Neither student solved the equation for k correctly because k = 2 and 1/8.
Both Adler and Erika made errors in their calculations. Adler incorrectly equated 13/8 with k + 1/2, and then subtracted 1/2 from both sides, resulting in 9/8 = k. This is incorrect because k should be equal to 2 and 1/8, not 9/8. On the other hand, Erika correctly set up the equation as 13/8 = k + 1/2, but she made an error when subtracting 1/2 from both sides. Instead of obtaining 9/8 as she claimed, it should be 12/8 or simply 3/2. Therefore, neither student solved for k correctly, and the correct answer is that k is equal to 2 and 1/8, which was not obtained by either of them.
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Raymond works in an electronics store and gets a 12 percent employee discount. The original cost of a video game system is $175. What is the discounted price of the game system? $154. 00 $163. 00 $187. 00 $196. 0.
The discounted-price of the game system is $154.00, given the original-cost of a video game system is $175 and Raymond works in an electronics store and gets a 12 percent employee discount.
The discounted price, we need to find 12% of $175 which is equal to: [tex]\frac{12}{100}\times175=21[/tex]
The employee discount is $21.
We need to subtract this discount from the original cost:
175 - $21 = 154
So, the discounted price of the game system is $154.00.
Therefore, the correct option is $154.00
The discounted price of the game system is indeed $154.00.
The original cost of the game system is $175, and
Raymond receives a 12% employee discount.
We calculate 12% of $175, which is $21.
By subtracting this discount from the original cost, we get $154.00, which is the final discounted price.
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At a high school, students can choose between three art electives, four history electives, and five computer electives. Each student can choose two electives. What is the approximate probability that a student chooses a computer elective and an art elective? 0. 11364 0. 21212 0. 22727 0. 42424.
The approximate probability that a student chooses a computer elective and an art elective is 1 or 100%.
To determine the approximate probability that a student chooses a computer elective and an art elective, we need to consider the total number of electives available and the specific choices a student can make.
To calculate the probability, we can follow these steps:
Determine the total number of possible elective combinations: Since each student can choose two electives, we multiply the number of options for each elective category. In this case, it would be 3 art electives * 5 computer electives = 15 possible combinations.
Determine the number of favorable outcomes: We want to find the number of combinations where a student chooses one art elective and one computer elective. Since there are 3 art electives and 5 computer electives, the number of favorable outcomes is 3 art electives * 5 computer electives = 15 combinations.
Calculate the probability: To find the approximate probability, we divide the number of favorable outcomes by the total number of possible combinations. Therefore, the probability is 15/15 = 1. Therefore, the approximate probability that a student chooses a computer elective and an art elective is 1 or 100%.
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The average yearly temperature in New York is 56 F The Average yearly temps tire in Alaska is -11 F
The average yearly temperature in New York is 56°F, while the average yearly temperature in Alaska is -11°F. This is because New York is located in a temperate climate zone, while Alaska is located in an arctic climate zone. The temperate zone has warm summers and cool winters, while the arctic zone has long, cold winters and short, cool summers.
The average temperature in New York is higher because it is closer to the equator and therefore receives more sunlight throughout the year. In contrast, Alaska is farther from the equator and receives less sunlight, leading to colder temperatures. Additionally, Alaska is known for its large snowfall amounts, which contributes to the low average temperature. New York and Alaska are two of the most popular states in the United States of America. The average yearly temperature in New York is 56°F, while the average yearly temperature in Alaska is -11°F. This is because New York is located in a temperate climate zone, while Alaska is located in an arctic climate zone.
The temperate zone has warm summers and cool winters, while the arctic zone has long, cold winters and short, cool summers. The average temperature in New York is higher because it is closer to the equator and therefore receives more sunlight throughout the year. In contrast, Alaska is farther from the equator and receives less sunlight, leading to colder temperatures. Additionally, Alaska is known for its large snowfall amounts, which contributes to the low average temperature. The difference in temperature between these two states is significant and can be attributed to various factors such as geography, climate, latitude, and distance from the equator. These factors impact the amount of sunlight that each state receives and, in turn, affect the overall temperature. Furthermore, these factors also influence other aspects of life, such as plant growth and wildlife, making each state unique.
