To find the pairs of consecutive positive perfect square numbers with a difference less than 3022, we can set up an inequality and solve it.
Let's assume the first perfect square number is n². The next consecutive perfect square number is (n+1)².
The difference between these two perfect square numbers is given by:
(n+1)² - n² = (n² + 2n + 1) - n² = 2n + 1
We want the difference to be less than 3022, so we can set up the inequality:
2n + 1 < 3022
Subtracting 1 from both sides:
2n < 3021
Dividing both sides by 2:
n < 1510.5
Since n must be a positive integer, the largest possible value for n is 1510.
Therefore, there are 1510 pairs of consecutive positive perfect square numbers such that their difference is less than 3022.
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Which algebraic property is used to manipulate this expression
The algebraic property that could be used to rewrite 4x + 2y as 2y + 4x is option C: Commutative Property of Addition.
What algebraic property is been used?From the question. if a, b and c are any numbers,
Based on Associative Property of Addition, it state that:
a + ( b + c ) = ( a + b ) + c
Based on Associative Property of Multiplication, it state that:
a(bc) = (ab)c
Based on Commutative Property of Addition it state that:
a + b = b + a
Based on Commutative Property of Multiplication it state that:
ab = ba
Note that , 4x + 2y = 2y + 4x
So, Commutative Property of Addition is used in the expression.
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See text below
Which algebraic property could be used to rewrite 4x + 2y as 2y + 4x? A. Associative Property of Addition
B. Associative Property of Multiplication
C. Commutative Property of Addition
D. Commutative Property of Multiplication
Find the sum of £1. 54, 64p and 29p. I) Write your answer in pounds, £. Ii) Write your answer in pence, p
I) The sum of £1.54, 64p, and 29p is £2.47.
II) The sum of £1.54, 64p, and 29p is 247p.
The sum of £1.54, 64p, and 29p is £2.47 or 247p.
To find the sum, we need to add the values together. First, we add the pounds: £1.00 + £0.54 = £1.54. Then, we add the pence: 64p + 29p = 93p. To express the result in pounds and pence, we convert the pence to pounds by dividing by 100: 93p ÷ 100 = £0.93.
Finally, we add the pounds and pence together: £1.54 + £0.93 = £2.47. So, the sum of £1.54, 64p, and 29p is £2.47 or 247p.
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Kendrick is trying to determine if a painting he wants to buy will fit in the space on his wall. If the rectangular frame's diagonal is 76. 84 inches and forms a 51. 34° angle with the bottom of the frame, what is its height? Round your answer to the nearest inch. 96 inches 60 inches 50 inches 48 inches.
Answer:
Step-by-step explanation:
An urn contains 4 balls: 1 white, 1 green and 2 red. We draw 3 balls with replacement. Find the probability that we did not see all three colors. Use two different calculations, as specified by (a) and (b) below. (a) Define the event W = {white ball did not appear} and similarly for G and R. Use inclusion-exclusion. (b) Compute the probability
Both methods will yield the same result, which represents the probability of not seeing all three colors when drawing three balls with replacement from the given urn. The answer in this case is 3/4.
(a) Using the inclusion-exclusion principle, we define events W, G, and R for the white, green, and red balls not appearing, respectively. To calculate the probability that we did not see all three colors, we use the formula P(W U G U R) = P(W) + P(G) + P(R) - P(W ∩ G) - P(W ∩ R) - P(G ∩ R) + P(W ∩ G ∩ R). Each individual probability can be calculated by considering the number of ways each event can occur divided by the total number of possible outcomes. For example, P(W) = (3/4)^3, P(G) = (3/4)^3, P(R) = (1/2)^3, P(W ∩ G) = (2/4)^3, and so on.
(b) In the direct computation method, we calculate the probability of not seeing all three colors by subtracting the probability of seeing all three colors from 1. The probability of seeing all three colors is calculated by considering the number of ways to select one ball of each color divided by the total number of possible outcomes. There are 4 possible outcomes for each ball drawn, so the probability of seeing all three colors is 4/4 * 4/4 * 2/4 = 1/4. Therefore, the probability of not seeing all three colors is 1 - 1/4 = 3/4.
Both methods will yield the same result, which represents the probability of not seeing all three colors when drawing three balls with replacement from the given urn. The answer in this case is 3/4.
