a) The ratio of lemon juice to water in Saru's lemonade, in its simplest form, is 1:5. b) If Saru uses 8 liters of water to make lemonade of the same strength, he will end up with a total volume of 1.68 liters of lemonade.
a) To find the ratio of lemon juice to water in Saru's lemonade, we divide the amount of lemon juice by the amount of water. In this case, the ratio is 42 ml (lemon juice) : 210 ml (water). We can simplify this ratio by dividing both values by their greatest common divisor, which is 42. So the simplified ratio is 1:5, meaning there is 1 part lemon juice for every 5 parts of water in the lemonade.
b) If Saru uses 8 liters of water to make lemonade of the same strength, we can use the ratio from part a) to determine the volume of lemon juice needed. Since the ratio is 1:5, for every part of lemon juice, there are 5 parts of water. Thus, 8 liters of water correspond to (8/5) liters of lemon juice. Adding these amounts together, Saru will have a total volume of (8/5 + 8) liters of lemonade, which simplifies to 1.68 liters.
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Let g be the piecewise defined function shown.
g(x)=
x + 4, −5 ≤ x ≤ −1
2 − x, −1 < x ≤ 5
Evaluate g at different values in its domain.
g(−4) =
g(−2) =
g(0) =
g(3) =
g(4) =
Please show step-by-step, I would really like to understand too.
The given function, g(x), is defined piecewise: g(x)= x+4, & -5 leq x leq -1
2-x, & -1 < x leq 5
To find the value of the function g at different values of x in its domain, we simply need to plug in the value of x into the function. This means that if we know the value of x, we can use the appropriate formula in the piecewise definition to find g(x).
g(-4) when x = -4, we use the first formula since -5 ≤ -4 ≤ -1:
g(-4) = -4 + 4
g(-4) = 0
Therefore, g(-4) = 0.g(-2)
when x = -2, we use the first formula since -5 ≤ -2 ≤ -1:
g(-2) = -2 + 4
g(-2) = 2
Therefore, g(-2) = 2.g(0)
when x = 0, we use the second formula since -1 < 0 ≤ 5:
g(0) = 2 - 0
g(0) = 2
Therefore, g(0) = 2.g(3)
when x = 3, we use the second formula since -1 < 3 ≤ 5:
g(3) = 2 - 3
g(3) = -1
Therefore, g(3) = -1.g(4)
when x = 4, we use the second formula since -1 < 4 ≤ 5:
g(4) = 2 - 4
g(4) = -2
Therefore, g(4) = -2
The final answers are: g(-4) = 0g(-2) = 2g(0) = 2g(3) = -1g(4) = -2. Therefore, the answer is in 120 words.
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Complete the division problem by determining the number that should be placed in the box.Division bracket with 13 on the left, 4498 inside, and 346 above it. Underneath the 4498, there is a minus 3900. Then there is a solid line with 598 under the line. There is a minus sign and an empty box followed by a solid line. Beneath the line, there is a 78 minus 78 underneath. There is a solid line and a 0 to end the problem.
The number that should be placed in the empty box is 13.
In the given division problem, we start by dividing 4498 by 346. The quotient obtained is written above the solid line as 13. Then, we subtract 13 times 346 (which is 4498) from 4498 itself and write the result, -3900, below the line. Next, we bring down the 598 and subtract 598 from -3900, resulting in -3498.
We continue the process, bringing down the minus sign and subtracting 78 from -3498, which gives us -3576. Finally, we bring down the 0 and subtract 0 from -3576, resulting in 0. Since there is no remainder, the division is complete. Therefore, the number that should be placed in the empty box is 13.
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Write a simplified equivalent expression for the SUM. (5x – 2) + (2x + 9)
The simplified equivalent expression for the sum (5x – 2) + (2x + 9) is 7x + 7.
This can be obtained by combining like terms, which involves adding the coefficients of x and the constant terms separately.
