To prove that AAGE and AOLD are congruent by SAS, the other information that is needed is: GE = LD.Explanation:To prove that two triangles are congruent using SAS (side-angle-side) postulate, we need to know.
Two sides and the angle between them in one triangle are congruent to the corresponding sides and angle in the other triangle.So, given AG = OL, AGE = OLD, and AEG = ODL, we can conclude that two angles and a side are equal in both triangles.However, to apply the SAS postulate, we need to have another pair of equal sides in both triangles. And that is given by GE = LD. Hence, option 1) is the correct answer.Other options don't provide the necessary information to prove the congruence of the two triangles using SAS.
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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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A grocer wants to make a 10-pound mixture of peanuts and cashews that he can sell for $4. 75 per pound. If peanuts cost $4. 00 per pound and cashews cost $6. 50 per pound, how many pounds of each should he use? Let p = pounds of peanuts and let c = pounds of cashews. Write a system of equations that could be used to solve the problem.
The system of equations that could be used to solve the problem is:
1. p + c = 10 (equation representing the total weight of the mixture)
2. 4.00p + 6.50c = 4.75(10) (equation representing the cost of the mixture)
Let's break down the given information and use it to set up the system of equations.
1. Total weight equation:
The grocer wants to make a 10-pound mixture of peanuts and cashews. Since we are given that p represents the pounds of peanuts and c represents the pounds of cashews, we can write the equation:
p + c = 10
2. Cost equation:
The grocer wants to sell the mixture for $4.75 per pound. The cost of the peanuts is $4.00 per pound and the cost of cashews is $6.50 per pound. To calculate the total cost, we multiply the cost per pound by the weight of each component (peanuts and cashews) and sum them up. This can be expressed as:
4.00p + 6.50c = 4.75(10)
By setting up this system of equations, we can solve for the values of p and c, which represent the pounds of peanuts and cashews, respectively, that the grocer should use in order to make the 10-pound mixture.
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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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Well exercising Ned walked 1/9 of a mile in one 1/2 of an hour at this rate how far will he have traveled after 1 hour
Ned will have travelled 2/9 mile after 1 hour
How to determine how far will he have traveled after 1 hourFrom the question, we have the following parameters that can be used in our computation:
Ned walked 1/9 of a mile in one 1/2
using the above as a guide, we have the following:
Rate = (1/9)/(1/2)
Evaluate the the quotient
Rate = 2/9
This means that he will have travelled 2/9 mile after 1 hour
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which statement is true about this comparison
0.739 > 0.7380
The statement that is true about this comparison is that they differ in the thousandths place, with 0.739 being greater than 0.7380.
The statement that is true about the comparison
0.739 > 0.7380
is that they differ in the thousandths place. The difference between the two numbers is
0.001 or 1/1000,
which is why we can say that they differ in the thousandths place. This difference is very small, but it is enough to make
0.739 greater than 0.7380.
The comparison between
0.739 and 0.7380
is true in that the former is greater than the latter by a small margin. The two numbers differ in the thousandths place, with 0.739 having a value of
0.739 and 0.7380
having a value of 0.738.
The difference between the two values is
0.001 or 1/1000,
which is very small.
However, this difference is enough to make 0.739 greater than 0.7380.
Therefore, the statement that is true about this comparison is that they differ in the thousandths place, with
0.739 being greater than 0.7380.
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Abby drew a scale drawing to represent her living room. The drawing is rectangular. The longer sides measure 40. 5 centimeters and the shorter sides measure 34. 5 centimeters. Abby decides she wants the drawing to be smaller. She will reduce it by a scale factor of 13. What will be the measure of the shorter sides? Select from the drop-down menu to correctly complete the statement. The measure of the shorter sides will be Choose. Cm.
`The measure or dimensions of the shorter sides will be 2.65 cm, given that the longer sides measure 40. 5 centimeters and the shorter sides measure 34. 5 centimeters and the scale-factor used for reduction is 13.
Given that,
The longer sides of the rectangular measure 40.5 cm.
The shorter sides of the rectangular measure 34.5 cm.
Scale factor = 13.
The scale factor is the ratio of the length of a side of one figure to the length of the corresponding side of the second figure.
To find the measure of the shorter sides of a rectangle, multiply the length of the shorter sides by the scale factor.Abby decides to reduce the scale drawing of her living room by a scale factor of 13.
Multiply 34.5 cm by 1/13 to find the length of the shorter sides in the reduced scale drawing as follows;`
34.5*1/13=2.65
The measure of the shorter sides will be 2.65 cm.
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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 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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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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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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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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An IV blood administration is in place. A bag of 376 ml is hung at
1100hrs. How long will this bag take to infuse at maximum time?
