Two triangles created by the intersection of two transversals between parallel lines will always be similar. This is because when two parallel lines are cut by a transversal, two of which are congruent alternate interior angles.
Since the third angle of a triangle is equal to 180 degrees minus the sum of the other two angles, both triangles will have an equal third angle, making them similar. Additionally, the fourth angle in both triangles will also be congruent. This means that the two triangles will share two congruent angles and a proportional side. Therefore, the two triangles are similar.
If the parallel lines and the transversal are drawn to scale, then the sides of the triangles will also be proportional to each other. This is because the transversal divides the parallel lines into segments with the same ratio as the corresponding sides of the triangles. This means that the sides of the triangles will be proportional to each other, making them similar.
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Every year, a teacher surveys his students about the number of hours a week they watch television. In 2002, his students watched an average of 12 hours of television per week. In 2012, the number of hours spent watching television decreased to five per week. What is the percent decrease in the hours of television watched, rounded to the nearest tenth? 5. 8% 4. 2% 41. 7% 58. 3%.
The percent decrease in the hours of television watched, rounded to the nearest tenth is 58.3%. option 4
To determine the percent decrease in the hours of television watched, rounded to the nearest tenth, given that every year, a teacher surveys his students about the number of hours a week they watch television, in 2002, his students watched an average of 12 hours of television per week, while in 2012, the number of hours spent watching television decreased to five per week.
We can use the formula:
percent decrease = [(original value - new value) / original value] × 100%
Substituting the values given in the formula,
percent decrease = [(12 - 5) / 12] × 100%
percent decrease = (7 / 12) × 100%
percent decrease = 0.58333 × 100%
percent decrease = 58.333%
Therefore, the percent decrease in the hours of television watched, rounded to the nearest tenth is 58.3%.
Thus, option 4 (58.3%) is correct.
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A florist company makes regular and mini bouquets for sale. The florist has 100 bouquets and 60 peonies to use. Each regular bouquet has 6 roses and 2 peonies and each minibouquet has 2
roses and 2 peonies. How many of each type of bouquet does the florist make?
Let's assume the number of regular bouquets as "x" and the number of mini bouquets as "y".
According to the given information, each regular bouquet has 6 roses and 2 peonies, and each mini bouquet has 2 roses and 2 peonies.
Therefore, the total number of roses used in the regular bouquets would be 6x, and the total number of peonies used in the regular bouquets would be 2x.
Similarly, the total number of roses used in the mini bouquets would be 2y, and the total number of peonies used in the mini bouquets would be 2y.
We also know that the florist has a total of 60 peonies available.
So, the equation for the total number of peonies used in both types of bouquets would be:
2x + 2y = 60
Now, let's consider the total number of bouquets. The florist has a total of 100 bouquets.
So, the equation for the total number of bouquets would be:
x + y = 100
We have two equations:
2x + 2y = 60
x + y = 100
We can solve these equations to find the values of x and y, representing the number of regular and mini bouquets, respectively.
Using any suitable method for solving linear equations, we find that x = 30 and y = 70.
Therefore, the florist makes 30 regular bouquets and 70 mini bouquets.
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The depth of a river changes after a heavy rainstorm. Its depth, in feet, is modeled as a function of time in hours. Consider this graph of the function. Image What is the average rate of change for the depth of the river, measured as feet per hour, between hour 9 and hour 18? Show your work.
The average rate of change for the depth of the river between hour 9 and hour 18 is 1.5 feet per hour.
To calculate the average rate of change, we need to find the difference in the depth of the river between the two time points (18 - 9 = 9) and divide it by the time elapsed (18 - 9 = 9). The depth increases by 13.5 feet (16 - 2.5 = 13.5) during this time period. Therefore, the average rate of change is 13.5 feet / 9 hours = 1.5 feet per hour.
To calculate the average rate of change for the depth of the river between hour 9 and hour 18, we first need to find the difference in the depth of the river between these two time points. By examining the graph, we can see that the depth at hour 9 is approximately 2.5 feet, and the depth at hour 18 is approximately 16 feet.
The difference in depth between these two time points is 16 - 2.5 = 13.5 feet. This represents the overall change in depth during the given time period.
Next, we need to determine the time elapsed between hour 9 and hour 18, which is 18 - 9 = 9 hours.
Finally, to find the average rate of change, we divide the change in depth (13.5 feet) by the time elapsed (9 hours). This gives us an average rate of change of 13.5 feet / 9 hours = 1.5 feet per hour.
