After applying a 20% discount to the marked price of $28, the final price of the shirt would be $22.40.
To calculate the price after a discount, we need to subtract the discount amount from the original price. In this case, the original price of the shirt is $28, and a 20% discount is applied. To find the discount amount, we calculate 20% of $28, which is $5.60. Subtracting $5.60 from the original price gives us the final price of $22.40. Discount = 20% of $28 = (20/100) * $28 = $5.60. Discounted Price = $28 - $5.60 = $22.40. Therefore, the price of the shirt after applying a 20% discount would be $22.40.
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#Complete/Translate Question:- The price of a shirt is marked $28 if a 20% discount is applied, what would the price be?
Write a real world situation that could be modeled by the expression ""x - 12""
The expression "x - 12" can be modeled in a real world situation where you are trying to find the difference between a number x and 12. Here is an example:Suppose you have a jar containing x marbles.
You give away 12 marbles to your friend. The number of marbles you have left in the jar can be modeled by the expression "x - 12". In this situation, x represents the original number of marbles in the jar, and 12 represents the number of marbles given away to your friend. The expression "x - 12" calculates the number of marbles you have left after giving away 12.
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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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what is the mean for 5,5,5,4,4,2,2what is the mean for 7, 5, 1, 2, 8, 3, 3what is the mean for 8, 4, 2, 8, 7what is the mean for 3, 3, 7, 6, 3, 3, 3, 5, 4
The mean for the first set of numbers is 4. The mean for the second set of numbers is 4. The mean for the third set of numbers is 5. The mean for the fourth set of numbers is 4.11.
To calculate the mean, we sum up all the numbers in the set and divide the sum by the total count of numbers.
For the first set of numbers (5, 5, 5, 4, 4, 2, 2), the sum is 27. There are 7 numbers in the set, so the mean is 27/7 = 4.
For the second set of numbers (7, 5, 1, 2, 8, 3, 3), the sum is 29. There are 7 numbers in the set, so the mean is 29/7 = 4.
For the third set of numbers (8, 4, 2, 8, 7), the sum is 29. There are 5 numbers in the set, so the mean is 29/5 = 5.
For the fourth set of numbers (3, 3, 7, 6, 3, 3, 3, 5, 4), the sum is 37. There are 9 numbers in the set, so the mean is 37/9 = 4.11 (rounded to two decimal places).
Therefore, the mean for the respective sets of numbers are 4, 4, 5, and 4.11.
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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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For the past `12` school days, Mai has recorded how long her bus rides to school take in minutes. The times she recorded are shown below. `9`, `12`, `6`, `9`, `10`, `7`, `6`, `12`, `9`, `8`, `10`, `10` Find the mean for Mai's data.
The mean for Mai's data is 8.9167.
To find the mean of the data given by Mai for the past 12 school days, we need to add all the values together and then divide by the total number of values.
Here is the solution: Given data are: 9, 12, 6, 9, 10, 7, 6, 12, 9, 8, 10, 10
To find: The mean for Mai's data
To calculate the mean, we will add up all the values and then divide by the total number of values.
Mean (average) = sum of values / total number of values
Sum of values = 9 + 12 + 6 + 9 + 10 + 7 + 6 + 12 + 9 + 8 + 10 + 10= 107
Total number of values = 12
Therefore, Mean (average) = sum of values / total number of values
= 107 / 12
= 8.9167 (rounded to four decimal places)
Hence, the mean for Mai's data is 8.9167.
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Marjorie has 3 pink ribbons, 1 green ribbon, and 2 blue spools of thread for art. what fraction of marjories ribbons are green??
1/6 is the fraction of Marjorie's ribbons that are green. Marjorie has a total of 6 ribbons and spools of thread for art, consisting of 3 pink ribbons, 1 green ribbon, and 2 blue spools of thread.
1. To determine the fraction of Marjorie's ribbons that are green, we divide the number of green ribbons by the total number of ribbons.