The time it would take for the bag to infuse at the maximum time would be the value of 1. 5 hours.
How to find the time ?The maximum rate of infusion for an IV bag is 250 ml/hour. This means that the maximum time it would take for the bag to infuse is:
= Quantity in bag / Maximum rate of infusion
Therefore, it will take:
= 376 ml / 250 ml/hour
= 1. 5 hours to infuse the entire bag
In conclusion, the time it would take for the bag to infuse at the maximum time is 1. 5 hours.
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What is the explicit formula for the sequence below?4, – 12, 36, – 108,...A.tn=(−3)n−1B.tn=4(−3)n−1C.tn=4(3)n−1D.tn=4(−3)n
The explicit formula for the given sequence 4, -12, 36, -108,... is D. tn = 4(-3)n. Option D
In the given sequence, each term is obtained by multiplying the previous term by -3. This indicates an exponential decay pattern with a common ratio of -3.
To derive the explicit formula, we start with the initial term 4 and observe that each subsequent term can be obtained by multiplying the previous term by -3:
Term 1: 4
Term 2: -3 × 4 = -12
Term 3: -3 ×(-12) = 36
Term 4: -3 × 36 = -108
We can generalize this pattern by using the formula tn = ar^(n-1), where tn represents the nth term, a is the initial term, and r is the common ratio. In this case, a = 4 and r = -3. Thus, the explicit formula for the sequence is tn = 4(-3)n which matches option D.
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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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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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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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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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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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1. Use each of the Numbers once, In any order. To form at least TWO number sentences that equal the target number
TARGET NUMBER: 2
17, 5, 8, 2, 9
2. Let A=3 B=28 C=50
D=12 E=2 F=18
Write a minimum of 5 different
relationship statements for the
variables.
Ex. DE=B-2E
Using 17 + 5 - 8 + 9 - 2 = 21 and 2 + 9 - 8 + 17 - 5 = 15 as two number sentences, we can form the target number of 2.
1) 2C = BF
2) B - 3E = A
3) C - A = 2D
4) F - A + B = 47
5) 3E - B + 2A = 8
In the first statement, the variable C is multiplied by 2, and the result is equal to the product of variables B and F. In the second statement, the product of variables E and 3 is subtracted from B, and the result is equal to A.
In the third statement, the difference between variables C and A is equal to twice the value of variable D. In the fourth statement, the sum of variables F and B is subtracted from A, and the result is equal to 47.
In the fifth statement, twice the value of variable A is added to 3 times the value of variable E, and this sum is subtracted from the value of variable B, which gives 8.
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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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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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What is the answer?
(x^2+4x-43.61)
Limit -----------------------
(x^2-0.2x-23.03)
----> 4.9
The limit of the expression (x^2+4x-43.61)/(x^2-0.2x-23.03) as x approaches 4.9 is equal to a specific value. The limit of the given expression as x approaches 4.9 is approximately 1.51.
To find the limit as x approaches 4.9, we substitute 4.9 into the expression and evaluate it. Plugging in 4.9 for x, we get ((4.9)^2 + 4(4.9) - 43.61)/((4.9)^2 - 0.2(4.9) - 23.03). Simplifying this expression gives us (24.01 + 19.6 - 43.61)/(24.01 - 0.98 - 23.03), which further simplifies to 0/0.
When we encounter an indeterminate form like 0/0, we can apply mathematical techniques to evaluate the limit. One approach is to use L'Hôpital's Rule, which states that if the limit of the ratio of two functions f(x)/g(x) is of the form 0/0 or ∞/∞ as x approaches a certain value, then the limit of the ratio is equal to the limit of the derivative of f(x) divided by the derivative of g(x) as x approaches the same value.
In this case, we can differentiate the numerator and denominator separately and apply L'Hôpital's Rule. After differentiating, we obtain the new expression (2x + 4)/(2x - 0.2). Evaluating this expression at x = 4.9 gives us (2(4.9) + 4)/(2(4.9) - 0.2), which simplifies to 14.8/9.8. Therefore, the limit of the given expression as x approaches 4.9 is approximately 1.51.
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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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James, Gilbert, Matthew, and Simon ran in a relay race. Their times are
listed in the chart below.
James
2/3
Gilbert
11/12
Matthew
5/6
Simon
7/12
1. Find the difference between the fastest boy’s time and the slowest
boy’s time
The difference between the fastest boy's time and the slowest boy's time can be found by comparing their respective times and calculating the difference.
To determine the fastest and slowest times among James, Gilbert, Matthew, and Simon, we examine their recorded times: 2/3, 11/12, 5/6, and 7/12.