Therefore, the average rate of change for the depth of the river between hour 9 and hour 18 is 1.5 feet per hour.
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An object is moving at a speed of 6 feet per day. Express this speed in miles per year. Round your answer to the nearest hundredth.
The speed of the object, which is moving at 6 feet per day, can be expressed as approximately 0.00114 miles per year. To calculate this, we convert the feet to miles and the days to years.
To convert feet to miles, we divide the distance in feet by the number of feet in a mile. Since there are 5,280 feet in a mile, we divide 6 feet by 5,280 feet/mile, which gives us 0.00113636 miles.
Next, we convert the speed from per day to per year. Since there are approximately 365.25 days in a year (accounting for leap years), we multiply the speed in miles per day by 365.25 days/year. Multiplying 0.00113636 miles/day by 365.25 days/year gives us 0.41475 miles/year.
Rounding this answer to the nearest hundredth, we get approximately 0.41 miles per year.
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What is the total area of the top surface of all 16 solar panels? Describe the process you used to solve the problem. (4 points)
To find the total area of the top surface of all 16 solar panels, we need to know the dimensions of each individual panel and then multiply the area of one panel by the total number of panels.
To solve the problem, we first need to determine the dimensions of a single solar panel. Let's assume the length of a panel is L and the width is W. The area of one panel can be calculated by multiplying the length and width: A = L * W.
Once we have the area of one panel, we can calculate the total area of all 16 panels by multiplying the area of one panel by the total number of panels: Total Area = A * 16.
By knowing the specific dimensions of a single solar panel, we can substitute the values into the equation and calculate the total area of the top surface of all 16 panels.
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Juan got paid $40 for mowing a yard. He spent $5.99 on lunch and $1.79 on water later that day. Juan used the model below to explain to his parents how much money he had left.
Juan earned $40 for mowing a yard and incurred expenses of $5.99 for lunch and $1.79 for water. Therefore, his total expenses amount to $5.99 + $1.79 = $7.78.
To calculate the amount of money he has left, we subtract his total expenses from his initial earnings: $40 - $7.78 = $32.22.
Juan's earnings of $40 are his starting point. From this, we deduct the expenses he incurred, which consist of the lunch cost of $5.99 and the water cost of $1.79.
Combining these expenses gives us a total of $7.78. By subtracting this total from his initial earnings, we find that Juan has $32.22 remaining. This represents the amount of money he has left after paying for his lunch and water. Juan can now inform his parents that he still has $32.22 available.
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A 3-gallon bottle of bleach costs $15.60. What is the price per quart?
We know that the bottle contains 3 gallons of bleach. More than 250 quarts can be produced from 3 gallons. Let's find out how many quarts there are in a gallon.1 US gallon is equivalent to 4 US quarts.
So 3 gallons equal 12 quarts. Hence, More than 250 quarts can be obtained from 3 gallons, since more than 250 is greater than 12.Therefore, we can find the price per quart by dividing the total cost by the total number of quarts: Price per quart = Total cost ÷ Total number of quarts Since the cost of a 3-gallon bottle of bleach is $15.60, the cost of 1 gallon would be $15.60 ÷ 3 = $5.20.The cost of one quart is $5.20 ÷ 4 = $1.30.Therefore, the price per quart is $1.30.
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Plane 1 travels 450 miles south in 2 hours with a very strong tailwind. Plane 2 travels 525 miles north in 3 hours, this time against the same wind speed, with an air speed 3 times faster than plane 1.
- Plane 1 travels at a speed of 225 mph.
- Plane 2 has an airspeed of 3 times faster than Plane 1, which is 3 * 225 mph = 675 mph.
- The wind speed is 500 mph.
Let's analyze the information provided:
Plane 1:
- Distance traveled: 450 miles
- Direction: South
- Time taken: 2 hours
Plane 2:
- Distance traveled: 525 miles
- Direction: North
- Time taken: 3 hours
- Airspeed: 3 times faster than Plane 1
We can calculate the speed of Plane 1 and the wind speed by dividing the distance traveled by the time taken.
Plane 1's speed = Distance / Time = 450 miles / 2 hours = 225 miles per hour (mph)
Let's assume the speed of the wind is W mph.