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ABCD - FECG
B
5
E
6
100°
LO
A
600
n
4
120°
у
G
w
D
y = [?]
Given the figure, we have to find the value of y.Using the angle sum property of a quadrilateral, we know that the sum of angles in a quadrilateral is 360 degrees.
Therefore:
∠A + ∠B + ∠C + ∠D = 360°
We know that
∠A = 600°,
∠B = 120°, and
∠C = 100°
∠A + ∠B + ∠C + ∠D = 360°
600° + 120° + 100° + ∠D = 360°
820° + ∠D = 360°
∠D = 360° - 820°
∠D = -460°
Since angle D is not possible to be negative, we know that there must be a mistake in the diagram. We need to make sure that the figure is correct before we can find the value of y.
Therefore, the value of y cannot be determined with the information given in the figure.
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Choose all of the conversions that are true for the capacity of the pitcher of orange juice.
the pitcher is 3. 5liters a 0. 35 kL
B. 0. 035 kL
C. 0. 0035 kL
D. 3,500 mL
E. 350 mL
The correct conversions are D. 3,500 mL and E. 350 mL.
To determine which conversions are true for the capacity of the pitcher of orange juice, we can use the following conversion factors:
1 liter (L) = 1,000 milliliters (mL)
1 kiloliter (kL) = 1,000 liters (L)
Given that the pitcher has a capacity of 3.5 liters, we can convert it to the following units:
A. 0.35 kL: This is incorrect since 0.35 kL would be equivalent to 350 liters, not 3.5 liters.
B. 0.035 kL: This is incorrect since 0.035 kL would be equivalent to 35 liters, not 3.5 liters.
C. 0.0035 kL: This is incorrect since 0.0035 kL would be equivalent to 3.5 liters, not 3.5 liters.
D. 3,500 mL: This is correct since 3.5 liters is equivalent to 3,500 milliliters.
E. 350 mL: This is correct since 3.5 liters is equivalent to 350 milliliters.
Therefore, the correct conversions are D. 3,500 mL and E. 350 mL.
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How is President Reagan's word choice effective?
Check the three boxes that apply.
President Reagan's word choice is effective in various ways, which can be summarized by selecting three applicable options.
Clarity: President Reagan's word choice is effective in conveying clear and concise messages. By using simple and straightforward language, he ensured that his ideas were easily understood by a wide audience. This allowed him to connect with people from different backgrounds and effectively communicate his policies and vision.
Persuasiveness: President Reagan's word choice is effective in persuading his audience. He had a skill for using persuasive language that appealed to people's emotions and values. Through his speeches, he often employed rhetorical techniques such as vivid imagery, metaphors, and powerful phrases that resonated with his listeners. This helped him build support for his policies and gain public trust.
Inspirational: President Reagan's word choice is effective in inspiring and motivating people. He had a natural ability to use uplifting and optimistic language that instilled hope and confidence in the American people. His speeches often contained aspirational messages, emphasizing the strength and potential of the nation. By employing words that invoked a sense of pride and unity, he was able to rally support and encourage positive change.
In conclusion, President Reagan's word choice was effective in multiple ways. His clarity, persuasiveness, and ability to inspire through his language contributed to his success as a communicator and leader. These attributes allowed him to effectively convey his ideas, gain support for his policies, and leave a lasting impact on the American public.
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A number cube, labeled 1-6, is rolled 4
times. What is the probability that cube
will land on an even number three out of
four rolls?
When rolling a number cube four times, the probability of obtaining an even number in three of the four rolls is 1/4.
To calculate the probability that a number cube will land on an even number three out of four rolls, we need to consider the total number of possible outcomes and the number of favorable outcomes.
