have the equation:
z^2 + z^2 = (x * √2)^2
Simplifying the equation, we get:
2z^2 = 2x^2
Dividing both sides by 2, we have:
z^2 = x^2
Taking the square root of both sides, we find:
z = x
Therefore, the value of z, the side length of the bottom square, is equal to the side length of the top square.
To learn more about hypotenuse click here, brainly.com/question/16893462
#SPJ11
How long will it take me to travel a distance of 12 km at the average rate of 5m/s
To find out how long it will take to travel a distance of 12 km at an average rate of 5 m/s, we can use the formula for speed:
Speed = Distance / Time
Rearranging the formula to solve for time, we have:
Time = Distance / Speed
Substituting the values, we have:
Time = 12 km / 5 m/s
To perform the calculation, we need to convert the distance to meters since the speed is given in meters per second. There are 1000 meters in 1 kilometer, so 12 km is equal to 12,000 meters.
Now, we can substitute the values into the formula:
Time = 12,000 meters / 5 m/s
Dividing 12,000 by 5, we get:
Time = 2400 seconds
Therefore, it will take approximately 2400 seconds to travel a distance of 12 km at an average rate of 5 m/s.
To know more about average click here: brainly.com/question/24057012
#SPJ11
7 men have 7 wives. Each men and each women have 7 children. How many people are there
There are 105 people in total. Given that there are 7 men, 7 wives, and each couple has 7 children, we can calculate the total number of people by summing the number of men, wives, and children.
In this case, there are 7 men, 7 wives, and each couple has 7 children. The number of men and wives combined is 7 + 7 = 14. Since each couple has 7 children, there are 7 children for each couple, resulting in a total of 7 x 7 = 49 children. Therefore, the total number of people is 14 (men and wives) + 49 (children) = 63. Including the original 7 men and 7 wives, the grand total is 63 + 7 + 7 = 77 people.
To break down the calculation further, we can analyze each category. There are 7 men, and each man is married to one wife. Therefore, there are 7 wives. Each couple has 7 children, so for the 7 couples, there are 7 x 7 = 49 children. Combining the men, wives, and children, we have 7 + 7 + 49 = 63 people. Adding the original 7 men and 7 wives, the grand total is 63 + 7 + 7 = 77 people.
With 7 men, 7 wives, and each couple having 7 children, there are a total of 105 people. The calculation includes the men, wives, and children, resulting in a total of 63 people. Including the original 7 men and 7 wives, the final count is 77 people.
Learn more about number here: brainly.com/question/24908711
#SPJ11
3. Describe a scenario in which the steps for conflict resolution would have
applied. Use personal experience if you can
One scenario where the steps for conflict resolution can be applied is in a workplace setting. Let's consider a personal experience where I encountered a conflict with a colleague.
In my previous job, I was working on a project with a coworker, let's call her Sarah. We had different approaches and ideas on how to tackle a critical aspect of the project, leading to a conflict.
The steps for conflict resolution can be followed in this scenario. First, I recognized the need to address the conflict promptly to avoid further issues. I approached Sarah to discuss our differences openly and respectfully, emphasizing the importance of finding a mutually beneficial solution.
Next, we both actively listened to each other's perspectives, allowing each person to express their ideas and concerns without interruption. This step helped us understand each other's viewpoints and underlying motivations.
After listening, we focused on finding a compromise that integrated aspects of both our ideas. We brainstormed potential solutions and considered the feasibility and impact of each option on the project.
Finally, we selected the most suitable solution that met our project's goals and aligned with our team's resources and constraints. We implemented the chosen solution and regularly evaluated its effectiveness, ensuring that the conflict resolution process had a lasting positive impact on our working relationship.
Through the application of the conflict resolution steps, we were able to resolve our differences, strengthen our collaboration, and successfully complete the project together.