To compare these fractions, we need to find a common denominator. In this case, the least common multiple of the denominators 3, 12, 6, and 12 is 12.
Converting the fractions to have a denominator of 12, we get:
James: 2/3 = 8/12
Gilbert: 11/12 (already in terms of 12)
Matthew: 5/6 = 10/12
Simon: 7/12 (already in terms of 12)
Now, we can clearly see that the fastest time is 8/12 (James) and the slowest time is 11/12 (Gilbert).
To find the difference between these two times, we subtract the slowest time from the fastest time:
8/12 - 11/12 = -3/12 = -1/4
Therefore, the difference between the fastest boy's time and the slowest boy's time is -1/4, or in other words, the fastest boy is 1/4 of a unit of time faster than the slowest boy.
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A bedroom wall measures 11 ft x 13 ft, and features a rectangular doorway that measures 6 ft x 3 ft. How many square of paint will be needed to cover the wall only?
The wall area that needs to be painted, excluding the doorway, is 125 square feet.
The total area of the wall is obtained by multiplying its length and width:
Total area = 11 ft * 13 ft = 143 square feet.
The area of the doorway is given by multiplying its length and width:
Doorway area = 6 ft * 3 ft = 18 square feet.
To find the area of the wall that needs to be painted, we subtract the area of the doorway from the total area:
Painting area = Total area - Doorway area = 143 square feet - 18 square feet = 125 square feet.
Therefore, you will need 125 square feet of paint to cover the wall only.
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A rectangular swimming pool is 28 feet wide. Jason drew the pool at the scale below. 1 inch : 4 feet How many inches wide is Jason's drawing?
The actual width of the rectangular swimming pool is given as 28 feet. Jason's drawing is made to a scale of 1 inch : 4 feet.
To find out how many inches wide Jason's drawing is, we need to divide the actual width of the pool by the scaling factor (4 feet).
28 feet / 4 feet = 7
Therefore, Jason's drawing of the pool is 7 inches wide.
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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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Elizabeth’s credit card computes her finance charges using the previous balance method and a 30-day billing cycle. The table below shows Elizabeth’s credit card transactions in July. Date Amount ($) Transaction 7/1 969. 26 Beginning balance 7/3 45. 00 Payment 7/10 67. 48 Purchase 7/12 20. 00 Payment 7/28 85. 00 Payment If Elizabeth has an APR of 14. 61%, how much will her July finance charge be? a. $9. 97 b. $12. 62 c. $11. 80 d. $10. 80.
To calculate Elizabeth's finance charge using the previous balance method, we need to determine the average daily balance and then apply the APR (Annual Percentage Rate) to calculate the finance charge.
First, let's calculate the average daily balance:
Beginning Balance: $969.26
Days until payment: 2 (from July 1st to July 3rd)
Payment: $45.00
Days until purchase: 7 (from July 3rd to July 10th)
Purchase: $67.48
Days until payment: 2 (from July 10th to July 12th)
Payment: $20.00
Days until payment: 16 (from July 12th to July 28th)
Payment: $85.00
To calculate the average daily balance, we sum up the balances for each day and divide it by the total number of days in the billing cycle (30 days).
Average Daily Balance = (969.26 × 2 + 0 × 7 + 67.48 × 2 + 0 × 16) / 30 = $85.95
Next, we can calculate the finance charge using the APR:
Finance Charge = Average Daily Balance × (APR / 365) × Number of Days in the Billing Cycle
Finance Charge = 85.95 × (0.1461 / 365) × 30 ≈ $9.97
Therefore, Elizabeth's July finance charge will be approximately $9.97. The correct answer is option a.
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The perimeter of a rectangle is 22cm and the length of each side is a natural number. How many different areas in centimeter squared can the rectangle have?
option B is the correct answer.
The perimeter of a rectangle is 22 cmLet the length of the rectangle be 'l' and the breadth be 'b'As per the question, the perimeter of the rectangle is given by;Perimeter = 2(l + b) => 2(l + b) = 22 => l + b = 11.As we know that the area of a rectangle is given by;Area = l × b
Therefore, the different areas of the rectangle are; l × b1 × (11 - 1) = 10 cm²2 × (11 - 2) = 18 cm²3 × (11 - 3) = 24 cm²4 × (11 - 4) = 28 cm²5 × (11 - 5) = 30 cm²6 × (11 - 6) = 30 cm²7 × (11 - 7) = 28 cm²8 × (11 - 8) = 24 cm²9 × (11 - 9) = 18 cm²10 × (11 - 10) = 10 cm²Hence, there are only 8 different areas of the rectangle i.e., 10 cm², 18 cm², 24 cm², 28 cm², 30 cm².
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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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