For Plane 2, since it is traveling against the wind, we need to consider the effect of the wind on its speed. The effective speed of Plane 2 against the wind can be calculated as the airspeed of Plane 2 minus the wind speed.
Effective speed of Plane 2 = Airspeed of Plane 2 - Wind speed = 3 * Plane 1's speed - W
Now we can use the formula: Speed = Distance / Time to calculate the wind speed.
For Plane 2:
Effective speed of Plane 2 = Distance / Time = 525 miles / 3 hours = 175 mph
175 mph = 3 * 225 mph - W
W = 3 * 225 mph - 175 mph
W = 675 mph - 175 mph
W = 500 mph
The wind speed is calculated to be 500 mph.
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Luna is building a scale model of the Empire State building for the youth center the real empire staple building is 1250 feet high if Luna is making the motto at a scale of 1 foot to 250 feet how tall will her model be
Answer: If Luna is making the model of the Empire State Building at a scale of 1 foot to 250 feet, we can determine the height of her model by multiplying the height of the actual building by the scale factor.
Height of the model = Height of the actual building * Scale factor
Given that the height of the actual Empire State Building is 1250 feet, and the scale factor is 1 foot to 250 feet, we can calculate the height of Luna's model as follows:
Height of the model = 1250 feet * (1/250) = 5 feet
Therefore, Luna's model of the Empire State Building will be 5 feet tall.
4. A ruby crystal has a composition (Al0.99 Cr0.01 )2 O3 . How many Cr3. ions are there in a ruby of dimensions 1 cm3
In a ruby crystal with the composition (Al0.99Cr0.01)2O3, there are approximately 3.7 x 10^18 Cr3+ ions in a ruby of dimensions 1 cm^3. It is based on the molar mass and Avogadro's number.
To determine the number of Cr3+ ions in the ruby crystal, we need to consider the composition of the crystal and use some basic calculations. The composition (Al0.99Cr0.01)2O3 indicates that for every two formula units of the crystal, there is a total of 0.01 moles of Cr present.
First, we calculate the molar mass of Cr3+, which is 51.996 g/mol. Since the crystal has a composition of 0.01 moles of Cr, we can calculate the mass of Cr in the crystal as follows:
Mass of Cr = (0.01 moles) * (51.996 g/mol) = 0.52 g
Next, we convert the mass of Cr to the number of Cr3+ ions using Avogadro's number, which is approximately 6.022 x 10^23 ions/mol. The number of Cr3+ ions is given by:
Number of Cr3+ ions = (Mass of Cr) / (Molar mass of Cr3+) * Avogadro's number
Number of Cr3+ ions = (0.52 g) / (51.996 g/mol) * (6.022 x 10^23 ions/mol)
Calculating this expression gives us approximately 3.7 x 10^18 Cr3+ ions.
Therefore, in a ruby crystal with the given composition and dimensions of 1 cm^3, there are approximately 3.7 x 10^18 Cr3+ ions present.
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The amount of money Ms. Haley spends on nice restaurants is normally distributed with a mean of $180 and a standard deviation of $30. Using the Empirical Rule, what percent of Ms. Haley's nice...
68% of Ms. Haley's nice restaurant Expenses are between $150 and $210.
- 95% of her expenses are between $120 and $240.
- 99.7% of her expenses are between $90 and $270.
The Empirical Rule, we can determine the percentage of Ms. Haley's nice restaurant expenses based on the mean and standard deviation of her spending.
The Empirical Rule states that for a normally distributed dataset:
- Approximately 68% of the data falls within one standard deviation of the mean.
- Approximately 95% of the data falls within two standard deviations of the mean.
- Approximately 99.7% of the data falls within three standard deviations of the mean.
In this case, the mean of Ms. Haley's nice restaurant expenses is $180, and the standard deviation is $30.
1. Within one standard deviation:
The range within one standard deviation of the mean is from $180 - $30 = $150 to $180 + $30 = $210. This represents approximately 68% of the data.
2. Within two standard deviations:
The range within two standard deviations of the mean is from $180 - 2*$30 = $120 to $180 + 2*$30 = $240. This represents approximately 95% of the data.
3. Within three standard deviations:
The range within three standard deviations of the mean is from $180 - 3*$30 = $90 to $180 + 3*$30 = $270. This represents approximately 99.7% of the data.
Therefore, approximately:
- 68% of Ms. Haley's nice restaurant expenses are between $150 and $210.
- 95% of her expenses are between $120 and $240.