In the given expression, we have (5x – 2) and (2x + 9). To simplify, we can add the coefficients of x together: 5x + 2x = 7x. Similarly, we can add the constant terms: -2 + 9 = 7. Therefore, the simplified expression becomes 7x + 7, where 7x represents the combined coefficient of x and 7 represents the combined constant term.
Overall, by combining like terms, we obtain the simplified equivalent expression of the sum (5x – 2) + (2x + 9) as 7x + 7.
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Some energy workers are considered to work in the agriculture industry because their work relates to
Some energy workers are considered to work in the agriculture industry because their work relates to providing power and energy solutions specifically tailored for agricultural processes.
How to complete the statementThese employees are engaged in the creation and execution of environmentally-friendly energy systems specifically designed for agricultural operations and farming facilities.
One possible rephrased sentence could be: In order to produce renewable energy for farming activities such as irrigation and utilizing machinery, farmers could prioritize the implementation of solar panels, wind turbines, or biomass systems.
Moreover, professionals who work with energy in the agricultural sector can focus on enhancing energy effectiveness, incorporating intelligent farming techniques, or incorporating mechanisms for storing energy.
Their primary objective is to advocate for sustainable farming methods by decreasing dependence on conventional energy sources and advancing ecologically sound alternatives.
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There were 36 students that signed up to go on a field trip . On the day of the trip only 29 students were present
There were 7 students who signed up but did not attend the field trip. There were 36 students who initially signed up to go on the field trip. However, on the day of the trip, only 29 students showed up.
On the day of the field trip, only 29 students were present out of the 36 students who initially signed up.
There were 36 students who initially signed up to go on the field trip. However, on the day of the trip, only 29 students showed up. This means that 7 students who had originally signed up did not attend the trip.
The difference between the initial number of sign-ups (36) and the number of students present (29) gives us the number of students who did not show up:
36 - 29 = 7.
Therefore, there were 7 students who signed up but did not attend the field trip.
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Below is a table of approximate eye color ratios in the United States. In a random * group of 1200 U.S. people, how many people do you expect have brown eyes? Eye Color Blue Brown Green Hazel Percentage of U.S. Population 32 41 12 15
Proportion of U.S. Population with Brown Eyes = 41% / 100 = 0.41. In a random group of 1200 U.S. people, you would expect approximately 492 people to have brown eyes.
To find the expected number of people with brown eyes in a group of 1200 U.S. people, we need to calculate the proportion of people with brown eyes in the U.S. population and then apply that proportion to the group size.
First, let's calculate the proportion of people with brown eyes in the U.S. population based on the given eye color ratios:
Percentage of U.S. Population with Brown Eyes = 41%
Next, we convert this percentage to a decimal:
Proportion of U.S. Population with Brown Eyes = 41% / 100 = 0.41
Now, we can find the expected number of people with brown eyes in the group of 1200 U.S. people:
Expected Number of People with Brown Eyes = Proportion of U.S. Population with Brown Eyes * Group Size
Expected Number of People with Brown Eyes = 0.41 * 1200 = 492
Therefore, in a random group of 1200 U.S. people, you would expect approximately 492 people to have brown eyes.
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An hour before show time, only people are seated for a. According to ticket sales, % of the people have yet to arrive. How many tickets were sold for the ? Explain your thinking
An hour before show time, only people are seated for a. According to ticket sales, % of the people have yet to arrive. How many tickets were sold for the ?
Solution:Since only 200 people are seated for a show an hour before the showtime, the remaining number of people who have yet to arrive can be found by subtracting the number of people who are seated from the total number of tickets sold.Let the total number of tickets sold be t.Then the number of people who have yet to arrive is `t - 200`.The percent of people who have yet to arrive is given to be More than 250 percent. Since percentages cannot be greater than 100%, this is impossible and the problem is incorrectly stated. Therefore, the number of tickets sold cannot be determined from the given information.
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_ questions can only be answered in your head
A- random
B- on-the-page
C-out-of-left-field
D- From-my-brain
Random questions can be solved in your head. option A
What is random questions?In common usage, randomness is the apparent or actual lack of pattern or predictability in information.