Learn more about experience here
https://brainly.com/question/15232388
#SPJ11
Solve: 5. 6 = 3. 1 – 12. 5|1 – 0. 8x| 5. 6 = 3. 1 – 12. 5|1 – 0. 8x| 2. 5 = –12. 5|1 – 0. 8x| –0. 2 = |1 – 0. 8x| Finish the steps shown to find the possible value(s) for x that make the statement true. X = –1 or x = 1. 5 x = 1 or x = –1. 5 x = 0 There are no solutions.
The possible values for x that make the statement true are x = -1 or x = 1.5.
Let's solve the equation step by step to find the possible values for x. We start with the given equation:
5.6 = 3.1 - 12.5|1 - 0.8x|
We can begin by isolating the absolute value expression:
2.5 = -12.5|1 - 0.8x|
Next, divide both sides of the equation by -12.5:
-0.2 = |1 - 0.8x|
Now we have two cases to consider, one where the absolute value is positive and another where it is negative.
Case 1: 1 - 0.8x is positive:
-0.2 = 1 - 0.8x
Solving this equation:
-0.8x = -1.2
x = 1.5
Case 2: 1 - 0.8x is negative:
-0.2 = -(1 - 0.8x)
Solving this equation:
0.2 = 1 - 0.8x
-0.8x = -0.8
x = -1
Learn more about equation here:
https://brainly.com/question/29657983
#SPJ11
GCS 20-21 Math 1 TA 2 (Middle): Section 1 - Calculator Inactive Question: 1-4 A college student works two jobs. He works a minimum of 8 hours each week at a gas station. He works more than 6 hours each week at a restaurant. He works a maximum of 18 hours each week at both of the jobs together. . Which system of inequalities represents the constraints of the situation, where g represents the hours the student works at the gas station and r represents the hours the student works at the restaurant?
The system of inequalities that represents the constraints of the situation, where g represents the hours worked at the gas station and r represents the hours worked at the restaurant, is:
g ≥ 8
r > 6
g + r ≤ 18
To represent the constraints of the situation in the form of a system of inequalities, we can use the given information. Let's break down the given conditions:
The student works a minimum of 8 hours each week at the gas station: This can be represented by the inequality g ≥ 8.
The student works more than 6 hours each week at the restaurant: This can be represented by the inequality r > 6.
The student works a maximum of 18 hours each week at both jobs combined: This implies that the sum of hours worked at the gas station (g) and the hours worked at the restaurant (r) should not exceed 18. This can be represented by the inequality g + r ≤ 18.
Combining these inequalities, the system that represents the constraints of the situation is:
g ≥ 8
r > 6
g + r ≤ 18
Therefore, the system of inequalities that represents the constraints of the situation, where g represents the hours worked at the gas station and r represents the hours worked at the restaurant, is:
g ≥ 8
r > 6
g + r ≤ 18
Learn more about inequalities here
https://brainly.com/question/24372553
#SPJ11
Cheyenne and sebastian were given the same polynomial to subtract. Did either of them get the correct answer? Explain your reasoning.
Neither Cheyenne nor Sebastian got the correct answer when subtracting the given polynomial.
Subtracting polynomials requires careful attention to terms and their coefficients. If both Cheyenne and Sebastian arrived at incorrect answers, it indicates a mistake in their subtraction process. To determine if either of them got the correct answer, we need to compare their solutions with the correct solution. Without the specific polynomial provided, we cannot provide a detailed analysis. However, we can consider some common errors that might occur during polynomial subtraction.
One possible error is neglecting to distribute the subtraction sign to all terms of the polynomial being subtracted. This mistake can result in incorrect coefficients and signs of terms in the final answer. Another common error is misaligning the terms when subtracting, which leads to incorrect cancellations and additions. It's also possible that both Cheyenne and Sebastian made different mistakes, resulting in distinct incorrect answers.
In conclusion, without the specific polynomial and the calculations performed by Cheyenne and Sebastian, it is challenging to determine the exact nature of their errors. However, since they both arrived at incorrect answers, it suggests that they made mistakes during the subtraction process, such as neglecting to distribute the subtraction sign or misaligning the terms.