2. To find the fraction of Marjorie's ribbons that are green, we need to calculate the ratio of green ribbons to the total number of ribbons. The total number of ribbons is the sum of all the ribbons and spools of thread, which is 3 pink ribbons + 1 green ribbon + 2 blue spools of thread, equaling 6 ribbons in total.
3. Since Marjorie has only 1 green ribbon, we can say that the fraction of her ribbons that are green is 1 out of the total 6 ribbons. This can be expressed as 1/6. Therefore, 1/6 is the fraction of Marjorie's ribbons that are green.
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Point R is located on segment QS. If QR=10 and RS= 7, what is the measure of QS?
The measure of segment QS can be determined by adding the lengths of QR and RS. In this case, since QR is 10 units long and RS is 7 units long, the measure of QS would be 17 units.
To find the measure of segment QS, we need to add the lengths of QR and RS. Given that QR is 10 units long and RS is 7 units long, we can calculate the measure of QS by adding these two lengths together. Therefore, QS = QR + RS = 10 + 7 = 17. Hence, the measure of segment QS is 17 units. By adding the lengths of the two segments that make up QS, we obtain the total length of the segment itself.
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The price of a nine minute phone call is $3. 15 what is the price of a 12 minute phone call
The cost of a 12-minute phone call is $4.20.
The cost of a nine-minute phone call is $3.15. To find the cost of a 12-minute phone call, we must first determine the cost per minute. We can do this by dividing the cost of a nine-minute call by 9 minutes, which gives us the cost per minute.
3.15 ÷ 9 = $0.35 (cost per minute) Now that we know the cost per minute, we can find the cost of a 12-minute phone call by multiplying the cost per minute by the number of minutes. 12 × $0.35 = $4.20 Therefore, the price of a 12-minute phone call is $4.20.
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Darrel divided 8,675 by 87. His work is shown below. Which answer choice correctly identifies the error Darrel made when dividing? A. He made an error when multiplying. B. He made an error when subtracting. C. He forgot to place a zero in the quotient. D. He did not make an error, his work is correct.
According to given information, option C is the correct answer.
Given that Darrel divided 8,675 by 87.
His work is shown below.
Step 1: Set up the problem with the dividend under the division symbol and the divisor outside.
Step 2: Estimate a reasonable quotient and place it above the dividend. Then multiply and subtract. Bring down the next digit of the dividend.
Step 3: Repeat step 2 until the dividend has been brought down completely.
The given picture shows the steps done:
Option C: Darrel forgot to place a zero in the quotient.
Thus option C is the correct answer.
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Aika is building a square garden. She places a garden post at (3.5, 3.5). What is the location of the corner that reflects (3.5, 3.5) across the y-axis? Express your answer using decimal notation.
Given, Aika is building a square garden. She places a garden post at (3.5, 3.5)
To find: The location of the corner that reflects (3.5, 3.5) across the y-axis.
We know that the y-axis is the vertical line through the point (0,0) and it divides the plane into two parts: left and right. When we reflect a point across the y-axis, the x-coordinate changes sign. For example, the reflection of (2,3) is (-2,3).Therefore, the reflection of (3.5, 3.5) across the y-axis is (-3.5, 3.5)
Since Aika is building a square garden, the corner opposite to (3.5, 3.5) will have coordinates (-3.5, -3.5).
Hence, the location of the corner that reflects (3.5, 3.5) across the y-axis is (-3.5, -3.5).
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Which expression can be simplified to find the slope of the trend line in the scatterplot?
To find the slope of the trend line in a scatterplot, we need to use the formula for slope, which is: Slope = (Change in y)/(Change in x).
The expression that can be simplified to find the slope of the trend line in the scatterplot is the formula for slope. Therefore, the expression that can be simplified to find the slope of the trend line in the scatterplot is:Slope = (Change in y)/(Change in x).
Here, "y" represents the dependent variable, and "x" represents the independent variable in the scatterplot. The slope of the trend line shows how steep the line is.
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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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A population of 1000 alligators has a birthrate of 400 per year. Each year, 150 alligators die, and 150 leave the population to look for new territory, but 30 alligators arrive from other territories to join the population. What is the annual population growth rate per thousand animals
The annual population growth rate per thousand animals in this scenario is 130.