A random sequence of events, symbols or steps often has no order and does not follow an intelligible pattern or combination. Individual random events are, by definition, unpredictable, but if the probability distribution is known, the frequency of different outcomes over repeated events (or "trials") is predictable
A random question has no particular pattern therefore it can be asked any how.
Therefore, we can conclude that random questions can only be answered in your heard with any research.
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Select all the expressions that are equivalent to 3 to the fourth power. 7 4 cubed 12 81 64 9 squared
Expressions that are equivalent to 3 to the fourth power are 81, 3³, and 9².
To calculate 3 to the fourth power, you need to multiply 3 by itself four times. That is, 3 x 3 x 3 x 3. The result is 81, which is one of the equivalent expressions. Another equivalent expression is 3³. This is because 3³ is equal to 3 to the third power, which is equal to 3 x 3 x 3 = 27. Multiplying 27 by 3 gives 81. Finally, 9² is also an equivalent expression because 9² is equal to 81. Therefore, the three equivalent expressions of 3 to the fourth power are 81, 3³, and 9².
Expressions that are equivalent to 3 to the fourth power are 81, 3³, and 9².To calculate 3 to the fourth power, you need to multiply 3 by itself four times. That is, 3 x 3 x 3 x 3. The result is 81, which is one of the equivalent expressions.Another equivalent expression is 3³. This is because 3³ is equal to 3 to the third power, which is equal to 3 x 3 x 3 = 27. Multiplying 27 by 3 gives 81. Finally, 9² is also an equivalent expression because 9² is equal to 81.Therefore, the three equivalent expressions of 3 to the fourth power are 81, 3³, and 9².
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The cost c of supplies for school depends on other factors lost at least 2 independent variables that could effect the cost of school supplies
Here are two independent variables that could affect the cost of school supplies:1. Inflation Rate: The inflation rate is a measure of the overall increase in prices over time.
It can impact the cost of various goods and services, including school supplies. If the inflation rate is high, the prices of school supplies may increase, leading to higher costs for purchasing these items.
2. Demand for School Supplies: The demand for school supplies can also influence their cost. Probability of Higher demand typically leads to increased prices, as suppliers may adjust their prices to match the demand. Factors such as back-to-school seasons, educational policies, and population growth can affect the demand for school supplies.
By considering the inflation rate and the demand for school supplies as independent variables, we can better understand how these factors can impact the cost of school supplies.
However, it's important to note that there could be other variables that can also affect the cost, such as production costs, supply chain disruptions, and changes in government policies related to education or trade.
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The cost c of supplies for school depends on other factors lost at least 2 independent variables that could effect the cost of school supplies?
Eric completed 75 math problems. That is 5 times as many math problems as Katie completed. How many math problems did Katie complete?
Katie completed 15 math problems. That is 5 times as many math problems as Katie completed.
Let's suppose the number of math problems that Katie solved is x.Therefore, 5 times the number of math problems that Katie solved is 5x. Eric completed 75 math problems.So, the expression representing the number of math problems that Eric solved is 75. Hence, the following equation can be written to determine the number of math problems that Katie solved:5x = 75Divide both sides by 5:x = 15Therefore, the number of math problems that Katie solved is 15.
Eric completed 75 math problems. That is 5 times as many math problems as Katie completed. How many math problems did Katie complete?Let's suppose the number of math problems that Katie solved is x.Therefore, 5 times the number of math problems that Katie solved is 5x. Eric completed 75 math problems.So, the expression representing the number of math problems that Eric solved is 75. Hence, the following equation can be written to determine the number of math problems that Katie solved:5x = 75Divide both sides by 5:x = 15Therefore, the number of math problems that Katie solved is 15.
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5. If two angles
are not adjacent, then they do not form
a linear pair.
Converse statement
inverses statement
Contrapositive statement
conditional statement
The given statement describes a relationship between two angles that are not adjacent, stating that they do not form a linear pair. The different types of logical statementsstatements from this statement are the converse statement, inverse statement, contrapositive statement, and conditional statement.
Converse statement: The converse of a conditional statement switches the hypothesis and the conclusion. In this case, the converse statement would be: If two angles do not form a linear pair, then they are not adjacent.