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To find the probability that we did not see all three colors when drawing 3 balls with replacement from an urn containing 1 white, 1 green, and 2 red balls, we can use the inclusion-exclusion principle or calculate directly by counting the number of ways.
Explanation:To find the probability that we did not see all three colors, we can use two different calculations.
(a) Let W be the event that the white ball did not appear, G be the event that the green ball did not appear, and R be the event that the red ball did not appear. We can use the inclusion-exclusion principle to calculate the probability:
P(W ∪ G ∪ R) = P(W) + P(G) + P(R) - P(W ∩ G) - P(W ∩ R) - P(G ∩ R) + P(W ∩ G ∩ R)
(b) Alternatively, we can directly compute the probability by counting the number of ways that we did not see all three colors and dividing by the total number of possible outcomes.
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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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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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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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Norman has four less than triple the amount of candy Devin has. If Norman has twenty candies, how many candies does Devin have?
Devin has 2 candies. The problem states that Norman has four less than triple the amount of candy Devin has which is given by:20=3x-4.We add 4 to both sides of the equation:20+4=3x-4+4.24=3x.
Let the amount of candy that Devin has be x.
Then, triple the amount of candy that Devin has is 3x.
The problem states that Norman has four less than triple the amount of candy Devin has which is given by:20=3x-4.We add 4 to both sides of the equation:20+4=3x-4+4.24=3x.
Divide both sides by 3:24/3=3x/3.x=8.We now know that Devin has 8 candies.
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One diameter makes ____________ parts of the circle .
One diameter makes two parts of the circle. A diameter is a chord that passes through the center of a circle. When a circle is divided into two halves by the diameter, each half is called a semicircle.
When a line segment that passes through the center of a circle is drawn, it is referred to as a diameter. A circle has a diameter, its longest chord, and its endpoints lie on the circle itself. The midpoint of the diameter is the center of the circle. A diameter divides a circle into two equal parts, known as semicircles. A semicircle is the region enclosed by the arc and the diameter.
The semicircle's area is half the circle from which it was derived. The diameter is the longest chord that a circle has, and it passes through the center of the circle. The diameter divides the circle into two halves. Every chord's perpendicular bisector passes through the center of the circle. This property of the diameter is also applicable to chords. The perpendicular bisector of the chord passes through the circle's center, and the chord is divided into two equal parts.
Therefore, one diameter makes two parts of the circle. A diameter is a chord that passes through the center of a circle. When a circle is divided into two halves by the diameter, each half is called a semicircle.
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You perform a dilation on a shape with a vertex at (2, 6). That vertex moves to (−8, −24). What is the dilation centre? What is the dilation factor?
In the given scenario, a dilation has been performed on a shape with a vertex at (2, 6). The vertex after the dilation is located at (-8, -24). The dilation center can be determined as well as the dilation factor. To find the dilation center and the dilation factor, we compare the coordinates of the original vertex and its image after the dilation.
The dilation center is the point around which the shape is dilated or expanded. In this case, the dilation center can be determined by finding the midpoint between the original vertex and its image. Using the midpoint formula, we calculate:
x-coordinate of the midpoint = (2 + (-8)) / 2 = -6/2 = -3
y-coordinate of the midpoint = (6 + (-24)) / 2 = -18/2 = -9
Therefore, the dilation center is (-3, -9).
The dilation factor represents the scale factor or the ratio of the distances between corresponding points of the original shape and its image after the dilation. In this case, we can determine the dilation factor by calculating the ratio of the distances between the x-coordinates and y-coordinates of the original vertex and its image.
Original x-coordinate: 2
Image x-coordinate: -8
Dilation factor for x-coordinates = Image x-coordinate / Original x-coordinate = -8 / 2 = -4
Original y-coordinate: 6
Image y-coordinate: -24
Dilation factor for y-coordinates = Image y-coordinate / Original y-coordinate = -24 / 6 = -4
Since the dilation factor is the same for both x and y coordinates, we can conclude that the dilation factor is -4. In summary, in the given scenario where a dilation has been performed on a shape with a vertex at (2, 6) resulting in the vertex moving to (-8, -24), the dilation center is (-3, -9), and the dilation factor is -4.
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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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Tomás earned $38. 25 for cleaning the garage. He was paid $4. 25 per hour. Write and solve an equation to find how many hours it took him to clean the garage
The equation is 38.25 = 4.25h and Tomás worked for 9 hours.