In the given population of 1000 alligators, the birthrate is 400 per year. This means that 400 new alligators are born each year. However, there are also factors that decrease the population. Each year, 150 alligators die and 150 leave the population to search for new territory. On the other hand, 30 alligators arrive from other territories to join the population.
To calculate the annual population growth rate per thousand animals, we can subtract the total number of deaths and departures (150 + 150) from the total number of births and arrivals (400 + 30). This gives us a net increase of 130 alligators.
To calculate the growth rate per thousand animals, we divide the net increase (130) by the initial population size (1000) and multiply the result by 1000. This gives us a growth rate of 130/1000 * 1000 = 130.
Therefore, the annual population growth rate per thousand animals in this scenario is 130.
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Explain how the number line can be used to determine the sum of the location of point T and -1 1/2.
The number line can be used to determine the sum of the location of point T and -1 1/2. By visually representing the positions of these points on the number line, we can determine their sum by adding their locations.
To determine the sum of the location of point T and -1 1/2, we can plot the point T on the number line and then locate -1 1/2 on the number line. We can then add the locations of these points on the number line to find their sum.
For example, if point T is located at 3 on the number line and -1 1/2 is located at -1.5, we can add 3 and -1.5 to find their sum, which would be 3 + (-1.5) = 1.5.
By using the number line, we can visually represent the locations of the points and perform addition to find their sum accurately.
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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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what is the circumference of a cylinder with the diameter of 6cm and height of 12cm
The diameter of a cylinder is given as 6 cm and the height as 12 cm. We can use the formula of the circumference of a cylinder to calculate the circumference. We know that the circumference of a circle is πd, where d is the diameter of the circle.
Now, the circumference of a cylinder is nothing but the perimeter of its circular base. Therefore, the circumference of a cylinder is 2πr where r is the radius of the circular base. In this question, the diameter is given as 6 cm, which means the radius will be half of it. Hence the radius of the circular base will be 6/2 = 3 cm. The height of the cylinder is given as 12 cm, which means the circumference will be the perimeter of the circular base times the height of the cylinder. The circumference will be:2πr = 2π(3) = 6π cm. The circumference of a cylinder with the diameter of 6 cm and height of 12 cm is 6π cm.
The circumference of a cylinder with the diameter of 6 cm and height of 12 cm is 6π cm. The diameter of a cylinder is given as 6 cm and the height as 12 cm. We can use the formula of the circumference of a cylinder to calculate the circumference. We know that the circumference of a circle is πd, where d is the diameter of the circle. Now, the circumference of a cylinder is nothing but the perimeter of its circular base. Therefore, the circumference of a cylinder is 2πr where r is the radius of the circular base. In this question, the diameter is given as 6 cm, which means the radius will be half of it. Hence the radius of the circular base will be 6/2 = 3 cm. The height of the cylinder is given as 12 cm, which means the circumference will be the perimeter of the circular base times the height of the cylinder. The circumference will be:2πr = 2π(3) = 6π cm. The circumference of a cylinder with the diameter of 6 cm and height of 12 cm is 6π cm, where π is pi and is equal to approximately 3.14.
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The boom of a sailboat is 26 feet long. If the sail is an equilateral triangle how much cloth will be required to make the sail of the boat?
The area or amount of cloth that will be required to make the sail of the boat is 50.5 square feet (approx.).
Given that the boom of a sailboat is 26 feet long and the sail is an equilateral triangle. We have to determine the amount of cloth that will be required to make the sail of the boat.
The formula to calculate the area of an equilateral triangle is:
A = (√(3)/4)*a²,
where
A represents the area of the equilateral triangle
a represents the side of the equilateral triangle.
Here, the sail is an equilateral triangle.
Therefore, the length of each side of the sailboat is given as:
Length of each side of the sailboat = 26 feet / 3
= 8.67 feet or 8 feet (approximately)
We can calculate the area of the sail using the below formula;
A = (√(3)/4)×a²,
where,
A represents the area of the equilateral triangle
a represents the length of each side of the sailboat.