Inverse statement: The inverse of a conditional statement negates both the hypothesis and the conclusion. The inverse statement would be: If two angles are adjacent, then they form a linear pair.
Contrapositive statement: The contrapositive of a conditional statement switches and negates both the hypothesis and the conclusion. The contrapositive statement would be: If two angles form a linear pair, then they are adjacent.
Conditional statement: The original statement itself is the conditional statement. It follows the form: If two angles are not adjacent, then they do not form a linear pair.
These different logical statements provide alternative ways to express the relationship between angles that are not adjacent and their formation of a linear pair.
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A triangle has coordinates F(−2, 3), G(−4, 1), and H(−2, −2). The triangle is translated and its image has coordinates F’(0, 0), G’(−2, −2), and H’(0, −5). What is the correct rule for the translation? (x, y) Right-arrow (x 2, y 3) (x, y) Right-arrow (x 2, y – 3) (x, y) Right-arrow(x – 2, y 3) (x, y) Right-arrow (x – 3, y 2).
So, option (d) is the correct answer. A triangle with coordinates F(−2, 3), G(−4, 1), and H(−2, −2) is translated and its image has coordinates F’(0, 0), G’(−2, −2), and H’(0, −5). The correct rule for the translation is (x, y) → (x - 2, y - 3).
Let's find the distance and direction that the triangle is translated. The coordinates of the image are (0,0), (-2,-2) and (0,-5). We are going to get these coordinates from the original coordinates by applying a translation. Consider the vertex F first.The translation takes F to F'. In other words, we go from (-2,3) to (0,0).What did we do to get from F to F'?We subtracted 2 from the x-coordinate and 3 from the y-coordinate. In other words, we applied the rule(x, y) → (x - 2, y - 3)Thus the rule for the translation is (x, y) → (x - 2, y - 3). Therefore, option (d) (x, y) → (x - 2, y - 3) is the correct answer.
First of all, we will plot the coordinates of the initial and final triangle on the coordinate axis and name the initial triangle as FGH and the final triangle as F'G'H'As per the question, the coordinates of initial triangle are F(-2,3), G(-4,1) and H(-2,-2)The coordinates of final triangle are F'(0,0), G'(-2,-2) and H'(0,-5)Now let's find out the horizontal and vertical translation of the initial triangle to get the final triangle. To get F', we have to move 2 units in the right direction and 3 units in the upward direction. Let's see how this can be calculated:F to F' will move 2 units in the right direction and 3 units in the upward direction.-2 → 0 (2 units to the right)-3 → 0 (3 units upward)Therefore, we can say that the rule of translation is (x,y) → (x-2,y-3). So, option (d) is the correct answer.
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An X-15 flew at a top speed of 4520 mph with a max altitude of 354,200 ft. a) What would the stagnation temperature on the nose of the airplane be under those conditions
Under the given conditions and assuming an ambient temperature of 20°C, the stagnation temperature on the nose of the X-15 airplane would be approximately 2337.8 Kelvin.
We have,
Let's proceed by assuming a general value for the ambient temperature. We'll use 20°C as an approximation.
Given:
V = 7274.69 km/h
T = 20°C = 20 + 273.15 K = 293.15 K (conversion to Kelvin)
c_p = 1005 J/kg°C
Now we can substitute these values into the total temperature equation:
T(0) = T + (V² / (2 x c(p)))
T(0) = 293.15 K + ((7274.69 km/h)² / (2 x 1005 J/kg°C))
First, we need to convert the velocity from km/h to m/s:
V = 7274.69 km/h x (1000 m/km) / (3600 s/h) ≈ 2026.86 m/s
Now we can calculate the stagnation temperature:
T(0) = 293.15 K + ((2026.86 m/s)² / (2 x 1005 J/kg°C))
T(0) = 293.15 K + (4111017.56 m²/s² / 2010 J/kg°C)
T(0) ≈ 293.15 K + 2044.65 K
T(0) ≈ 2337.8 K
Therefore,
Under the given conditions and assuming an ambient temperature of 20°C, the stagnation temperature on the nose of the X-15 airplane would be approximately 2337.8 Kelvin.
