Using coordinate geometry,
The y-intercept is the starting value (true).The slope is 1/2 or 0.5, not 121 or 3/41 (false).The y-intercept is 3/41 is also false as it contradicts the first true statement, therefore, the y-intercept is the starting value and the y-intercept of 3/41 is also true.The problem provides two pieces of information about Hannah's jogging routine: she started with 3 41 miles and added 1/21 miles every week. We can use this information to create a linear equation that represents the number of miles Hannah jogged as a function of the number of weeks she has been jogging.
To create this equation, we first identify the starting value, which is 3 41 miles. This is also the y-intercept of the line. Next, we determine the slope of the line, which is the rate at which the number of miles increases each week. The slope is equal to the change in y (miles) divided by the change in x (weeks), which in this case is (1/21 - 3/41)/1 = -2/1 = -2. Therefore, the slope of the line is -2.
Putting these two pieces of information together, we get the equation y = -2x + 3 41, where y is the number of miles jogging and x is the number of weeks of jogging. This is a linear equation in slope-intercept form, where the slope is -2 and the y-intercept is 3 41.
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a group of observations measured at successive time intervals is known as a(n) . a. additive time series model b. forecast c. time series
A group of observations measured at successive time intervals is known as a(n) time series. So, correct option is C.
A time series is a collection of observations or measurements that are taken at regular intervals over time. These observations can be of any variable that changes over time, such as stock prices, weather patterns, or population growth. Time series analysis is a statistical technique used to understand and interpret the patterns and trends in such data.
The data in a time series can be analyzed to identify trends, seasonal variations, and other patterns that may exist over time. These patterns can be used to develop forecasts and make predictions about future values of the variable being measured.
On the other hand, an additive time series model is a specific type of model used to analyze time series data. It involves decomposing a time series into its underlying components, such as trend, seasonality, and random fluctuations, and modeling each component separately.
This approach can help to improve the accuracy of forecasts and predictions based on the time series data.
In summary, a time series is a collection of observations measured at successive time intervals, while an additive time series model is a specific type of statistical model used to analyze and forecast time series data.
Therefore, Option C is correct answer.
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in a deli, the ratio of ham subs to cheese subs sold in a day was 9:4. If 36 cheese subs were sold, how many ham subs were sold?
Answer: 81 ham subs
Step-by-step explanation:
4 times 9 is 36. That means you have to multiply 9 by 9, to get 81 ham subs. The ratio is 81:36. :)
Which can cover a greater area, 2 quarters, each with a diameter of 1 inch, or 1 half dollar, with a diameter of 1. 2 inches?
The area of the half-dollar coin with a diameter of 1.2 inches is greater.
Both the given objects have a circular shape with a different diameter.
One of the objects is made up of two separate quarters of a circle, each with a diameter of 1 inch.
On the other hand, the second object is one half-dollar coin with a diameter of 1.2 inches.
We will use the formula of the area of a circle that is : A = πr²
Where A is the area of the circle.
π is the constant value (3.14)
r is the radius of the circle.
Let's calculate the area of 2 quarters each with a diameter of 1 inch.
The radius will be half of the diameter.
So, the radius is 1/2 inch for each quarter of the circle.
A = πr²A = π × (1/2)²A = π × 1/4A = 0.7854 square inches.
The total area of both quarters will be = 2 × 0.7854 square inches
The total area of both quarters = 1.5708 square inches
Now, let's calculate the area of the half-dollar coin with a diameter of 1.2 inches.
The radius will be half of the diameter.
The radius of the half-dollar coin = 1.2 / 2 = 0.6 inch
A = πr²A
= π × 0.6²A
= π × 0.36A
= 1.1318 square inches
The half-dollar coin has a greater area as compared to the two quarters of a circle.
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Dylan has $20.00 on his gift card. After some purchases, he has $0.06 remaining on his gift card. Dylan has _____% of the original amount remaining on the gift card.