The total number of possible outcomes when rolling a number cube four times is 6^4, which is equal to 1,296. This is because each roll has six possible outcomes (numbers 1 to 6), and the rolls are independent events, so we multiply the number of outcomes for each roll.
Now, let's consider the favorable outcomes. We want the cube to land on an even number three out of four times. There are two cases that satisfy this condition: either the first, second, and third rolls are even, or the second, third, and fourth rolls are even.
Case 1: First, second, and third rolls are even.
The probability of rolling an even number on a single roll is 3/6, or 1/2 since there are three even numbers (2, 4, and 6) out of six total numbers on the cube.
So, the probability of the first, second, and third rolls being even is (1/2) * (1/2) * (1/2) = 1/8.
Case 2: Second, third, and fourth rolls are even.
Again, the probability of rolling an even number on a single roll is 1/2.
So, the probability of the second, third, and fourth rolls being even is (1/2) * (1/2) * (1/2) = 1/8.
Now, we need to add the probabilities from both cases because we are interested in the probability of either of these events occurring:
1/8 + 1/8 = 2/8 = 1/4.
Therefore, the probability that the cube will land on an even number three out of four rolls is 1/4.
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A business owner opens one store in town A. The equation mc024-1. Jpgrepresents the anticipated profit after t years. The business owner opens a store in town B six months later and predicts the profit from that store to increase at the same rate. Assume that the initial profit from the store in town B is the same as the initial profit from the store in town A. At any time after both stores have opened, how does the profit from the store in town B compare with the profit from the store in town A? 65% 96% 104% 154%.
The profit from the store in town B compared with the profit from the store in town A is the ratio represented by 96%.
In the question, we are given that a business owner opens one store in town A.
The equation p(x) = [tex]10,000 * 1.075^{t}[/tex]represents the anticipated profit after t years.
The business owner opens a store in town B six months later and predicts the profit from that store to increase at the same rate.
We are asked to assume that the initial profit from the store in town B is the same as the initial profit from the store in town A and find the comparison between the profits from the store in town B to the store in town A.
We take the time for the store in town A as t₁.
Then the time for the store in town B is t₁ - 0.5, as store in town B is opened 6 months after the store in town A.
To compare the profits, we take the ratio of the profits from the stores.
= Profit from the store in town B/Profit from the store in town BA
= [tex]10,000 (1.075)^{t_{1}- 0.5 } / 10,000 (1.075)^{t_{1} }[/tex]
= [tex](1.075)^{t_{1}- 0.5-t_{1} }[/tex]
= [tex]1.075^{- 0.5}[/tex]
= 0.96448
= 96% (approx.)
Therefore, the profit from the store in town B compared with the profit from the store in town A is the ratio represented by 96%.
Refer to the attachment for the proper question.
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A business advertises that everything in the store is an additional 10% off the already reduced prices. Marcus picks out 2 shirts that are on a 30% off rack. If the shirts are originally priced at $28. 99 and $30. 29 and there is 6% sales tax, how much does Marcus end up paying for them? a. $39. 59 b. $37. 70 c. $37. 35 d. $35. 57.
Marcus ends up paying $37.70 for the two shirts. To calculate the final price Marcus pays for the shirts, we need to follow these steps:
Calculate the discounted price of each shirt: Since the shirts are on a 30% off rack, the discounted price of the first shirt is 0.70 * $28.99 = $20.29, and the discounted price of the second shirt is 0.70 * $30.29 = $21.20.
Calculate the total cost of the shirts before tax: The total cost of the two shirts is $20.29 + $21.20 = $41.49.Apply the additional 10% off discount: To calculate the final price after the additional discount, we need to subtract 10% from the total cost. 10% of $41.49 is 0.10 * $41.49 = $4.15. Subtracting this amount from the total cost gives us $41.49 - $4.15 = $37.34.
Add the sales tax: To calculate the final price including the 6% sales tax, we need to add 6% of $37.34 to the total cost. 6% of $37.34 is 0.06 * $37.34 = $2.24. Adding this amount to the total cost gives us $37.34 + $2.24 = $39.58.