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The campers asked their counselor to tell them her ag. She replied, "If you add 4 years to my present age, the result will be 2 times my campers. Five years ago my age was 3/4 of what hers will be in eight years. How old is the counslor?
To determine the age of the counsellor, we can set up a system of equations based on the given information. By solving the equations simultaneously, we find that the counsellor is currently 28 years old.
Let's denote the counsellor's present age as x and the campers' age as y. Based on the given information, we can set up the following equations:
Equation 1: x + 4 = 2y
Equation 2: x - 5 = (3/4)(y + 8)
To solve this system of equations, we can substitute the value of x from Equation 1 into Equation 2:
(2y - 4) - 5 = (3/4)(y + 8)
2y - 9 = (3/4)(y + 8)
Multiplying both sides by 4 to eliminate the fraction:
8y - 36 = 3y + 24
5y = 60
y = 12
Substituting the value of y back into Equation 1:
x + 4 = 2(12)
x + 4 = 24
x = 20
Therefore, the counsellor is currently 28 years old.
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Select at least two digital communication strategies you can control to protect yourself. Explain why you chose them and how they can safeguard you if you feel like someone is trying to cause you harm.
Two digital communication strategies you can control to protect yourself are:
1. **Strong Passwords**: One of the most effective ways to safeguard your digital communication is by using strong, unique passwords for your online accounts. A strong password should be a combination of upper and lowercase letters, numbers, and special characters. By using strong passwords and regularly updating them, you can prevent unauthorized access to your accounts. This can safeguard you if someone is trying to cause harm by attempting to gain unauthorized access to your personal information or accounts.
2. **Two-Factor Authentication (2FA)**: Enabling two-factor authentication adds an extra layer of security to your digital communication. With 2FA, you need to provide a second form of verification, such as a unique code sent to your mobile device, in addition to your password, to access your accounts. This can protect you if someone manages to obtain your password, as they would still need the second factor to gain access. 2FA makes it significantly harder for malicious individuals to compromise your accounts, providing an added safeguard against potential harm.
By implementing strong passwords and enabling two-factor authentication, you enhance the security of your digital communication and reduce the risk of unauthorized access and potential harm. These strategies provide an additional barrier against malicious activities and help ensure the confidentiality and integrity of your personal information and online accounts.
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The area of a rectangle is 400 square inches and its length is 4 times its width how many inches wide is the rectangle
The width of the rectangle is 10 inches, as it is calculated by finding the square root of the ratio of the area to the length.
Let's denote the width of the rectangle as "w" inches. According to the given information, the length of the rectangle is 4 times its width, so the length can be expressed as "4w" inches.
The formula for the area of a rectangle is length multiplied by width. In this case, the area is 400 square inches, so we have the equation:
Area = Length × Width
400 = (4w) × w
400 = 4w^2
To find the width, we can rearrange the equation and solve for "w":
4w^2 = 400
w^2 = 100
w = √100
w = 10
Therefore, the width of the rectangle is 10 inches. This means that the length of the rectangle is 4 times the width, which is 40 inches.
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Classify each statement about the function f(x)=2x3 3 as true or false.
The degree of the polynomial is 3.True. The degree of the polynomial is determined by the highest power of x, which is 3 in this case.The coefficient of the x^3 term is 2.True. The coefficient of the x^3 term is indeed 2.
The y-intercept is (0, 3).True. The y-intercept is found by setting x = 0, which results in f(0) = 2(0)^3 + 3 = 3.The graph of the function is always increasing.False. The graph of the function may not always be increasing. It depends on the sign of the coefficient of the x^3 term and the values of x. The function is an even function. False. The function is not an even function because it does not exhibit symmetry around the y-axis (i.e., f(-x) ≠ f(x)). The given function is f(x) = 2x^3 + 3. By analyzing the properties of the function and its equation, we can determine the truth or falsehood of each statement. The degree and coefficient of the x^3 term can be identified directly from the equation. The y-intercept is obtained by substituting x = 0. To determine whether the graph is increasing, we would need to examine the derivative or analyze the function's behavior at different intervals. The evenness or oddness of a function can be determined by evaluating f(-x) and comparing it to f(x).