By substituting the value of a = 8.67 in the above equation, we get the area of the sail as follows:
A = (√(3)/4)×a²
A = (√(3)/4)*(8.67)²
A = 50.5 square feet (approx.)
Hence, the amount of cloth that will be required to make the sail of the boat is 50.5 square feet (approx.).
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If ray QS bisects ∠PQR, m∠PQS = (7x – 6)°, andm∠SQR = (4x + 15)°, the m∠PQT is 9.TrueTruefalse
The statement "m∠PQT is 9" is false.In the given scenario, ray QS bisects ∠PQR. This means that ∠PQS and ∠SQR are equal in measure because they are the two halves of the same angle.
Let's denote the measure of ∠PQS as (7x - 6)° and the measure of ∠SQR as (4x + 15)°. Since these two angles are equal, we can set up an equation: (7x - 6) = (4x + 15). Solving this equation, we find x = 7.
Now, to find the measure of ∠PQT, we need to substitute the value of x into the expression (7x - 6)°. Plugging in x = 7, we get (7 * 7 - 6)° = 43°. Therefore, the correct statement should be "m∠PQT is 43," not 9. Thus, the statement "m∠PQT is 9" is false.
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Write the sentence as an inequality: the difference of number n and 5 is at least 32
The inequality that represents the given sentence is: n - 5 ≥ 32.
In this inequality, "n" represents the number in question. The phrase "the difference of number n and 5" indicates that we are subtracting 5 from n. The phrase "is at least 32" implies that the result of the subtraction must be greater than or equal to 32. Therefore, we write the inequality as n - 5 ≥ 32.
To explain this further, if we want to find a value for n that satisfies the given condition, we need to find a number that, when 5 is subtracted from it, gives us a result of at least 32. By adding 5 to both sides of the inequality, we can rewrite it as n ≥ 37, which means n must be greater than or equal to 37 for the difference between n and 5 to be at least 32.
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Triangle ABC is formed by the vertices A(1, 2, -1), B(-1,1,2)and C(-3,-1,0).
If D is the midpoint of BC, the the length (distance) of AD.
Write the midpoint
• Write the distance
The midpoint of the line segment connecting two points can be found by averaging their corresponding coordinates. Therefore, to obtain the midpoint of line BC, we add the coordinates of B and C and divide by 2.
Midpoint of line BC is given by:
\[\left(\frac{-1-3}{2},\frac{1-1}{2},\frac{2+0}{2}\right)=(-2,0,1)\]
The length of line AD is found by using the distance formula, which is given as:
\[d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\]
Thus, we need to find the coordinates of point D and A to determine the length of AD. The coordinates of D are the average of the coordinates of B and C.
\[\left(\frac{-1-3}{2},\frac{1-1}{2},\frac{2+0}{2}\right)=(-2,0,1)\]The coordinates of A are (1,2,-1).
The distance between A and D is found by substituting these values into the distance formula:
\[d=\sqrt{(x_2-x_1)^2+(y_2-y_1)^2+(z_2-z_1)^2}\] \[d=\sqrt{(1-(-2))^2+(2-0)^2+(-1-1)^2}\] \[d=\sqrt{(3)^2+(2)^2+(-2)^2}\] \[d=\sqrt{9+4+4}\] \[d=\sqrt{17}\]
Thus, the distance between points A and D is sqrt(17).Therefore, the midpoint of line BC is (-2,0,1) and the distance between points A and D is sqrt(17).
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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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Write the first five terms of the sequence defined by the explicit formula an=(-2)^n-1
The first five terms of the sequence defined by the explicit formula an = (-2)^(n-1) are 1, -2, 4, -8, 16.
To find the first five terms of the sequence defined by the explicit formula an = (-2)^(n-1), we can substitute the values of n from 1 to 5 into the formula and calculate the corresponding terms:
The explicit formula for the sequence is given by an = (-2)^(n-1).