- 99.7% of her expenses are between $90 and $270.
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JoAnn and Lupe live straight down the street form their school. JoAnn walks 5/6 mile and Lupe walks 7/8 mile home from school everyday. Draw a number line to mode how far each girl walks. Who walks the lease?
Given JoAnn and Lupe live straight down the street from their school. JoAnn walks 5/6 mile and Lupe walks 7/8 mile home from school every day. JoAnn walks less than Lupe.
Mark the number line at 0, 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8 to represent the distance Lupe walks. Thus, JoAnn walks less than Lupe.
A number line is used to represent the distance traveled by the girls home from school. To construct the number line, you should use a ruler, and draw a straight line from left to right. Using the ruler, mark off equally spaced points on the line. Each mark represents the same distance.
For the first girl, JoAnn, she walks 5/6 mile. Hence, the number line should be drawn in 6 equal parts. So, mark the line at 0, 1/6, 2/6, 3/6, 4/6 and 5/6 to represent the distance she walks. Then, JoAnn’s mark should be placed at 5/6 on the number line. For the second girl, Lupe, she walks 7/8 mile. Hence, the number line should be drawn in 8 equal parts. So, mark the line at 0, 1/8, 2/8, 3/8, 4/8, 5/8, 6/8, 7/8 to represent the distance she walks. Then, Lupe’s mark should be placed at 7/8 on the number line.
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Your teacher is looking to purchase TWOactivities to use next week. She finds a smallonline store called Charlie's Angels. The store ha28 pixel activities, 18 puzzles, and 11 mazes forsale. Your teacher thinks they are all fantasticand has a hard time choosing. She is going torandomly select TWO of them for purchase. Foobvious reasons, she does not want to purchasithe same activity twice, so once it is chosen itdoes not get put back. Express the probabilitythat she selects TWO puzzles in lowest terms
The teacher wants to buy two activities from an online store that has 28 pixel activities, 18 puzzles, and 11 mazes. She is going to randomly choose two of these activities without returning them to the group of choices.
We need to calculate the probability that she selects two puzzles and express the answer in lowest terms. To find the probability that she selects two puzzles, we need to use the formula for probability of independent events :P(A and B) = P(A) × P(B), where P(A and B) is the probability of selecting A and B, and P(A) and P(B) are the probabilities of selecting A and B respectively. Let P(puzzle) be the probability of selecting a puzzle from the group of choices. The probability of selecting a puzzle on the first draw is: P(puzzle on first draw) = 18/(28 + 18 + 11) = 18/57.
For the second draw, there will be one less puzzle to choose from, since the teacher will not choose the same activity twice. the probability of selecting a puzzle on the second draw is: P(puzzle on second draw) = 17/(28 + 17 + 11) = 17/56.Now we can use the formula to find the probability of selecting two puzzles:P(puzzle and puzzle) = P(puzzle on first draw) × P(puzzle on second draw) = (18/57) × (17/56) = 153/1148 = 0.133.The probability of selecting two puzzles in lowest terms is 153/1148.
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in order to open a mystery door you must put in a 3 diget code hints -the last two digets are the least common multiple of 5 and 6 the hundrends diget is the greatest common factor of 12 and 18
To open the mystery door, you need to input a 3-digit code. The code calculated using least common multiple to open the mystery door is 630.
Based on the given hints, let's determine the code.
Hint 1: The last two digits are the least common multiple of 5 and 6.
The least common multiple (LCM) of 5 and 6 is 30.
Hint 2: The hundreds digit is the greatest common factor of 12 and 18.
The greatest common factor (GCF) of 12 and 18 is 6.
Putting these hints together, we can construct the 3-digit code:
The hundreds digit is 6, and the last two digits are 30.
Therefore, the code to open the mystery door is 630.
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What is the slope of a line perpendicular to the line whose equation is
4x — 6y = –24. Fully simplify your answer.
The slope of a line perpendicular to the line given by the equation 4x - 6y = -24 is -3/2.
To find the slope of a line perpendicular to the line given by the equation 4x - 6y = -24, we first need to put this equation in slope-intercept form: y = mx + b, where m is the slope and b is the y-intercept.
Rearranging the given equation, we get:
4x - 6y = -24
-6y = -4x - 24
y = (2/3)x + 4
So the slope of the original line is m = 2/3.
For a line that is perpendicular to this line, the slope will be the negative reciprocal of the original slope. That is, if the original slope is m, then the slope of the perpendicular line will be -1/m.