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Q15 shelly want to attend the community college fro 2 years and transfer to the university for 2 years what will her total cost be after 4 years
Total cost after 4 years = (2 * X) + (2 * Y) + (2 * Z) + (2 * W).
To determine Shelly's total cost after 4 years of attending community college and transferring to the university, we need to consider the costs associated with each institution separately.
Community College:
Let's assume the cost of tuition per year at the community college is $X.
Shelly will attend the community college for 2 years, so the total cost for tuition at the community college would be 2 * X.
In addition to tuition, there may be other expenses such as textbooks, supplies, and fees. Let's assume these additional expenses for each year at the community college amount to $Y per year. So, the total additional expenses for 2 years would be 2 * Y.
Therefore, the total cost for Shelly's education at the community college for 2 years would be:
Total cost at community college = (2 * X) + (2 * Y)
University:
Let's assume the cost of tuition per year at the university is $Z.
Shelly will transfer to the university for 2 years, so the total cost for tuition at the university would be 2 * Z.
Similarly, there will be additional expenses for each year at the university, which we'll assume amount to $W per year. Thus, the total additional expenses for 2 years at the university would be 2 * W.
Therefore, the total cost for Shelly's education at the university for 2 years would be:
Total cost at university = (2 * Z) + (2 * W)
To calculate the total cost for Shelly's education after 4 years, we sum up the costs at the community college and the university:
Total cost after 4 years = Total cost at community college + Total cost at university
Total cost after 4 years = (2 * X) + (2 * Y) + (2 * Z) + (2 * W)
Please note that the values of X, Y, Z, and W represent the respective costs per year at the community college and the university, and these values are not provided in the question.
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On a map, the scale is 2 inches = 7 miles. What is the actual distance between the two cities if the map distance is 3 inches?
Please help
The actual distance between the two cities is 10.5 miles
How to calculate the actual distance between the two citiesFrom the question, we have the following parameters that can be used in our computation:
Scale: 2 inches = 7 miles
Given that
Map distance = 3 inches
using the above as a guide, we have the following:
1.5 * 2 inches = 7 miles * 1.5
Evaluate the products
3 inches = 10.5 miles
Hence, the actual distance between the two cities is 10.5 miles
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For a ski trip a girl sells 300 DVDs for 2 pound each she sells 250 DVDs for 2 pound and then reduces the price by 1/3 rest of the DVDs are sold for 6 pounds each What is the profit?
The profit from selling the DVDs for the ski trip is £850.
To calculate the profit, we need to determine the total revenue and the total cost.
The total revenue is calculated by adding the revenue from selling 300 DVDs at £2 each (£600), the revenue from selling 250 DVDs at £2 each (£500), and the revenue from selling the remaining DVDs at £6 each (£300). This gives us a total revenue of £1,400.
The total cost is calculated by adding the cost of purchasing 300 DVDs (£300) and the cost of purchasing 250 DVDs (£250), which gives us a total cost of £550.
To find the profit, we subtract the total cost (£550) from the total revenue (£1,400), resulting in a profit of £850.
Therefore, the profit from selling the DVDs for the ski trip is £850.
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A group of students collected distance versus time data for a model car
Which describes how the speed of the car is changing over time?
A The speed is increasing because the distance traveled during each time increment is increasing.
B The speed is increasing because the distance traveled during each time increment is decreasing.
C The speed is decreasing because the distance traveled during each time increment is increasing.
D The speed is decreasing because the distance traveled during each time increment is decreasing.
Pls help! No trolls
The correct option is C) The speed is decreasing because the distance traveled during each time increment is increasing.
The answer to the question is option C) The speed is decreasing because the distance traveled during each time increment is increasing.
Explanation:A group of students collected distance versus time data for a model car. There could be many types of data that can be collected with respect to distance and time.