When n = 1: a1 = (-2)^(1-1) = (-2)^0 = 1
When n = 2: a2 = (-2)^(2-1) = (-2)^1 = -2
When n = 3: a3 = (-2)^(3-1) = (-2)^2 = 4
When n = 4: a4 = (-2)^(4-1) = (-2)^3 = -8
When n = 5: a5 = (-2)^(5-1) = (-2)^4 = 16
Therefore, the first five terms of the sequence are:
1, -2, 4, -8, 16
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A goalie's saves (⋅ ) and goals scored against (x) are shown. What percent of shots did the goalie save?
will name person with correct answer brainlest.
To determine the percentage of shots that the goalie saved, we need the actual numbers of saves and goals scored against the goalie. Since the specific values are not provided in the question, it is not possible to calculate the exact percentage.
However, I can explain the general process for calculating the percentage of savings.
To find the percentage of saves, we need to divide the number of saves by the total number of shots and then multiply by 100. The formula for calculating the percentage is:
Percentage of saves = (Number of saves / Total number of shots) * 100
For example, if the goalie made 30 saves out of 40 total shots, the calculation would be:
Percentage of saves = (30 / 40) * 100 = 75%
In this case, the goalie saved 75% of the shots.
Without the specific values of saves and shots, it is not possible to determine the exact percentage.
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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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What rational number falls between 1/13 and 2/13?
The rational number that falls between 1/13 and 2/13 is 3/13 by using average method
To find a rational number between two fractions, we can use the average method.
To find the average of two fractions a/b and c/d, we add them up and then divide them by 2.
The question is asking what rational number falls between 1/13 and 2/13.
The average of these fractions can be calculated by adding them and dividing them by 2:
1/13 + 2/13 = 3/13 Now, to check whether 3/13 is between 1/13 and 2/13, we can compare the three fractions:
1/13 < 3/13 < 2/13 Therefore, the rational number that falls between 1/13 and 2/13 is 3/13.
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With one method of a procedure called acceptance sampling, a sample of items is randomly selected without replacement and the entire batch is accepted if every item in the sample is okay. The ABC Electronics Company has just manufactured 1200 write-rewrite CDs, and 90 are defective. If 3 of these CDs are randomly selected for testing, what is the probability that the entire batch will be accepted?
Acceptance sampling is a statistical procedure that involves taking a sample of a product or a lot of products and determining if it meets the required standards or specifications.
One method of acceptance sampling involves randomly selecting a sample of items without replacement and accepting the entire batch only if every item in the sample is okay.The ABC Electronics Company has just manufactured 1200 write-rewrite CDs, out of which 90 are defective. The question is asking about the probability that the entire batch will be accepted if 3 of these CDs are randomly selected for testing.We know that out of 1200 CDs, 90 are defective.
Therefore, the number of good CDs is:1200 - 90 = 1110If 3 CDs are randomly selected, the probability of getting a good CD on the first try is:1110/1200 = 37/40The probability of getting a good CD on the second try is:1109/1199The probability of getting a good CD on the third try is:1108/1198The probability of getting all three CDs that are good is:37/40 * 1109/1199 * 1108/1198 = 0.7978Therefore, the probability that the entire batch will be accepted is 0.7978 or approximately 79.78%.
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Natalie went on a jog 3 nights in a row. She jogged the same distance each night. This model represents the situation. Each column represents one mile and the shaded parts of each column represent the fraction of a mile that Natalie jogged each night.
Which expression can be used to determine the total distance in miles Natalie jogged over these 3 nights?
The expression that can be used to determine the total distance in miles Natalie jogged over these 3 nights is:
The model for finding the total distanceNatalie went on a jog 3 nights in a row and jogged the same distance each night.
The model for finding the total distance that Natalie jogged during the 3 nights is shown below:
Model for finding the total distance where each column represents one mile, and the shaded parts of each column represent the fraction of a mile that Natalie jogged each night.
From the model, we can find the total distance in miles Natalie jogged by counting the number of shaded parts in each column and then adding them together.
The number of shaded parts in each column represents the fraction of a mile that Natalie jogged each night.