To find the number of hours it took Tomás to clean the garage, we can set up an equation using the given information.
Let's assume the number of hours Tomás worked is "h."
We know that Tomás was paid $4.25 per hour, so the total amount he earned can be calculated by multiplying the hourly rate by the number of hours worked:
Total earnings = Hourly rate * Number of hours
In this case, the total earnings are $38.25, and the hourly rate is $4.25:
$38.25 = $4.25 * h
To solve for "h," we need to isolate the variable on one side of the equation. We can do this by dividing both sides of the equation by $4.25:
$38.25 / $4.25 = h
Simplifying the right side:
9 = h
Therefore, it took Tomás 9 hours to clean the garage.
By setting up the equation and solving it, we determined that Tomás worked for 9 hours.
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The box is a right triangular prism shaped box, it is 7 inches long ang the triangular base measures 3inx4inx5in What is the surface area
The surface area of the box is 76 square inches.
The box in the given problem is a right triangular prism shaped box, it is 7 inches long and the triangular base measures 3 in x 4 in x 5 in. We need to determine the surface area of this box.
Therefore, let's first calculate the surface area of the base of the box. The base is a right-angled triangle. Its area can be calculated using the formula for the area of a triangle:
A = (1/2) x base x height = (1/2) x 3 x 4 = 6 square inches.
Now, we need to calculate the area of each of the three rectangular faces. Two of these faces are congruent rectangles and have dimensions 7 in x 3 in. The other face is a rectangle with dimensions 7 in x 4 in. Thus, the area of each of the congruent rectangles is:Area = length x width = 7 x 3 = 21 square inches. Therefore, the area of both rectangles is 21 + 21 = 42 square inches.Now, the area of the third rectangle is:Area = length x width = 7 x 4 = 28 square inches.So, the total surface area of the box can be found by adding the area of the base to the area of all three faces:S.A. = 6 + 42 + 28 = 76 square inches.
Therefore, the surface area of the box is 76 square inches.
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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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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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Sketch a normal curve and label the axis using the mean and standard deviation. Be sure to label one, two, and three standard deviations on either side of the mean
A normal distribution is a bell-shaped distribution that occurs in nature. The mean and standard deviation are used to characterize normal distributions.
A normal distribution is a probability distribution that is symmetric around its mean, with the greatest probability density at the center and tapering off to the left and right. The mean and standard deviation of the distribution describe the distribution. The normal curve depicts a standard normal distribution with a mean of 0 and a standard deviation of 1. To sketch a normal curve, follow the steps below: Step 1: Draw a horizontal axis and label it with the mean µ and the standard deviation σ.Step 2: Draw a bell-shaped curve on the axis, centered at the mean, with the highest point above the mean. The area under the curve must equal 1.0.Step 3: Divide the horizontal axis into thirds on either side of the mean, then label one, two, and three standard deviations away from the mean using σ. This provides us with the following standard normal curve, as shown below: Image credit: Cliffs Notes .Therefore, this is how we can sketch a normal curve and label the axis using the mean and standard deviation.
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Suzy had been working for 15 minutes when she finished problem 5. She complete all 20 questions in 45 minutes. Answer in decimal form, round to the nearest tenth if necessary.
Hence, the correct option is B) 11.1.
Given that Suzy had been working for 15 minutes when she finished problem 5 and she completed all 20 questions in 45 minutes.To find what fraction of the questions Suzy had finished when she finished problem 5; we need to subtract the time taken to finish problem 5 from total time and divide it by total time and the multiply it by 20. The answer can be rounded off to the nearest tenth if necessary.
Fraction of questions completed by Suzy = [(45-15)/45] × 20= 0.556 × 20= 11.12
As we see that Suzy had completed 11.12 questions when she finished the fifth problem.
Therefore, rounding it to the nearest tenth, the decimal form of the answer is 11.1.
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Ryan and Dylan walk toward each other at a constant rate, meet up, and then continue past each other in opposite directions. WE will call where they meet up 0 feet and the time when they meet up 0 seconds
Dylan's Velocity is 12 feet per second
Ryan's velocity is -10 feet per second
When is each person at the position -10 feet from the meeting place use each answer in a complete sentence in the context of the problem
Dylan is at a position 10 feet from the meeting place after 5/6 seconds, while Ryan is not at a position 10 feet from the meeting place.