Rounding to the nearest cent, Marcus ends up paying $39.59 for the two shirts. Therefore, the correct answer is option a. $39.59.
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Use the information to answer the question.
Information
Tim has 3 tooth picks. Amilia has 60 tooth picks.
Question
Amilia has how many times as many tooth picks as Tim? Enter the answer in the box.
Amilia has 20 times as many toothpicks as Tim. Tim has 3 tooth picks. Amilia has 60 tooth picks.
To determine how many times as many toothpicks Amilia has compared to Tim, we can divide the number of toothpicks Amilia has by the number of toothpicks Tim has.
Amilia has 60 toothpicks, while Tim has 3 toothpicks.
To calculate the ratio, we divide the number of toothpicks Amilia has by the number of toothpicks Tim has:
60 / 3 = 20
Therefore, Amilia has 20 times as many toothpicks as Tim. This means that the number of toothpicks Amilia has is twenty times greater than the number of toothpicks Tim has. It indicates a significant difference in the quantity of toothpicks possessed by the two individuals.
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Question 3 (4 points)(02.01)The figure shows a pair of parallel line segments on a coordinate grid:A coordinate plane is shown. Line segment GH runs from -1 comma negative 1 to 3 comma negative 1. Line segment EF runs from negative 1 comma -2 to 3 comma negative 2.The line segments are translated 2 units to the right to form E′F′ and G′H′. Which statement describes E′F′ and G′H′? (4 points)aLine segments E′F′ and G′H′ do not intersect and are closer together than EF and GH.bLine segments E′F′ and G′H′ intersect at (−2, 0) and are two times farther apart than EF and GH.cLine segments E′F′ and G′H′ intersect at (0, −2) and are two times closer together than EF and GH.dLine segments E′F′ and G′H′ do not intersect and are the same distance apart as EF and GH.
The statement is d) Line segments E'F' and G'H' do not intersect and are the same distance apart as EF and GH.
The figure shows a pair of parallel line segments on a coordinate grid: Line segment GH runs from (-1, -1) to (3, -1), and line segment EF runs from (-1, -2) to (3, -2).
To determine the characteristics of line segments E'F' and G'H' after being translated 2 units to the right, we need to apply the translation to the endpoints of the original line segments.
Applying a translation of 2 units to the right:
Endpoint E: (-1, -2) + (2, 0) = (1, -2)
Endpoint F: (3, -2) + (2, 0) = (5, -2)
Endpoint G: (-1, -1) + (2, 0) = (1, -1)
Endpoint H: (3, -1) + (2, 0) = (5, -1)
Now, let's analyze the statements:
a) Line segments E'F' and G'H' do not intersect and are closer together than EF and GH.
This statement is false. E'F' and G'H' do not intersect, but they are not closer together than EF and GH. They are actually farther apart.
b) Line segments E'F' and G'H' intersect at (-2, 0) and are two times farther apart than EF and GH.
This statement is false. E'F' and G'H' do not intersect at (-2, 0). They have different coordinates for their endpoints.
c) Line segments E'F' and G'H' intersect at (0, -2) and are two times closer together than EF and GH.
This statement is false. E'F' and G'H' do not intersect at (0, -2). They have different coordinates for their endpoints.
d) Line segments E'F' and G'H' do not intersect and are the same distance apart as EF and GH.
This statement is true. E'F' and G'H' do not intersect, and they have the same distance between them as EF and GH.
Therefore, the correct statement is d) Line segments E'F' and G'H' do not intersect and are the same distance apart as EF and GH.
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Which group of three squares will form a right triangle when joined at their vertical vertices?
A right triangle is a type of triangle that has a 90° angle. Three squares in a group can be arranged to form a right triangle, but only if they meet certain criteria.
So, let's take a look at the options provided in the question.