So for the line given by the equation 4x - 6y = -24, the slope of a line perpendicular to it is:
-1/m = -1/(2/3) = -3/2
Therefore, the slope of a line perpendicular to the line given by the equation 4x - 6y = -24 is -3/2.
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1. Is it possible for Jada to have 4 quarters and 13 dimes in her pocket? Explain how you know.
2. How many quarters and dimes must Jada have? Explain your reasoning
It is not possible for Jada to have 4 quarters and 13 dimes in her pocket. This is because there are only 25 cents in one quarter, so having 4 quarters would give a total value of 4 * 25 = 100 cents.
On the other hand, there are 10 cents in one dime, so having 13 dimes would give a total value of 13 * 10 = 130 cents. Therefore, the combined value of 4 quarters and 13 dimes would be 100 + 130 = 230 cents, which is not equivalent to any commonly used currency value. Hence, it is not possible for Jada to have 4 quarters and 13 dimes in her pocket.
To determine how many quarters and dimes Jada must have, we need to consider the value of each coin and find a combination that matches the desired total value. Let's assume Jada wants to have a total value of $1.00. Since one quarter is worth 25 cents and one dime is worth 10 cents, we can create the equation:
(25 * q) + (10 * d) = 100
where q represents the number of quarters and d represents the number of dimes. By solving this equation, we can find the values of q and d that satisfy the condition.
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A local little leaguehas a total of 95 players of whom 40 precent left handed how many left handed players are there
There are 38 left-handed players in the local little league.
Given that a local little league has a total of 95 players, of whom 40 percent are left-handed.
Formula used: Percentage = (Given value/Total value) × 100
According to the problem,
Given total number of players = 95
Given Percentage of left-handed players = 40%
We need to find the number of left-handed players.
So, we will use the formula of the percentage to find the number of left-handed players:
Percentage = (Given value/Total value) × 100
Number of left-handed players = (40/100) × 95
Number of left-handed players = 38
Therefore, there are 38 left-handed players in the local little league.
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P(sum of 4) when a four sided number polyhedron with numbers 1 through 4 is rolled twice
The probability of obtaining a sum of 4 when rolling a four-sided number polyhedron twice is 2/16 or 1/8.
A four-sided number polyhedron, also known as a tetrahedron, has four faces labeled with the numbers 1, 2, 3, and 4. When rolling this polyhedron twice, we need to determine the probability of obtaining a sum of 4.
To find the total number of outcomes, we multiply the number of outcomes for each roll. Since there are four possible outcomes for each roll, the total number of outcomes is 4 * 4 = 16.
Next, we need to count the number of favorable outcomes, which are the combinations of rolls that result in a sum of 4. The possible combinations are (1, 3), (2, 2), and (3, 1). Therefore, there are three favorable outcomes.
Finally, we calculate the probability by dividing the number of favorable outcomes by the total number of outcomes. The probability of obtaining a sum of 4 is 3/16.
In fraction form, this simplifies to 1/8, indicating that the probability of rolling a sum of 4 when using a four-sided number polyhedron twice is 1 out of 8 possible outcomes.
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The academic motivation and study habits of female students as a group are better than those of males. The Survey of Study Habits and Attitudes (SSHA) is a psychological test that measures these factors. The distribution of SSHA scores among the women at a college has mean 120 and standard deviation 28, and the distribution of scores among male students has mean 105 and standard deviation 35. You select a single male student and a single female student at random and give them the SSHA test.
What is the expected value of the difference (female minus male) between their scores?
What is the probability that a randomly selected Male would have a higher score than a Randomly selected female?
The probability that a randomly selected male would have a higher SSHA test score than a randomly selected female is approximately 0.385.
To find the expected value of the difference (female minus male) between their SSHA test scores, we need to use the formula:
Expected value = E(female) - E(male)
where E(female) is the expected value of the SSHA test score for a female student, and E(male) is the expected value of the SSHA test score for a male student.
Using the given means and standard deviations, we can find the expected values:
E(female) = 120
E(male) = 105
Therefore, the expected value of the difference (female minus male) between their SSHA test scores is:
Expected value = E(female) - E(male) = 120 - 105 = 15
So we can expect that the female student will score, on average, 15 points higher than the male student.