Answer:
Step-by-step explanation:
To find the percentage of the original amount that Dylan has remaining on his gift card, we can divide the remaining amount by the original amount and then multiply by 100 to express it as a percentage.
The original amount on the gift card was $20.00, and the remaining amount is $0.06, so the percentage of the original amount that Dylan has remaining on his gift card is:
($0.06 ÷ $20.00) x 100% =
0.003 x 100% =
0.3%
Therefore, Dylan has 0.3% of the original amount remaining on his gift card.
graph
y = -6
4x + y = 2
if hope has 4 more quarters than nickels and they have a combined value of 280 cents, how many of each coin does she have?
Hope has 6 nickels (x) and 10 quarters (x + 4).
How many of each coin Hope has if she has 4 more quarters than nickels and they have a combined value of 280 cents. To solve this problem, we can use algebraic equations.
Let's assume the number of nickels Hope has is x. Then, the number of quarters she has would be x + 4.
Now, we need to find the total value of the coins. Each nickel is worth 5 cents, so the total value of nickels is 5x cents. Similarly, each quarter is worth 25 cents, so the total value of quarters is 25(x + 4) cents. The combined value of the coins is 280 cents, so we can set up an equation:
5x + 25(x + 4) = 280
Simplify and solve for x:
5x + 25x + 100 = 280
30x = 180
x = 6
Therefore, Hope has 6 nickels (x) and 10 quarters (x + 4).
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shen wants to earn more than $33 trimming trees. he charges $8 per hour and pays $7 in equipment fees. what are the possible numbers of hours shen could trim trees?
The answer is 4.375 hours.
Since this is not a whole number, Shen will need to trim trees for at least 5 hours in order to earn more than 33.
In order to answer this question, we need to know how much Shen is wanting to earn and what his rate of pay and equipment fees are. You've stated that Shen wants to earn more than 33 trimming trees and that he charges 8 per hour and pays 7 in equipment fees.
The formula to solve this problem is:
Earnings = Rate of Pay x Number of Hours – Equipment Fees
Therefore, we can calculate the number of hours Shen needs to trim trees in order to earn more than 33.
Number of Hours = (Earnings + Equipment Fees) / Rate of Pay
Substituting in the values provided in the question:
Number of Hours = (33 + 7) / 8
+ 4.375 hours.
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a sample of 90 adult randolph county residents showed that 59 own a home. what is the risk of owning a home?
The risk of owning a home in Randolph County based on the given sample can be calculated as:
Risk of owning a home = Number of residents who own a home / Total number of residents in the sample
Risk of owning a home = 59 / 90
Therefore, the risk of owning a home in Randolph County based on the given sample is approximately 0.656 or 65.6%.
Need help it’s due tomorrow for test corrections!!
We know that the temperature was 56°F at midnight, so we can plot the point (24, 56)
What is graph ?
Graph can be defined as visual representation of given data using the ordered pairs.
To graph Elroy's data, we can use the x-axis to represent the time of day in hours and the y-axis to represent the temperature in degrees Fahrenheit.
First, we can plot the point (6, 50) to represent the temperature at 6am.
Next, we can use the information that the temperature rose 3° per hour for the next 4 hours. This means that at 10am, the temperature would be 50 + 3(4) = 62°F. We can plot this point at (10, 62). Similarly, we can find the temperature at 7am, 8am, and 9am using the same formula and plot those points as well.
Then, we can use the information that the temperature rose 2° per hour for the next 6 hours. This means that at 4pm, the temperature would be 62 + 2(6) = 74°F. We can plot this point at (16, 74). Similarly, we can find the temperature at 11am, 12pm, 1pm, 2pm, and 3pm using the same formula and plot those points as well.
The temperature then stayed steady until 6pm, so we can draw a horizontal line at y = 74 from 4pm to 6pm.
For the next 2 hours, the temperature dropped 1° per hour. This means that at 8pm, the temperature would be 74 - 2 = 72°F. We can plot this point at (20, 72). Similarly, we can find the temperature at 7pm using the same formula and plot that point as well.
