To find the values of x for which the perimeter of a rectangle is less than 140, we can use the formula for the perimeter of a rectangle, which is given by:
Perimeter = 2 * (Length + Width)
Let's assume the length of the rectangle is L and the width is W. We can then rewrite the formula as:
Perimeter = 2 * (L + W)
According to the problem, we want the perimeter to be less than 140. Therefore, we can write the inequality as:
2 * (L + W) < 140
Dividing both sides of the inequality by 2:
L + W < 70
This inequality represents the condition for the perimeter of the rectangle to be less than 140.
However, since we don't have specific information about the relationship between the length and width (L and W), we cannot solve for the values of x explicitly. If you provide any additional constraints or information about the rectangle, I can assist you further in solving the inequality.
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Write an algebraic expression for the number of points scored by a football team that makes (t)6 touchdowns, (f)3 field goals, and (e)1 extra points. (write in the respective order: touchdowns, field goals, extra points)
The algebraic expression for the number of points scored by a football team that makes t touchdowns, f field goals, and e extra points is: 6t + 3f + 1e. Therefore, the team would have scored 15 points in this case.
To calculate the total number of points scored by a football team, we can assign variables to the number of touchdowns, field goals, and extra points. Let's use t for touchdowns, f for field goals, and e for extra points.
The points awarded for each touchdown is 6, for each field goal is 3, and for each extra point is 1. To find the total number of points, we multiply the number of touchdowns by 6, the number of field goals by 3, and the number of extra points by 1, and then add them together.
Hence, the algebraic expression for the number of points scored is: 6t + 3f + 1e.
For example, if a team scores 2 touchdowns, 1 field goal, and 0 extra points, we can substitute the values into the expression:
6(2) + 3(1) + 1(0) = 12 + 3 + 0 = 15.
Therefore, the team would have scored 15 points in this case.
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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
Lori is solving the equation 4x2 + 5x – 6 = 0 using the quadratic formula. Which expression shows the correct numbers substituted into the quadratic formula to solve?
Question 2 options:
−5±(5)2−4(4)(−6)√2
−5±(5)2−4√2(4)
−5±5−4(4)(−6)√2(4)
−5±(5)2−4(4)(−6)√2(4)
The correct expression with the substituted values is −5±√(5^2 - 4(4)(-6)) / (2(4)).
The expression that shows the correct numbers substituted into the quadratic formula to solve the equation 4x^2 + 5x - 6 = 0 is:
−5±√(5^2 - 4(4)(-6)) / (2(4))
In the quadratic formula, the general form is x = (-b ± √(b^2 - 4ac)) / (2a), where a, b, and c are the coefficients of the quadratic equation. In this case, a = 4, b = 5, and c = -6.
Substituting these values into the quadratic formula, we have:
x = (-5 ± √(5^2 - 4(4)(-6))) / (2(4))
Simplifying further:
x = (-5 ± √(25 + 96)) / (8)
x = (-5 ± √121) / 8
x = (-5 ± 11) / 8
Therefore, the correct expression with the substituted values is:
−5±√(5^2 - 4(4)(-6)) / (2(4))
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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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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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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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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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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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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 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 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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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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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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When rolling two standard number cubes, what is the probability of rolling at least one six?
Group of answer choices
6/36
11/36
1/36
12/36
The probability of rolling at least one six when rolling two standard number cubes is 11/36.
To determine the probability, we first need to find the total number of possible outcomes when rolling two standard number cubes. Each cube has 6 faces, numbered from 1 to 6, so the total number of outcomes is 6 multiplied by 6, which equals 36.
Next, we need to calculate the number of favorable outcomes, which is the number of outcomes where at least one six is rolled. There are three possible scenarios:
Rolling a six on the first cube and any number on the second cube.
Rolling any number on the first cube and a six on the second cube.
Rolling a six on both the first and second cubes.
For each scenario, there is a 1/6 probability of rolling a six on a single cube. Therefore, the number of favorable outcomes is 1 + 1 + 1 = 3.
Finally, we divide the number of favorable outcomes (3) by the total number of possible outcomes (36) to calculate the probability:
Probability = Number of favorable outcomes / Total number of possible outcomes
= 3 / 36
= 1 / 12
= 11 / 36
Therefore, the probability of rolling at least one six when rolling two standard number cubes is 11/36.
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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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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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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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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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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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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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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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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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At the international space station, a chemist cooled his solution for 20min at a steady rate. The temperature of his solution dropped from +5 degrees Celsius to -55 degrees Celsius. What was the temperature change per minute?
The temperature change per minute during the 20-minute cooling period at a steady rate was -3 degrees Celsius per minute.
To calculate the temperature change per minute, we need to determine the difference in temperature and divide it by the time in minutes. In this case, the initial temperature was +5 degrees Celsius, and the final temperature was -55 degrees Celsius. The temperature change is the difference between these two values: -55 - (+5) = -60 degrees Celsius.
Since the cooling period lasted for 20 minutes, we divide the temperature change by the time: -60 degrees Celsius / 20 minutes = -3 degrees Celsius per minute.
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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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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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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 y-intercept is (0,-4). The x-intercepts are (-2,0) and (2,0). The degree is 2. End behavior: as x \rightarrow- \infty , f(x) \rightarrow \infty , as x \rightarrow \infty , f(x) \rightarrow \infty .
The end behaviors of the graph of the function are given by:
as x → −∞, f(x) → ∞
as x → ∞, f(x) → ∞
Thus, this is the required answer.
Solution:
The given polynomial function is of degree 2 (quadratic function).f(x) = ax² + bx + c, Where a, b, and c are real numbers with a ≠ 0.
The quadratic function has the general form: f(x) = a(x - r)(x - s)where r and s are the x-intercepts.
The given x-intercepts are (-2,0) and (2,0) which means that:r = -2 and s = 2.
So, the quadratic function can be written as:
f(x) = a(x - (-2))(x - 2)f(x) = a(x + 2)(x - 2), where a is a non-zero constant.The y-intercept is (0,-4).
We know that the y-intercept occurs where x = 0.
Substituting x = 0 and y = -4 in the quadratic function:
f(x) = a(x + 2)(x - 2)
when x = 0,
y = -4.
-4 = a(0 + 2)(0 - 2)
=> -4 = -4a
=> a = 1
The quadratic function is:
f(x) = (x + 2)(x - 2)
The end behaviors of the graph of the function are given by:
as x → −∞, f(x) → ∞
as x → ∞, f(x) → ∞
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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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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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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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