To find the probability that a randomly selected male would have a higher SSHA test score than a randomly selected female, we need to use the formula for the standardized normal distribution:
z = (x - μ) / σ
where z is the standard score, x is the SSHA test score, μ is the mean, and σ is the standard deviation.
Using the given means and standard deviations, we can find the z-scores for the male and female students:
z_male = (x - 105) / 35
z_female = (x - 120) / 28
To find the probability that a randomly selected male would have a higher score than a randomly selected female, we need to find the probability that z_male is greater than z_female. This can be done using a standard normal distribution table or a calculator, and we find that the probability is approximately 0.385.
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Which two terms can be combined in this expression? 6 3. 2 m two-fifths n minus StartFraction m over 5 EndFraction 6 and 3. 2 m 3. 2 m and Negative StartFraction m over 5 EndFraction Two-fifths n and Negative StartFraction m over 5 EndFraction 6 and Negative StartFraction m over 5 EndFraction.
To combine terms, we look for similarities or coefficients that can be added or subtracted. In the given expression, the terms that can be combined are 6 and Negative (m/5).
The given expression includes various terms: 6, 3.2m, two-fifths n, and Negative (m/5). To combine terms, we look for similarities or coefficients that can be added or subtracted.
Among the given terms, the terms 6 and Negative (m/5) can be combined. Since they both have numerical coefficients, we can add or subtract them.
Therefore, we can combine the terms 6 and Negative (m/5) to simplify the expression.
It's important to note that the combination of terms depends on the context of the expression and the desired simplification. Other combinations may be possible depending on the specific requirements of the problem.
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Let x = a bi and y = c di and z = f gi. Which statements are true? Check all of the boxes that apply. X y = y x (x × y) × z = x × (y × z) x – y = y – x (x y) z = x (y z) (x – y) – z = x – (y – z).
The true statements are: - (x × y) × z = x × (y × z) and - (x – y) – z = x – (y – z)
Let's evaluate each statement:
1. X y = y x:
This statement is generally not true for complex numbers. Multiplication of complex numbers is not commutative, so in most cases, X y is not equal to y x.
2. (x × y) × z = x × (y × z):
This statement is true. The associative property holds for multiplication of complex numbers. The order of multiplication does not affect the final result.
3. x – y = y – x:
This statement is generally not true for complex numbers. Subtraction of complex numbers is not commutative, so in most cases, x - y is not equal to y - x.
4. (x y) z = x (y z):
This statement is true. The associative property holds for multiplication of complex numbers. The order of multiplication does not affect the final result.
5. (x – y) – z = x – (y – z):
This statement is true. The associative property holds for subtraction of complex numbers. The order of subtraction does not affect the final result.
To summarize, the true statements are:
- (x × y) × z = x × (y × z)
- (x – y) – z = x – (y – z)
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Is the following event Independent or Dependent:Yolanda grabs 2 red checkers, replacing between.
The correct answer is that the event you described is dependent.
When Yolanda grabs 2 red checkers and replaces them between each draw, the outcome of the first draw affects the probability of the second draw. This is because replacing the checkers means that the probability of drawing a red checker remains the same for each individual draw, but the overall probability changes after each draw.
Let's break it down:
In the first draw, Yolanda has a certain probability of drawing a red checker.
After the first draw, if Yolanda indeed drew a red checker, there is one less red checker in the pool and the total number of checkers has decreased.
In the second draw, Yolanda now has a different probability of drawing a red checker compared to the first draw because the pool of available checkers has changed.
Therefore, the outcome of the first draw affects the probability of the second draw, making the event dependent.
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Kylie has a box for her hair clips as shown below. Which equation did Kylie use to find the volume of her box of hair clips?
The length, width, and height of the box using appropriate units (e.g., centimeters, inches) and then multiply these measurements together to calculate the volume of the box.
Since there is no specific diagram or equation mentioned in the question, I am unable to determine the exact equation Kylie used to find the volume of her box of hair clips. However, I can provide a general equation for finding the volume of a rectangular prism, which is commonly used to represent a box shape.
The equation for finding the volume of a rectangular prism is:
Volume = Length × Width × Height
In the context of Kylie's box of hair clips, she would need to measure the length, width, and height of the box using appropriate units (e.g., centimeters, inches) and then multiply these measurements together to calculate the volume of the box.
It is important to note that without specific dimensions or additional information about the box's shape or size, we cannot determine the exact equation Kylie used.