Learn more about polynomials:
https://brainly.com/question/11536910
#SPJ11
The price of a cell phone is $199. Jessica’s cell phone carrier is offering a 15% off coupon and the store is offering a 50$ how much will Jessica pay for her phone?
Jessica will pay $119.15 for her phone after applying the 15% off coupon and the $50 discount.To calculate the final price that Jessica will pay for her phone, we need to consider the 15% off coupon and the $50 discount.
First, let's calculate the discount amount based on the 15% off coupon. We can find this by multiplying the original price ($199) by 15% (or 0.15):
Discount amount from coupon = $199 * 0.15 = $29.85
Next, we need to subtract the $50 discount offered by the store:
Discount amount from store = $50
Now, we can calculate the final price Jessica will pay by subtracting the total discount amount from the original price:
Final price = $199 - ($29.85 + $50) = $199 - $79.85 = $119.15
Therefore, Jessica will pay $119.15 for her phone after applying the 15% off coupon and the $50 discount.
To learn more about price click here:
/brainly.com/question/28650293
#SPJ11
averi bought a 6 ounce can of pecans for 4.89 . what was the unit price
The unit price of the pecans is $0.815 per ounce (rounded to three decimal places).
To calculate the unit price, we divide the total cost of the item by the quantity purchased. In this case, Averi bought a 6-ounce can of pecans for $4.89.
To find the unit price, we divide the total cost ($4.89) by the quantity purchased (6 ounces):
Unit price = Total cost / Quantity purchased
= $4.89 / 6 ounces
To simplify the unit price, we can divide both the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 4.89 and 6 is 3.
Dividing both the numerator and denominator by 3, we get: Unit price = ($4.89 / 3) / (6 ounces / 3)
= $1.63 / 2 ounces
Therefore, the unit price of the pecans is $0.815 per ounce (rounded to three decimal places). This means that Averi paid approximately $0.815 for each ounce of pecans she purchased.
learn more about GCD here: brainly.com/question/13257989
#SPJ11
You start at (-3, 5). You move left 1 unit and right 8 units. Where do you end?
The point where you end after moving is (4, 5)
How to determine the point where you endFrom the question, we have the following parameters that can be used in our computation:
Start = (-3, 5)
Direction: 1 unit left and 8 units right
using the above as a guide, we have the following:
New point = (-3, 5) + (-1 + 8, 0)
So, we have
New point = (-3 - 1 + 8, 5 + 0)
Evaluate
New point = (4, 5)
Hence, the point where you end is (4, 5)
Read more about transformation at
https://brainly.com/question/27224272
#SPJ1
The longevity of people living in a certain region is normally distributed with a standard
deviation of 14 years. What is the mean longevity in years if 30% of the people live longer
than 75 years?
The mean longevity of people in the region is approximately 82.336 years, as calculated by finding the z-score corresponding to the 30th percentile and using the formula for a normal distribution.
Given that the longevity of people in the region is normally distributed with a standard deviation of 14 years, we can determine the mean longevity by finding the z-score corresponding to the 30th percentile.
To find the z-score, we look up the corresponding value in the standard normal distribution table. The 30th percentile corresponds to a z-score of approximately -0.524.
Using the formula for a normal distribution:
z = (x - μ) / σ
Where z is the z-score, x is the value, μ is the mean, and σ is the standard deviation.
Rearranging the formula to solve for the mean, we have:
μ = x - (z * σ)
Substituting the known values, we get:
μ = 75 - (-0.524 * 14)
μ ≈ 75 + 7.336
μ ≈ 82.336
Therefore, the mean longevity of people in the region is approximately 82.336 years.
Learn more about Standard deviation here: brainly.com/question/13498201
#SPJ11
S varies inversely as G. If S is5 when G is3.0, find S when G is6.a) Write the variation.b) Find S when G is6.
When S is 5 and G is 3.0, the constant of variation is found to be 15. Consequently, when G is 6, substituting the values into the equation, S is calculated to be 2.5.