For instance, distance could be in miles or kilometers, whereas time could be in seconds, minutes, or hours.In this case, the relation between the distance and time of a model car is given, and we have to describe how the speed of the car is changing over time. If the distance traveled during each time increment is increasing, then the speed is decreasing.
Thus, the correct option is C) The speed is decreasing because the distance traveled during each time increment is increasing.
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Andrea joined a movie club in which members can purchase movies for$12 each, after paying the lifetime membership fee. Including the fee her average cost per movie is $16. If she has purchased 24 movies what is the cost of the lifetime membership?
The cost of the lifetime membership in the movie club is $96. To find the cost of the lifetime membership, we can subtract the cost of the movies from the total amount paid by Andrea.
The average cost per movie is $16, and she has purchased 24 movies. Therefore, the total cost of the movies is $16 * 24 = $384.
Since the membership fee is included in the average cost per movie, we can calculate the cost of the lifetime membership by subtracting the total cost of the movies from the total amount paid. So, the lifetime membership fee is $384 - ($12 * 24) = $96.
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find the median 0-10 10-20 20-30 30-40 40-50 50-60 frequency 5,8,20,12,7,5
The median 0-10 10-20 20-30 30-40 40-50 50-60 frequency 5, 8, 20, 12, 7, 5 is 39.58.
To find the median 0-10 10-20 20-30 30-40 40-50 50-60 frequency 5, 8, 20, 12, 7, 5, follow the steps below:
Step 1: Write the frequency of each class in a column.Frequency05,820,312,75,Step 2: Find the total frequency.
N = 5 + 8 + 20 + 12 + 7 + 5N = 57Step 3: Find the median class.
The median class is the class where the cumulative frequency is equal to N/2 or the total frequency divided by 2. Thus, N/2 = 57/2 = 28.5The cumulative frequency starting from the first class is 5, which is less than 28.5. Therefore, the median class falls within the 20-30 class.
Step 4: Find the lower limit and upper limit of the median class.
The lower limit of the median class is 20 and the upper limit is 30.Step 5: Find the class width. Class width = Upper limit – Lower limit Class width = 30 – 20Class width = 10Step 6: Find the median. Median = L + [(N/2 – CF) / f] × w Where, L = lower limit of the median class N = total frequency CF = cumulative frequency of the class preceding the median class f = frequency of the median class w = class width Substitute the values: Median = 20 + [(28.5 – 5) / 12] × 10Median = 20 + (23.5 / 12) × 10Median = 20 + 19.58Median = 39.58
Therefore, the median 0-10 10-20 20-30 30-40 40-50 50-60 frequency 5, 8, 20, 12, 7, 5 is 39.58.
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Find the value of CT. (Show all work) Given that RT || AC, SR = 25, SA = 15, and ST = 20, find CT. A T R Find the value of CT. (Show all work) Type only the number
The value of CT is 11.25 units. Given that RT || AC, SR = 25, SA = 15, and ST = 20,
Explanation: we need to find CT.As RT || AC,
we can apply the property, "If a line is parallel to a side of the triangle and it intersects the other two sides of the triangle in two distinct points, then the line divides those sides proportionally.
"Now, using this property, we can say; ST/SA = RT/CT20/15 = RT/CT4/3 = RT/CTCT = 3RT/4
Now, we can apply the Pythagoras theorem in triangle RST,
RS² + ST²
= RT²RT²
= RS² + ST²
= 25² - 20²RT
= √(25² - 20²)
= √225 = 15 units
CT = 3RT/4
= 3 × 15/4
= 45/4 units
= 11.25 units (approx)
Therefore, the value of CT is 11.25 units.
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What equation could you make when a quadratic equation has a vertical stretch of 4, shift to the left 2 units, and moved up 5 units?