Therefore, we know that the temperature was 56°F at midnight, so we can plot the point (24, 56).
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Which equation matches the hanger diagram?
Equations are collections of two or more statements with equal signs.
I must locate the solution that the hanger diagram matches. [tex]3x=4[/tex] is the equation that fits the hanger diagram. Thus, option C is correct.
What is a hanger diagram?The hanger shows a total weight of 7 units on one side that is balanced with 3 equal, unknown weights and a 1-unit weight on the other.
Two or more expressions containing equal signs are called equations. I need to find the equation that corresponds to the hanger diagram. The hanger model is a visual representation of the equation.
Both sides must have the same weight to keep the hanger balanced. Like scales and barbells. There are 3 x on the left side of the hanger and 4 x on the right side.
So [tex]3x=4[/tex] is an equation that satisfies the given trailer diagram.
So option C is correct. [tex]3x=4[/tex] is the equation that fits the hanger diagram.
From the diagram we have,
Left=x+x+x
Right [tex]=1+1+1+1[/tex]
This gives
Left=[tex]3x[/tex]
Right [tex]=4[/tex]
Therefore, the equation [tex]3x =4[/tex]
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Question 4 In which circuit represented below are meters properly connected to measure the current through resistor R1 and the potential difference across R2? A) LWA OAA OB.B OCC ODD
In Circuit B, the ammeter is connected in series with resistor R1 and the voltmeter is connected in parallel with resistor R2.
Therefore, the circuit is correctly setup to measure the desired quantities.
The correct circuit for measuring the current through resistor R1 and the potential difference across R2 is Circuit B. Circuit B is formatted with an ammeter measuring the current through R1 and a voltmeter measuring the potential difference across R2.
An ammeter is used to measure current and should be connected in series with the component it is measuring; whereas a voltmeter is used to measure potential difference and should be connected in parallel with the component it is measuring.
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Can y answer this question please in which number does the digit 3 have a value that is 10 times as great as the value of the digit 3 in 143,728
The answer of the given question based on the greatest value is One such number is 3,043,728.
What is Number System?A number system is a system of representing and expressing numbers in a clear, concise, and organized way. The most commonly used number system is the decimal system, which is based on the numbers 0 through 9. However, there are many other number systems, including binary, octal, hexadecimal, and more.
Each number system has a set of rules and conventions for representing numbers. For example, in the decimal system, each digit can represent a value from 0 to 9, and the position of each digit determines its value.
The digit 3 in 143,728 has a value of 3 x 1000 = 3000. To find a number in which the digit 3 has a value that is 10 times as great as this, we need to find a number in which the digit 3 has a value of 10 x 3000 = 30,000.
One such number is 3,043,728. In this number, the digit 3 appears in the hundred thousands place, which means its value is 3 x 100,000 = 300,000. This is indeed 10 times as great as the value of the digit 3 in 143,728.
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The number 137 has the same relationship to the number 143 as the numbers 398,389,392, which have a digit 3 that is 10 times greater than the number 137.
What is face and place value?A number's face value is the digit itself, while its place value is determined by its placement.
In order to answer the question, we must determine which of the following integers has a value for the digit 3 that is 10 times greater:
If we pay close attention, we can see that the number 137 has a third digit in its tens place while the number 143 has a third digit in its unit place. Additionally, there are 398,389,392, which has a digit 3 and is ten times bigger than the number 137.
These numbers will be written as follows if we now express their location and value in words:
143 = 1 × 100 + 4 × 10 + 3 × 1.
137 = 1 × 100 + 3 × 10 + 7 × 1.
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The complete question is:
In which number does the digit 3 have a value that is 10 times as great as the value of the digit 3 in 143,728? 137,982 142,398 292,389 392,097.
The volume of a right cone is 2016
�
π units
3
3
. If its diameter measures 24 units, find its height.