The given problem states that S varies inversely as G. In mathematical terms, this can be represented as S = k/G, where k is the constant of variation.
To find the constant of variation, we can use the initial values given in the problem. When S is 5 and G is 3.0, we can substitute these values into the equation: 5 = k/3.0. Solving for k, we find that k = 15.
Now, we can use the constant of variation to find S when G is 6. By substituting k = 15 and G = 6 into the equation S = k/G, we get S = 15/6 = 2.5.
Therefore, the answer to the problem is as follows:
The variation between S and G is inverse, given by the equation S = k/G, where k is the constant of variation. When S is 5 and G is 3.0, the constant of variation is found to be 15. Consequently, when G is 6, substituting the values into the equation, S is calculated to be 2.5.
Learn more about constant of variation:
https://brainly.com/question/29149263
#SPJ11
Two cyclists meet at the library and then go for a bike ride.
The distance each person has traveled from her home at x
hours from the start of the ride is linear, as shown.
Which statement must be true?
Two cyclists meet at the library and then go for a bike ride. The distance each person has traveled from her home at x hours from the start of the ride is linear, as shown.
Let's assume that cyclist A and B start at a distance x and y, respectively, from the library. Further, let's assume that cyclist A starts at t = 0. Then, the distance from the library for cyclist A at t hours after the start of the ride is represented by x + rt. The distance from the library for cyclist B at t hours after the start of the ride is represented by y + st.As the question says, the distance each person has traveled from her home at x hours from the start of the ride is linear. Thus, we can write their distances from the library as:dA(x) = x + rtdB(x) = y + st, where dA and dB represent the distance covered by cyclists A and B respectively.Now, if we want to find out the distance between the two cyclists at x hours after the start of the ride, we can use the following formula:distance between the two cyclists = dB(x) - dA(x)= (y + st) - (x + rt) = (y - x) + (s - r)tSince s and r are constants, the expression (y - x) + (s - r)t is linear with respect to t. Hence, the statement "The distance between the two cyclists is a linear function of x" must be true.
To know more about library , visit ;
https://brainly.com/question/25305703
#SPJ11
Find the area of triangle obc in terms of r and theta
The area of triangle OBC in terms of r and θ is (1/2) * r^2 * sin(θ), which simplifies to (1/2) * r^2.
To find the area of triangle OBC in terms of r and θ, we can utilize the formula for the area of a triangle: Area = (1/2) * base * height. In this case, the base of the triangle is the side BC, which has a length equal to r, and the height is the perpendicular distance from point O to side BC.
Considering that point O is the origin (0,0) and point B is located on the positive x-axis, the distance from the origin to the line BC is equal to the radius r. Thus, the height of the triangle is r.
To find the angle θ between the positive x-axis and the line BC, we can use trigonometry. Since the line BC forms an angle of θ with the positive x-axis, the perpendicular from point B to the x-axis creates a right triangle. Therefore, sin(θ) can be determined by dividing the height of the triangle (r) by the hypotenuse (also r), resulting in sin(θ) = r/r = 1.
Substituting the values into the formula for the area of a triangle, we have Area = (1/2) * r * r * 1 = (1/2) * r^2.
Therefore, the area of triangle OBC in terms of r and θ is (1/2) * r^2 * sin(θ), which simplifies to (1/2) * r^2.
Learn more about area of triangle here:
https://brainly.com/question/27683633
#SPJ11
Which sequence best represents the relationship between DNA and the traits of an organism?
DNA base sequence -> Protein shape -> Amino acid sequence -> Protein function -> Trait
DNA base sequence -> Amino acid sequence -> Protein shape -> Protein function -> Trait
DNA base sequence -> Amino acid sequence -> Protein function -> Protein shape -> Trait
DNA base sequence -> Protein function -> Amino acid sequence -> Protein shape -> Trait
The sequence that best represents the relationship between DNA and the traits of an organism is: DNA base sequence -> Amino acid sequence -> Protein function -> Protein shape -> Trait.