Given that a quadratic equation has a vertical stretch of 4, shift to the left 2 units, and moved up 5 units.In general form the equation for a quadratic function is given by y = ax2 + bx + c
If a is negative, the graph is reflected over the x-axis. And, if a is greater than 1 or less than -1, then the graph will be stretched/compressed in the y-direction and narrow/widen in the x-direction.To obtain the equation for the quadratic function with the given conditions we will use the transformation of quadratic functions. The transformation of a quadratic function
f(x) = ax2 + bx + c
is given by the following formulas:Vertical stretch or compression: g(x) = a · f(x)Horizontal shift:
g(x) = f(x ± h)
Vertical shift: g(x) = f(x) ± k
Therefore, the transformation of
f(x) = ax2 + bx + c to g(x) = a ·
f(x + h) + k is: $$\large
y = a(x-h)^2+k$$Where, a = 4
(vertical stretch), h = 2
(shift to the left) and k = 5
(moved up).Thus, the equation of the quadratic function with the given transformations is:
y = 4(x + 2)² + 5
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A ship’s sonar detects a submarine 880 feet below a point on the ocean’s surface 1450 ft dead ahead of the ship. To the nearest degree, find the angle x. A right triangle. Angle x is opposite to side with length 880 feet. Another side is 1450 feet. The hypotenuse is not labeled. A. 59º b. 37º c. 31º d. 53º.
The measure of the angle x is 59 degrees. Option A
How to determine the valuesThe different trigonometric identities are listed as;
sinecosinetangentcotangentsecantcosecantFrom the information given, we have that;
The measure of the adjacent is 880 feet
The opposite side is the ocean's surface = 1450 feet
The angle is x
Using the tangent identity, we have;
tan θ = opposite/adjacent
Now, we have to substitute the values, we get;
tan x = 1450/880
Divide the values, we get;
tan x = 1. 6477
Take the tangent inverse, we get;
x = 59 degrees
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If f(x)=x-1/3 and g(x)=3x+1 what is (f times g)(x)?
3x+1
x-3
3x
x
The expression (f times g)(x) represents the product of the functions f(x) and g(x). In this case, f(x) = x - 1/3 and g(x) = 3x + 1. To find the product, we substitute g(x) into f(x) and simplify the expression.
When we substitute g(x) into f(x), we get:
(f times g)(x) = f(g(x)) = f(3x + 1)
Now, substituting the expression for f(x) into f(g(x)), we have:
f(g(x)) = (3x + 1) - 1/3
Simplifying further, we combine like terms:
= 3x + 1 - 1/3
Thus, the product of f(x) and g(x), (f times g)(x), simplifies to:
(f times g)(x) = 3x + 1 - 1/3
(f times g)(x) equals 3x + 1 - 1/3.
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What is the greatest common factor of 24s3, 12s4, and 18s?
3
6
3s
6s
Mark this and return
The greatest common factor (GCF) of the given expressions 24s^3, 12s^4, and 18s is 6s.
To find the GCF, we need to identify the highest power of each variable (s) that appears in all the expressions. In this case, the highest power of s that appears in all the expressions is s^3.Next, we consider the numerical coefficients. The GCF of the numerical coefficients 24, 12, and 18 is 6.
Finally, we combine the GCF of the numerical coefficients (6) with the highest power of the variable (s^3) to obtain the GCF of the entire expressions, which is 6s^3.Therefore, the greatest common factor of 24s^3, 12s^4, and 18s is 6s^3.
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Handcuffs poem for grade 10
quote three aspects of fleas that the poem describes
In the poem "Handcuffs," three aspects of fleas that are described are their agility, resilience, and annoyance.
Agility: The poem portrays fleas as incredibly agile creatures, capable of leaping and maneuvering with great speed and precision. This is evident in lines such as "Fleas vault and vault and vault" and "Fast and still faster."
Resilience: The poem highlights the resilience of fleas, emphasizing their ability to withstand challenges and survive. It mentions how they "triumph over hand and fist" and how they continue to thrive despite efforts to capture and control them.
Annoyance: The poem presents fleas as annoying pests that invade and disrupt one's peace. The line "They come unbidden" signifies their intrusive nature and the annoyance they cause to the narrator.
Overall, the poem captures the agile, resilient, and bothersome qualities of fleas.
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