To find when each person is at a position 10 feet from the meeting place, we can use their velocities and the concept of relative motion.
For Dylan:
Dylan's velocity is 12 feet per second. Since Dylan is walking towards the meeting place, his velocity is positive. To find when Dylan is at a position 10 feet from the meeting place, we can set up the following equation:
Distance = Velocity × Time
10 = 12t
Solving for t, we divide both sides of the equation by 12:
t = 10/12
t = 5/6 seconds
Therefore, Dylan is at a position 10 feet from the meeting place after 5/6 seconds.
For Ryan:
Ryan's velocity is -10 feet per second. Since Ryan is walking in the opposite direction, his velocity is negative. To find when Ryan is at a position 10 feet from the meeting place, we can set up the following equation:
Distance = Velocity × Time
10 = (-10)t
Solving for t, we divide both sides of the equation by -10:
t = 10/(-10)
t = -1 second
Since time cannot be negative in this context, we can conclude that Ryan is not at a position 10 feet from the meeting place.
In summary, Dylan is at a position 10 feet from the meeting place after 5/6 seconds, while Ryan is not at a position 10 feet from the meeting place.
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Dividir 96 en tres partes tales que la primera sea el triple de la segunda y la tercera es igual a la suma de la primera y la segunda. (operaciónes porfas)
The three parts are: x = 24, y = 8, and z = 32. The first part is three times the second, and the third part is equal to the sum of the first and second.
Let's assume the three parts are x, y, and z.
According to the given conditions:
1) The first part is triple the second:
x = 3y
2) The third part is equal to the sum of the first and second:
z = x + y
We are also given that the sum of the three parts is 96:
x + y + z = 96
Now we can solve the equations simultaneously to find the values of x, y, and z.
Substituting the value of x from the first equation into the third equation:
(3y) + y + (3y + y) = 96
Simplifying the equation:
8y + 4y = 96
12y = 96
Dividing both sides by 12:
y = 96 / 12
y = 8
Now that we have the value of y, we can substitute it back into the first equation to find x:
x = 3y = 3(8) = 24
Lastly, substitute the values of x and y into the second equation to find z:
z = x + y = 24 + 8 = 32
Therefore, the three parts are:
x = 24
y = 8
z = 32
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Austin recorded the weights in pounds, of nine fish in an aquarium. The data is shown in the list.
8.7.5, 7.6, 3, 74, 7.9, 81,2,7.7
Move words to the blanks to describe the best measure of variability for this data.
The best measure of variability for the data is the
because the distribution is
The best measure of variability for the data is the range because the distribution is scattered.What is the range?The range of data is defined as the difference between the maximum value and the minimum value
. The list of weights is given below:8.7.5, 7.6, 3, 74, 7.9, 81,2,7.7The minimum value in the list is 3, and the maximum value in the list is 81. So, the drange is calculate as follows:Range = Maximum value – Minimum value= 81 – 3= 78The distribution is scattered because the range is relatively large.
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HELP ME THIS IS DUE TODAY
A shirt is on sale for 15% off the regular price. Josef determines the amount he will save by first calculating 15% of the regular price, s, and then subtracting that amount from the regular price of the shirt. Josef then determines the amount he will pay. Select all of the expressions that could be used to calculate the amount he will pay for the shirt on sale!
a 5-0. 855
b) s-0. 15s
c) 0. 855
d) 1. 155
e) (1 +0. 15)s
f) (1 -0. 15)s
To calculate the amount Josef will pay for the shirt on sale, we need to consider the discount of 15% off the regular price. Several expressions can be used to calculate the final amount, including options (a), (b), (c), and (f).
These expressions involve manipulating the regular price of the shirt and the discount percentage to determine the final price after the discount is applied.
(a) The expression "5-0.855" is not a valid calculation for the amount Josef will pay. It seems to be a typographical error.
(b) The expression "s-0.15s" is a valid expression to calculate the amount Josef will pay. It represents the regular price (s) minus the discount of 15% of the regular price.
(c) The expression "0.855" is not a valid calculation for the amount Josef will pay. It seems to be the result of mistakenly subtracting 15% from 100%.
(d) The expression "1.155" is not a valid calculation for the amount Josef will pay. It seems to be the result of mistakenly adding 15% to 100%.