1. DNA base sequence: The DNA molecule contains genetic information in the form of a sequence of nucleotide bases (adenine, thymine, cytosine, and guanine). This sequence acts as a template for protein synthesis.
2. Amino acid sequence: The DNA base sequence is transcribed into mRNA, which is then translated into a sequence of amino acids. The sequence of amino acids determines the primary structure of a protein.
3. Protein function: The specific sequence of amino acids in a protein determines its function. Proteins perform various roles in cells, such as enzymatic activity, structural support, and signaling.
4. Protein shape: The sequence of amino acids determines the folding and three-dimensional structure of a protein. The shape of a protein is crucial for its proper function.
5. Trait: Proteins play a fundamental role in the expression of traits. Traits are characteristics of an organism that result from the combined effects of various proteins and their functions.
Learn more about DNA : brainly.com/question/30993611
#SPJ11
On a certain map, 2.5 inches represents 22 miles. Cucumber City and Pickleville are 8 inches apart on the map. What is the actual distance between Cucumber City and Pickleville?
The actual distance between the two cities _____ miles.
The actual distance between Cucumber City and Pickleville is 70.4 miles.
To find the actual distance between Cucumber City and Pickleville, we can use the given scale on the map and set up a proportion.
According to the map scale, 2.5 inches represents 22 miles. This means that for every 2.5 inches on the map, the actual distance in the real world is 22 miles.
Let's denote the actual distance between Cucumber City and Pickleville as 'x' miles. We know that on the map, these two cities are 8 inches apart.
Using the proportion:
(2.5 inches) / (22 miles) = (8 inches) / (x miles)
2.5 inches * x miles = 8 inches * 22 miles
2.5x = 8 * 22
2.5x = 176
x = 176 / 2.5
x = 70.4
Therefore, the actual distance between Cucumber City and Pickleville is 70.4 miles.
To know more about distance, refer here:
https://brainly.com/question/31713805
#SPJ4
The number of lattes sold daily for a coffee shop is shown in the table: Lattes 55 52 56 48 57 20 45 41 Based on the data, what is the difference between the median of the data, including the outlier and excluding the outlier? 2 3 30 52.
The difference between the median of the data, including the possible outlier, and excluding the possible outlier is 9.
Given that
The number of lattes sold daily for two coffee shops is shown in the table: Lattes 55 52 56 48 57 45 41 Based on the data.
We have to determine
What is the difference between the median of the data, including the possible outlier, and excluding the possible outlier?
According to the question
The number of lattes sold daily for two coffee shops is shown in the table: 55 52 56 48 57 20 45 41 Lattes Based on the data.
The data set with the outlier is 55 52 56 48 57 20 45 41; Meaning the median falls in between 48 and 57, which is 52.5
Then the data set without the outlier is 55 52 56 48 57 20 45 41; Making the median here 52.5
Therefore, the difference between the median of the data, including the possible outlier, and excluding the possible outlier is = 57 - 48 = 9
Hence, The difference between the median of the data, including the possible outlier, and excluding the possible outlier is 9.
Learn more about Median here:
https://brainly.com/question/26174005
#SPJ4
The carpet Zac selected sells for $2.40 a square foot. How much will it cost Zac to carpet the entrance and hallway of his house?
The entrance measures 6 feet wide and 8 feet long, and the hallway is 3 feet wide and 14 feet long. We need to calculate the area of both and then multiply by $2.40. We can do that as follows:
Entrance area = 6 feet x 8 feet
= 48 square feet
Hallway area = 3 feet x 14 feet
= 42 square feet
Total area = 48 + 42
= 90 square feet
The cost of the carpet, we can multiply the total area by the cost per square foot: $2.40/square foot x 90 square feet = $216.00
It will cost Zac $216.00 to carpet the entrance and hallway of his house if he selects the carpet that sells for $2.40 a square foot.
To know more about square visit:
https://brainly.com/question/14198272
#SPJ11