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a number z is few then 3/4 answer
Answer:
[tex]\sf z - \dfrac{3}{4}[/tex]
Step-by-step explanation:
Algebraic expression:Subtract 3/4 from z.
[tex]\sf z - \dfrac{3}{4}[/tex]
At garage sale Georgia found some dvds and cds that she wanted to buy each dvd costs 3$ and each cd costs 2$ she also has the option of paying 25$ for entire box of dvds and cds evaluate the expression 3d + 2c when d = 4 and c = 7 to find the buying the entire box and buying items individually
Each dvd costs 3$Each cd costs 2$Georgia bought, d DVDs and c CDs Georgia found for buying the dvds and cds that she wanted to buy each dvd costs 3$ and each cd costs 2$ she also has the option of paying 25$ for entire box of dvds and cds.
Firstly, we will calculate the price of DVDs and CDs individually,Total cost of buying DVDs = $3×4 = $12Total cost of buying CDs = $2×7 = $14Now, we have the prices of buying DVDs and CDs individually that is $12 and $14, respectively. Georgia also has the option of paying $25 for the entire box. Now, we will calculate the cost of buying the entire box using the given expression:3d + 2c when d = 4 and c = 7By substituting the given values of d and c, we get:3(4) + 2(7) = 12 + 14 = $26So, buying the entire box would cost Georgia $25 while buying them individually would cost $12 and $14 for DVDs and CDs, respectively.
long answer:We are given that Georgia has found dvds and cds that she wanted to buy. Each DVD costs 3$ and each CD costs 2$. Georgia also has the option of paying 25$ for the entire box of DVDs and CDs.Now, we need to evaluate the given expression 3d + 2c when d = 4 and c = 7 to find the buying the entire box and buying items individually.We know that d represents the number of DVDs and c represents the number of CDs Georgia has bought. Given that d = 4 and c = 7, we can calculate the cost of buying these items individually as follows:Cost of buying DVDs = 3 x 4 = 12$Cost of buying CDs = 2 x 7 = 14$Hence, the cost of buying these items individually is 12$ + 14$ = 26$.Now, we need to evaluate the expression 3d + 2c when d = 4 and c = 7 to find the cost of buying the entire box. By substituting the values of d and c, we get:3 x 4 + 2 x 7 = 12 + 14 = 26$Therefore, the cost of buying the entire box is 25$, which is less than the cost of buying these items individually.
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for all values of x, f(x)=2x-3 and g(x)=x^2+1 find fg(x)
fg(x) is 2x³ - 3x² + 2x - 3.To find fg(x), we need to multiply f(x) and g(x).
The given functions are f(x) = 2x - 3 and g(x) = x² + 1.
We know that (f · g)(x) = f(x) · g(x).
So, (f · g)(x) = (2x - 3)(x² + 1)
(f · g)(x) = 2x³ - 3x² + 2x - 3.
Hence, the value of fg(x) is 2x³ - 3x² + 2x - 3
Given f(x) = 2x - 3 and g(x) = x² + 1
We have to find fg(x) = f(x)g(x)
= (2x - 3)(x² + 1)
We will use the distributive law of multiplication to multiply the given two functions.
(2x - 3)(x² + 1)= 2x(x² + 1) - 3(x² + 1)
Expanding further, we get the following:
2x³ + 2x - 3x² - 3=2x³ - 3x² + 2x - 3
Therefore,
fg(x) = 2x³ - 3x² + 2x - 3.
So, we get the value of fg(x) as 2x³ - 3x² + 2x - 3.
We have found that fg(x) is 2x³ - 3x² + 2x - 3 by multiplying f(x) = 2x - 3 and g(x) = x² + 1.
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a:b = 1:5
a:c = 2:1
how many times is b bigger than c
b is 10 times bigger than c. the ratio A:b is equivalent to the ratio a:c multiplied by 5: A:b = (a:c) * 5
To determine how many times b is bigger than c, we need to compare their respective ratios.
Given:
A:b = 1:5
a:c = 2:1
To make a comparison, we can find the relative sizes of b and c by considering the ratios they have with other variables.
From the ratio A:b = 1:5, we can rewrite it as A:b = 2:10 (multiplying both sides by 2).
Comparing the ratios A:b and a:c, we can see that the ratio A:b is equivalent to the ratio a:c multiplied by 5:
A:b = (a:c) * 5
Substituting the given ratios, we have:
2:10 = (2:1) * 5
Now, we can compare the values of b and c directly:
b = 10
c = 1
Therefore, b is 10 times bigger than c.