(e) The expression "(1+0.15)s" is not a valid calculation for the amount Josef will pay. It seems to mistakenly add 15% to the regular price.
(f) The expression "(1-0.15)s" is a valid expression to calculate the amount Josef will pay. It represents the regular price (s) multiplied by the factor of (1-0.15), which accounts for the 15% discount.
The expressions (b) "s-0.15s" and (f) "(1-0.15)s" can be used to calculate the amount Josef will pay for the shirt on sale, as they account for the 15% discount off the regular price.
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Aaron ate ½ as much pizza as David. If Aaron ate ¼ of a pie, what fraction of the pie did David eat? Write and solve an equation.
Given that Aaron ate half as much pizza as David and Aaron ate 1/4 of a pie, we can determine the fraction of the pie David ate by setting up an equation and solving for it.
Let's assume that David ate x amount of pizza, which represents the fraction of the pie he consumed. Since Aaron ate half as much pizza as David, we can express Aaron's portion as (1/2)x. We are also given that Aaron ate 1/4 of a pie, so we can set up the equation:
(1/2)x = 1/4
To solve for x, we can multiply both sides of the equation by 2 to eliminate the fraction:
2 * (1/2)x = 2 * (1/4)
x = 1/2
Therefore, David ate 1/2 of the pie. This means that Aaron ate half as much pizza as David, while David consumed the remaining half of the pie.
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A landscaper drew a scale drawing of a rectangular yard using the scale, 2 cm :3 m , before beginning to work on the yard.
(a) The landscaper plans to put a fence around the entire yard. How many meters of fencing does she need? Show your work.
(b) The landscaper plans to create a rectangular garden that is 1/3 the size of the actual yard. What is the area of the garden? Show your work
(a) The landscaper needs 3 times the sum of the length and width of the yard in meters for the fencing.
(b) The area of the garden is one-third of the area of the yard, multiplied by 2.25.
We have,
(a) To find the amount of fencing needed, we need to determine the perimeter of the yard in meters.
According to the scale, 2 cm on the drawing represents 3 m in reality. This means that 1 cm on the drawing represents 1.5 m in reality (since 3 m divided by 2 cm is 1.5 m/cm).
Let's assume the length of the yard in the drawing is L cm and the width is W cm.
Then, the length of the actual yard would be L x 1.5 m, and the width would be W * 1.5 m.
The perimeter of the yard is given by the formula:
Perimeter = 2 x (length + width)
Substituting the actual measurements, we have:
Perimeter = 2 x (L x 1.5 m + W x 1.5 m)
= 3 x (L + W) m
Therefore, the landscaper would need 3 times the sum of the length and width of the yard in meters for the fencing.
(b) The area of the garden can be determined by calculating 1/3 of the area of the actual yard.
Let's assume the area of the yard in the drawing is A square cm. Then, the area of the actual yard would be A x (1.5 m)², since each dimension is scaled by 1.5 m/cm.
To find the area of the garden, we calculate:
Area of garden = (1/3) x Area of yard
= (1/3) x (A x (1.5 m)^2)
= (1/3) x (A x 2.25) square meters
Therefore, the area of the garden would be one-third of the area of the yard, multiplied by 2.25.
Thus,
(a) The landscaper needs 3 times the sum of the length and width of the yard in meters for the fencing.
(b) The area of the garden is one-third of the area of the yard, multiplied by 2.25.
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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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A man needed to sell a car. He priced it at $2,700 the first day. The second day he reduced the price by 12%. What was the price of the car after this reduction?
After reducing the price by 12%, the price of the car would be $2,376. To find the price of the car after a 12% reduction, we can calculate 12% of the original price and subtract it from the original price.
To find the price of the car after the 12% reduction, we need to calculate 12% of $2,700 and subtract that amount from the original price. First, we find 12% of $2,700 by multiplying 0.12 (12% expressed as a decimal) by $2,700:
12% of $2,700 = 0.12 * $2,700 = $324
Next, we subtract $324 from the original price of $2,700:
$2,700 - $324 = $2,376
Therefore, after the 12% reduction, the price of the car would be $2,376. This reduction reflects a decrease in price from the original value, providing potential buyers with a discounted price for the car.
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Joshua buys 1/5 pound of mixed nuts. 1/2 pound of chocolate candies, and 1 1/4 pound of granola to make the trail mix.