The height of the cone is 13.38 units
What is volume of a cone?A cone is a three-dimensional shape in geometry that narrows smoothly from a flat base (usually circular base) to a point(which forms an axis to the centre of base) called the apex or vertex.
The volume of a cone = 1/3 πr²h
volume = 2016 units³
r = d/2 = 24/2 = 12 units
2016 = 1/3 × 3.14 × 12² h
6048 = 452.16h
h = 6048/452.16
h = 13.38units
therefore the height of the cone is 13.38 units
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answer two questions about the following rational division.
1. The quotient in lowest terms of the given rational division is (x+2)/(3x-9).
2. The values of r is A. x=-2 and B. x=0.
What is factor?Factor is a quantity which when multiplied by another quantity, produces a given product. Factors are used to simplify and solve equations, as well as in other areas of mathematics. Factors can be numbers, variables, and expressions.
To find the lowest terms, we must divide the numerator and denominator by the same number. The largest common factor of the numerator and denominator is 3. Dividing both the numerator and denominator by 3, we get (x+2)/(3x-9) = (x+2)/(x-3).
The values of r that must be excluded from the domains of the expressions are x=0 and x=3. x=0 must be excluded because it will create a zero in the denominator which is not allowed. x=3 must also be excluded because it will create a zero in the numerator, and thus make the entire expression equal to 0. Thus, the correct answer is A. x=-2 and B. x=0.
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A local store charges $1.97 per pound for bananas and $4.49 for a gallon of apple juice what is the cost of 1.5 lb of bananas and 1 gallon of apple juice
The expense of 1.5 lbs of bananas and 1 gallon of apple juice, according to the provided statement, is $7.45.
What does arithmetic multiple mean?Multiplication is one of the four basic operations in mathematics, along with adding, subtracting, and division. Multiply in mathematics refers to the continual adding of sets of identical size.
The cost of 1.5 lb of bananas can be found by multiplying the price per pound by the number of pounds:
Cost of 1.5 lb of bananas = 1.5 x $1.97 = $2.96 (rounded to the nearest cent)
The cost of 1 gallon of apple juice is $4.49.
So, the total cost of 1.5 lb of bananas and 1 gallon of apple juice is:
Total cost = Cost of bananas + Cost of apple juice
Total cost = $2.96 + $4.49
Total cost = $7.45
Therefore, the cost of 1.5 lb of bananas and 1 gallon of apple juice is $7.45.
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even a process that is functioning as it should will not yield output that conforms exactly to a standard. why not? multiple choice question. nonrandom variation natural variation measurement error standards change
Even a process that is functioning as it should will not yield output that conforms exactly to a standard because of natural variation.
The natural variation is the variability in the output of a system that is caused by factors that are not controlled.This type of variation is also known as common cause variation.
The output of the system is changed by natural variation in such a way that it deviates from a fixed standard. Despite this, natural variation is usually present in any system, and it cannot be entirely eliminated.
There will always be some variation, and it is vital to understand how much of it is acceptable. The output of the system may be brought back into conformity with the standard by removing the cause of special cause variation.
Measurement errors can be caused by a variety of factors, including incorrect equipment calibration, user error, or environmental factors.
These errors may be distinguished from natural variation and special cause variation because they are caused by the measurement process rather than the system itself.
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PLX SIMPLIFY -2.6+3.9b
Answer: 3.9b−2.6
Step-by-step explanation: Hope this helps
Answer:
1.3b
Step-by-step explanation:
The equation is -2.6+3.9b. A negative number acts like subtraction, so we would subtract 2.6 from 3.9 to get 1.3. The b is still there, and we don't know what it is, so we simplify the equation to 1.3b.
Sorry, this explanation isn't the best. Hope it helped! :)
Eugene had some paper with which to make note cards. on his way to his room he found 3 more pieces to use. in his room he cut each piece of paper in half. when he was done he had 12 half-pieces of paper. with how many sheets of paper did he start with?