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Two containers designed to hold water are side by side, both in the shape of a cylinder. Container A has a diameter of 14 fect and a height of 13 fect. Container B has a diameter of 12 feet and a height of 18 feet. Container A is full of water and the water is pumped into Container B until Container A is empty. After the pumping is complete. what is the volume of the empty portion of Container B, to the nearest tenth of a cubic foot?
The volume of the empty portion of Container B is given as follows:
34.6 ft³.
How to obtain the volume of the cylinder?The volume of a cylinder of radius r and height h is given by the equation presented as follows:
V = πr²h.
(the radius is half the diameter).
Hence the volume of Container A is given as follows:
V = π x 7² x 13
V = 2001.2 ft³.
The volume of container B is given as follows:
V = π x 6² x 18
V = 2035.8 ft³.
Then the volume of the empty portion of Container B is given as follows:
2035.8 - 2001.2 = 34.6 ft³.
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Devon has several toy car bodies and motors. The motors have the same mass, but they provide different amounts of force, as shown in this table. A 2 column table with 2 rows. Column 1 is labeled Motor with entries 1, 2. Column 2 is labeled Force (N) with entries 10, 15. The bodies have the masses shown in this table. A 2 column table with 2 rows. Column 1 is labeled Body with entries 1, 2. Column 2 is labeled Mass (kilograms) with entries 0. 2, 0. 6. Which motor and body should Devon use to build the car with the greatest acceleration? motor 1, with body 1 motor 1, with body 2 motor 2, with body 1 motor 2, with body 2.
Devon should use motor 2 with body 1 to build the car with the greatest acceleration.
To determine which combination of motor and body would result in the greatest acceleration for the toy car, we need to calculate the force-to-mass ratio for each combination. The greater the force-to-mass ratio, the greater the acceleration.
For motor 1 and body 1:
Force-to-mass ratio = Force / Mass
= 10 N / 0.2 kg
= 50 N/kg.
For motor 1 and body 2:
Force-to-mass ratio = Force / Mass
= 10 N / 0.6 kg
= 16.67 N/kg.
For motor 2 and body 1:
Force-to-mass ratio = Force / Mass
= 15 N / 0.2 kg
= 75 N/kg.
For motor 2 and body 2:
Force-to-mass ratio = Force / Mass
= 15 N / 0.6 kg
= 25 N/kg.
Comparing the force-to-mass ratios, we can see that the combination with the greatest acceleration would be motor 2 with body 1, as it has a force-to-mass ratio of 75 N/kg. Therefore, Devon should use motor 2 with body 1 to build the car with the greatest acceleration.
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--The given question is incomplete, the complete question is given below " Devon has several toy car bodies and motors. The motors have the same mass, but they provide different amounts of force, as shown in this table.
The bodies have the masses shown in this table.
Which motor and body should Devon use to build the car with the greatest acceleration?
motor 1, with body 1
motor 1, with body 2
motor 2, with body 1
motor 2, with body 2"--
Why should inequalities with absolute value be set up differently to solve if it is an ""and"" situation vs. an ""or"" situation?
Inequalities with absolute value need to be set up differently to solve based on whether it is an "and" situation or an "or" situation.
When dealing with an "and" situation, we use a compound inequality and solve two separate inequalities. For an "or" situation, we set up two separate inequalities and solve them independently.
The approach differs because the absolute value can result in both positive and negative solutions, which must be considered when determining the valid range of solutions.
When encountering an "and" situation in absolute value inequalities, we use a compound inequality to account for both the positive and negative solutions. For example, if we have |x - 3| ≤ 5 and need to find the valid range for x, we set up two separate inequalities: x - 3 ≤ 5 and -(x - 3) ≤ 5. Solving each inequality separately yields the range of valid solutions for x.
On the other hand, when dealing with an "or" situation, we set up two separate inequalities to handle the positive and negative solutions independently. For instance, if we have |x + 2| > 3 and need to find the valid range for x, we set up the inequalities: x + 2 > 3 and -(x + 2) > 3. Solving each inequality separately provides the distinct ranges of valid solutions for x in the given scenario.
The reason for this distinction lies in the absolute value's property of yielding both positive and negative solutions. By setting up separate inequalities for each case, we ensure that all possible valid solutions are considered and captured appropriately.
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