Therefore, the expression that can be used to determine the total distance in miles Natalie jogged over these 3 nights is:
[tex]$$3 \cdot 1 + \frac{1}{2} + \frac{3}{4}$$ $$= 3 + \frac{2}{4} + \frac{3}{4}$$$$= 3 + \frac{5}{4}$$$$= \frac{12}{4} + \frac{5}{4}$$$$= \frac{17}{4}$$$$= \boxed{4\frac{1}{4}}\ miles$$[/tex]
Therefore, Natalie jogged a total distance of 4 and 1/4 miles over these three nights.
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A marker is randomly selected from a drawer that contains 20 green, 44 orange, and 30 blue markers. Which statement is true? P(blue)≈0. 41 P(green)≈0. 21 P(orange)≈0. 53.
none of the provided approximations for the probabilities are accurate.To determine which statement is true, we need to calculate the probabilities of selecting each color marker.
Total number of markers = 20 green + 44 orange + 30 blue = 94 markers.
P(blue) = Number of blue markers / Total number of markers = 30 / 94 ≈ 0.319.
P(green) = Number of green markers / Total number of markers = 20 / 94 ≈ 0.213.
P(orange) = Number of orange markers / Total number of markers = 44 / 94 ≈ 0.468.
Based on the calculations, none of the given statements are true. The actual probabilities are approximately:
P(blue) ≈ 0.319,
P(green) ≈ 0.213,
P(orange) ≈ 0.468.
Therefore, none of the provided approximations for the probabilities are accurate.
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Alexa is designing a paper airplane whose final shape, when viewed from the top or bottom, is a trapezoid. A sketch of her plane, viewed from the top, is shown on the left.
A trapezoid has a base of 6 centimeters, a height of 3 centimeters, and a top side length of 2 centimeters
The dimensions of one of the identical triangular pieces of the paper airplane are A. 2 cm base, 3 cm height
How to find the dimensions ?From the given information, the paper airplane is designed in the shape of a trapezoid when viewed from the top. The trapezoid has a base of 6 centimeters, a height of 3 centimeters, and a top side length of 2 centimeters.
When we divide the trapezoid along the height, we get two congruent triangles. These triangles have the same shape and size, making them identical. The height of the triangle corresponds to the same height as the trapezoid, which is 3 centimeters.
Therefore, the dimensions of one of the identical triangular pieces of the paper airplane are a base of 2 centimeters and a height of 3 centimeters.
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Full question is:
Alexa is designing a paper airplane whose final shape, when viewed from the top or bottom, is a trapezoid. A sketch of her plane, viewed from the top, is shown on the left.
What are the dimensions of one of the identical triangular pieces of the plane?
2 cm base, 3 cm height
3 cm base, 3 cm height
3 cm base, 4 cm height
3 cm base, 6 cm height
Edgar cannot sleep because he is terribly worried about his research paper. So edgar decides to get out of bed and continue working on the paper. Although he stays up to nearly 3 a. M. , he is relieved that it is done and easily falls off to sleep. In the future, edgar will be more likely to finish his work before going to bed so that he can avoid the worry and sleeplessness. Such behavior is an example of.
To sum up, Edgar's behavior is an example of positive reinforcement as he has learned to associate finishing his work before going to bed with positive consequences.
Edgar's behavior is an example of a learning process known as operant conditioning. Operant conditioning is the concept that we learn to associate our behavior with its consequences, either positive or negative. We are motivated by rewards, such as praise, and punishments, such as criticism, that we experience as a result of our behavior.
In Edgar's case, his relief and ability to fall asleep after completing his research paper can be considered a reward. Thus, he has been conditioned to associate finishing his work before going to bed with positive consequences. This learning process is an example of positive reinforcement.
Positive reinforcement, in which a positive stimulus is used to encourage a desired behavior, is the most effective way to promote good behavior and discourage undesirable behavior. Positive reinforcement can take many forms, including praise, recognition, and tangible rewards.
By contrast, negative reinforcement, which involves removing an unpleasant stimulus, can also be used to encourage a desired behavior, but it is not as effective as positive reinforcement in the long term.
To sum up, Edgar's behavior is an example of positive reinforcement as he has learned to associate finishing his work before going to bed with positive consequences.
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