On his journey to his room, Eugene first found a few pieces of paper before discovering three more. Let's assume that he began with x bits of paper. Eugene started with [tex]3[/tex] pieces of paper.
What is the equation?Eugene started with some pieces of paper, and then he found 3 more on his way to his room. So, let's say he started with x pieces of paper.
After finding the 3 more pieces, he had a total of [tex]x + 3[/tex] pieces of paper.
He then cut each piece of paper in half, which means he doubled the number of pieces of paper. So, he ended up with [tex]2 \times (x + 3) = 2x + 6[/tex] half-pieces of paper.
We're given that he had 12 half-pieces of paper in the end, so we can set up the equation:
[tex]2x + 6 = 12[/tex]
Solving for x, we get:
[tex]2x = 6[/tex]
[tex]x = 3[/tex]
Therefore, Eugene started with 3 pieces of paper.
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A department store is holding a fall clothing sale where $9.99 will be taken off any clothes purchased. If Taylor wants to buy a pair of pants regularly priced $34.99, how much will he spend at the sale?
helppppppppp plsssssssssssssssssss
ccording to this statement, government is held accountable by the - a king b church c laws d citizens next pageback
According to the given statement, the government is held accountable by the citizens. Citizens are the ones who elect the government and, thus, have the power to hold it accountable. This is a fundamental principle of democracy that ensures that those in power are serving the people's interests.In a democratic society, the government is accountable to the people.
This means that citizens have the right to hold elected officials accountable for their actions. This is achieved through various means such as free and fair elections, the rule of law, and the right to free speech and expression.Government officials are elected to serve the people and carry out their wishes. This means that they must be transparent and open to criticism. They must be willing to listen to citizens' concerns and take action to address them. This is why democratic societies have mechanisms in place to ensure that citizens can hold their government accountable, such as a free press and independent judiciary.In conclusion, citizens are the ones who hold the government accountable in a democratic society. They have the power to elect officials and the right to criticize them if they are not serving their interests. This ensures that those in power are always acting in the best interests of the people.
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the physician orders lanoxin elixir 0.175 mg po q.am for the patient. the pharmacy sends a bottle labeled: lanoxin elixir 0.05 mg/ml. how many milliliters will the nurse administer to the patient? write your answer as a decimal number.
The nurse should administer 3.5 mL of Lanoxin elixir 0.05 mg/mL to the patient to achieve the desired dose of 0.175 mg.
First, we need to convert the prescribed dose of 0.175 mg to milligrams per milliliter (mg/mL) using the concentration of the Lanoxin elixir, which is 0.05 mg/mL.
To determine how many milliliters of Lanoxin elixir 0.05 mg/mL the nurse should administer to the patient, we need to use a simple formula:
Dose = Desired dose / Stock strength
Where:
Desired dose is 0.175 mg
Stock strength is 0.05 mg/mL
So, substituting the values into the formula:
Dose = 0.175 mg / 0.05 mg/mL
Dose = 3.5 mL
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In a class of students, the following data table summarizes how many students have a brother or a sister. What is the probability that a student chosen randomly from the class is an only child?
The probability that a student chosen randomly from the class is an only child is 0.23 or 23%.
What is the probability?
To find the probability that a student chosen randomly from the class is an only child, we need to add up the number of students who do not have a brother and do not have a sister, and then divide by the total number of students in the class.
From the table, we can see that there are 6 students who do not have a sister and do not have a brother. Therefore, the probability that a student chosen randomly from the class is an only child is:
P(only child) = number of only children / total number of students
= 6 / (2 + 13 + 5 + 6)
= 6 / 26
= 0.23 (rounded to two decimal places)
Therefore, the probability that a student chosen randomly from the class is an only child is 0.23 or 23%.
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in a recent survey of 619 salinas residents, 437 stated they experienced significant traffic delays within the last month. if one of the 619 residents is selected at random, what is the probability they have experienced delays?