How much did Joshua spend to make the trail mix?
Joshua spent an amount determined by the prices of mixed nuts, chocolate candies, and granola to make the trail mix.
The exact cost cannot be determined without the price per pound of each ingredient.
To calculate how much Joshua spent to make the trail mix, we need to know the price per pound of each ingredient: mixed nuts, chocolate candies, and granola. Without this information, we cannot provide an exact answer.
However, we can provide a general approach to calculate the cost if we have the price per pound for each ingredient. Let's assume the price per pound of mixed nuts is $x, the price per pound of chocolate candies is $y, and the price per pound of granola is $z.
To determine the cost of each ingredient, we multiply the weight in pounds by the respective price per pound. For mixed nuts, Joshua bought 1/5 pound, so the cost of mixed nuts would be (1/5) * x. For chocolate candies, he bought 1/2 pound, so the cost of chocolate candies would be (1/2) * y. Lastly, for granola, he bought 1 1/4 pounds, so the cost of granola would be (1 1/4) * z.
To find the total cost, we add the costs of all three ingredients: (1/5) * x + (1/2) * y + (1 1/4) * z.
Without the specific prices per pound, we cannot provide a numerical answer, but you can calculate the total cost using the given weights and the corresponding prices per pound.
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composting method in which earthworms are used is known as ????
Vermicomposting is the practice of composting with earthworms.
Vermicomposting is the term for the composting process that uses earthworms.
Vermicomposting is the process of turning organic waste products, like kitchen scraps, yard debris, and paper, into nutrient-rich compost by using different types of worms.
Castings, which the worms produce after eating the organic debris, are very good for the health of the soil and the growth of plants.
In particular for small-scale or indoor composting systems, vermicomposting is a well-liked and efficient form of composting.
Hence, Vermicomposting is the name given to the composting technique that uses earthworms.
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Write an exponential function in the form y=ab^xy=ab
x
that goes through points (0, 16)(0,16) and (2, 400)(2,400)
The values of a = 16 and b = 5 the exponential function in the form y = ab²x that passes through the given points is y = 16 × 5²x
An exponential function in the form y = ab²x that passes through the points (0, 16) and (2, 400), to determine the values of a and b.
Using the point (0, 16), substitute x = 0 and y = 16 into the exponential function:
16 = ab²0
16 = a ×1
a = 16
The value of a, which is 16.
Using the point (2, 400), substitute x = 2, y = 400, and a = 16 into the exponential function:
400 = 16b²
To solve for b, divide both sides of the equation by 16:
400/16 = b²
25 = b²
Taking the square root of both sides,
b = ±√25
Since are looking for a positive base, the positive square root:
b = 5
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Ali has hired Mark and Alexis to work for his shipping company. Mark can load a truck with packages in 120 minutes. Alexis can load the same number of packages in 240 minutes.
Ali has hired Mark and Alexis to work for his shipping company, and Mark can load a truck with packages in 120 minutes, while Alexis can load the same number of packages in 240 minutes.
To find out how long they will take to load a truck together, we'll use the formula below:T = (T₁ × T₂) ÷ (T₁ + T₂)Where T is the time it takes for Mark and Alexis to load a truck together, T₁ is the time it takes for Mark to load a truck alone, and T₂ is the time it takes for Alexis to load a truck alone.
We can plug in the given values: T = (120 × 240) ÷ (120 + 240) = 28,800 ÷ 360 = 80Therefore, it would take Mark and Alexis 80 minutes to load a truck together.
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Angles 1 and 2 are vertical angles. If angle 1 is 62 degrees, what is the measurement of angle 2?
If angles 1 and 2 are vertical angles, then they are congruent. If angle 1 measures 62 degrees, then angle 2 will also measure 62 degrees.
Vertical angles are formed by the intersection of two lines. They are opposite each other and have equal measures. In this case, if angle 1 measures 62 degrees, angle 2 will also measure 62 degrees because they are vertical angles.
This property of vertical angles can be understood based on the concept of a straight line. When two lines intersect, they form two pairs of vertical angles. Since a straight line measures 180 degrees, each pair of vertical angles will have a total measure of 180 degrees, and thus, each angle within the pair will have the same measure. Therefore, if angle 1 measures 62 degrees, angle 2 will also measure 62 degrees.
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