If one of the 619 residents is selected at random, the probability they have experienced delays is 70.6%.
To find the probability that a randomly selected Salinas resident has experienced significant traffic delays within the last month, we need to use the formula for probability:
Probability = Number of favorable outcomes / Total number of outcomes
In this case, the favorable outcome is the number of residents who have experienced significant traffic delays, which is 437. The total number of outcomes is the total number of residents surveyed, which is 619. Therefore, the probability is:
Probability = 437 / 619 ≈ 0.706
This means that there is a 70.6% chance that a randomly selected Salinas resident has experienced significant traffic delays within the last month, based on the given survey results.
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you need to study the satisfaction of customers of a specific restaurant. you decide to randomly select one customer at each table. this would most closely describe which type of sampling technique?
Systematic sampling is the term used to describe the sampling method portrayed in the scenario.
Systematic sampling is a form of probability sampling technique in which a researcher randomly selects a beginning point before selecting every nth item from the target population. The researcher is choosing one consumer at each table in this case, which can be interpreted as choosing every nth customer, where n is the average number of customers per table.
When the researcher wants to select a sample from a pre-defined list and the target population is broad and diverse, systematic sampling is a beneficial strategy. Because it takes less time and resources to choose the sample, it is also a more effective strategy than simple random sampling.
It is crucial to remember that systematic sampling might induce bias if the process of selection follows a pattern or is regular. For instance, bias could be introduced if the researcher only chooses consumers at tables with even numbers, producing a non-representative sample. To eliminate bias and get a representative sample, it is crucial to ensure that the selection procedure is truly random.
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a 13 foot ladder is leaning against a wall. if the top slips down the wall at a rate of 1.25 ft/s, how fast will the bottom of the ladder be moving away from the wall when the top is 12 feet above the ground?
The top of the ladder is 12 feet above the ground, the bottom of the ladder will be moving away from the wall at a rate of 0.096 ft/s.
The question is: a 13 foot ladder is leaning against a wall. If the top slips down the wall at a rate of 1.25 ft/s, how fast will the bottom of the ladder be moving away from the wall when the top is 12 feet above the ground?
To answer this question, we can use the concept of right triangle geometry. We know that when the top of the ladder is 12 feet above the ground, the bottom of the ladder is 13 feet away from the wall.
We can use the Pythagorean Theorem to calculate the hypotenuse of this right triangle, which is the total length of the ladder. This will allow us to calculate the rate at which the bottom of the ladder is moving away from the wall.
The Pythagorean Theorem states that
a^2 + b^2 = c^2,
where a and b are the lengths of the legs of a right triangle, and c is the length of the hypotenuse.
In this case, a is 12 and b is 13.
Therefore,
122 + 132 = c^2, or c^2 = 169.
Therefore, c = 13.04 feet.
This is the total length of the ladder.
We now have the total length of the ladder, so we can calculate the rate at which the bottom is moving away from the wall.
Since we know the top is moving at a rate of 1.25 ft/s, and the total length of the ladder is 13.04 feet, the bottom must be moving at a rate of (1.25/13.04) = 0.096 ft/s.
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The table below shows a set of points that have been dilated. The rule for the dilation is (x, y).
(x, y)
(0, 1)
(4,-2)
(-6,1)
True
False
Previous
(0,1)
(2,-1)
(-3,2)
O
Therefore, the table showing the original points and their corresponding dilated points is:
Original Point Dilated Point
(0,1) (0,1/2)
(4, -3) (2, -3/2)
(-6,1) (-3,1/2)
What is dilated point?I believe you might have meant "dilated point", which is a term commonly used in geometry. A dilated point is a point that has been enlarged or reduced in size with respect to a fixed center of dilation.
To dilate a point, you need to multiply its coordinates by a scale factor, which is a constant value greater than zero. If the scale factor is greater than one, the point will be enlarged, and if it is less than one, the point will be reduced in size. The fixed center of dilation is the point about which the dilated point is enlarged or reduced.
given by the question.
To apply the dilation rule of (1/2x, 1/2y) to a given point (x,y), we need to multiply the x-coordinate and y-coordinate of the original point by 1/2.
Using this rule, we can find the dilated points for the given set of points as follows:
For the point (0,1), we have:
1/2x = 1/2 * 0 = 0
1/2y = 1/2 * 1 = 1/2
So, the dilated point is (0, 1/2).
For the point (4, -3), we have:
1/2x = 1/2 * 4 = 2
1/2y = 1/2 * (-3) = -3/2
So, the dilated point is (2, -3/2).
For the point (-6,1), we have:
1/2x = 1/2 * (-6) = -3
1/2y = 1/2 * 1 = 1/2
So, the dilated point is (-3,1).
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HELP PLEASE NO ONE IS ANSWEING IT
What is the mean of this data set?
A table titled Length of Roses. The first column is labeled length in centimeters. The second column is labeled number of roses. The first row shows 2 roses measuring 22 centimeters in length. The second row shows 4 roses measuring 23 centimeters in length. The third row shows 5 roses measuring 24 centimeters in length. The fourth row shows 3 roses measuring 25 centimeters in length. The fifth row shows 1 rose measuring 26 centimeters in length.
24 cm
twenty-three and twelve-fifteenths
twenty-three and one-half
22 cm
Answer: To find the mean of the data set, you need to calculate the sum of the products of each length and its corresponding frequency, and then divide that sum by the total number of roses.
Using the data set given, the sum of the products is:
(2 * 22) + (4 * 23) + (5 * 24) + (3 * 25) + (1 * 26) = 221
The total number of roses is:
2 + 4 + 5 + 3 + 1 = 15
Therefore, the mean length of the roses is:
221 / 15 = 14.73 ≈ 24 cm
So, the answer is 24 cm.
Step-by-step explanation:
Answer:
24 but the test is wrong
Step-by-step explanation:
Soooo i dont know what the answer in the test is but the answer is 24. If you add them all up, 22 23 24 25 26, you get 120 which you then divide by 5. I dont know what the test wants u to answer tho.
there are 20 rows of seats on a concert hall: 25 seats are in the 1st row, 27 seats on the 2nd row, 29 seats on the 3rd row, and so on. if the price per ticket is $2,300, how much will be the total sales for a one-night concert if all seats are taken?
The total sales for a one-night concert with all seats taken will be $2,024,000.
To solve this problem, we need to find the total number of seats in the concert hall. We know that the first row has 25 seats, the second row has 27 seats, and the third row has 29 seats.
We can represent the number of seats in each row using an arithmetic sequence with a first term of 25 and a common difference of 2. The nth term of this sequence can be found using the formula:
a_n = a_1 + (n - 1)d
where a_1 is the first term (25), d is the common difference (2), and n is the number of the row.
Using this formula, we can find the number of seats in the 20th row
a_20 = 25 + (20 - 1)2
a_20 = 25 + 38
a_20 = 63
Therefore, the total number of seats in the concert hall is the sum of the seats in all 20 rows:
total seats = 25 + 27 + 29 + ... + 63
To find this sum, we can use the formula for the sum of an arithmetic sequence
S_n = (n/2)(a_1 + a_n)
where S_n is the sum of the first n terms of the sequence. In this case, n = 20, a_1 = 25, and a_n = 63.
S_20 = (20/2)(25 + 63)
S_20 = 10(88)
S_20 = 880
Therefore, there are a total of 880 seats in the concert hall. If all seats are taken, the total sales for the one-night concert will be
total sales = number of seats x price per ticket
total sales = 880 x $2,300
total sales = $2,024,000
Learn more about arithmetic sequence here
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In circle P with the measure of arc NQ= 82°, find m/NPQ.
Answer:
m<NPQ= 82°
Step-by-step explanation:
Below is the explanation for the answer to the assignment.