Option A: a 3x3 square, a 2x2 square, and a 1x1 squareIf we join these squares at their vertical vertices, we will get an L shape, which doesn't form a right triangle.
So, option A is not correct.
Option B: a 4x4 square, a 3x3 square, and a 1x1 squareIf we join these squares at their vertical vertices, we will get a right triangle with the 4x4 square being the hypotenuse. Therefore, option B is the correct answer.
Option C: a 3x3 square, a 2x2 square, and a 2x2 squareIf we join these squares at their vertical vertices, we will get a shape with two sides that are equal in length and one side that is shorter. This does not form a right triangle. Therefore, option C is not correct.
To sum up, the group of three squares that will form a right triangle when joined at their vertical vertices is a 4x4 square, a 3x3 square, and a 1x1 square, which is option B.
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Henry is making corn grits. The recipe calls for 1 4 cup of corn grits for every 1/2 cup of water. How much water will he need if he uses 1 1 2 cups of corn grits?.
If Henry uses 1 1/2 cups of corn grits, he will need 3 cups of water.
The recipe calls for 1/4 cup of corn grits for every 1/2 cup of water. To find out how much water Henry will need if he uses 1 1/2 cups of corn grits, we can set up a proportion.
Let's assume x represents the amount of water needed in cups. The proportion can be written as:
1/4 cup of corn grits / 1/2 cup of water = 1 1/2 cups of corn grits / x cups of water
To solve the proportion, we can cross multiply:
(1/4) × x = (1 1/2) × (1/2)
Simplifying the right side of the equation:
(1/4) × x = (3/2) × (1/2)
x/4 = 3/4
To isolate x, we can multiply both sides of the equation by 4:
x = (3/4) × 4
x = 3
Therefore, if Henry uses 1 1/2 cups of corn grits, he will need 3 cups of water.
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To convert a Celsius temperature c to a Fahrenheit temperature, Fthe formula F=9/5c+32is used. Water boils at 100°c. What Fahrenheit temperature is this
The Fahrenheit temperature of 100°C is 212°F. So, we can put the given Celsius temperature in the above formula:F = 9/5(100) + 32F = 180 + 32F = 212°FTherefore, the Fahrenheit temperature of 100°C is 212°F.
Given, Celsius temperature c = 100°FTo find Fahrenheit temperature, we can use the formula:F = 9/5C + 32Put the given Celsius temperature into the formula:F = 9/5(100) + 32F = 180 + 32F = 212°F. Therefore, the Fahrenheit temperature of 100°C is 212°F.
We know that the formula for converting Celsius to Fahrenheit is given by:F = 9/5C + 32Where, F is the temperature in Fahrenheit and C is the temperature in Celsius.Water boils at 100°C. So, we need to find the Fahrenheit temperature when Celsius temperature is 100°F.So, we can put the given Celsius temperature in the above formula:F = 9/5(100) + 32F = 180 + 32F = 212°FTherefore, the Fahrenheit temperature of 100°C is 212°F.
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The ratio of the side lengths of the smaller box to the side lengths of the larger box is lowest term is to
The calculted ratio of the side lengths is 2 : 3
How to determine the ratio of the side lengthsFrom the question, we have the following parameters that can be used in our computation:
Smaller box = 12 inchesLarger box = 18 inchesUsing the above as a guide, we have the following:
Ratio = Smaller box : Larger box
So, we have
Ratio = 12 inches : 18 inches
Simplify the ratio
Ratio = 2 : 3
Hence, the ratio is 2 : 3
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Question
A company is experimenting with two new boxes for packaging merchandise. Each box is a cube with the side lengths shown. (smaller box is 12 in, larger box is 18 in.)
What is the ratio of the side lengths of the smaller box to the side lengths of the larger box in lowest terms?
In a circle with radius 6.5, an angle measuring 5.5 radians intercepts an arc. Find the length of the arc to the nearest 10th.
L ≈ 35.8 ,the length of the arc to the nearest tenth is 35.8 units
The formula for calculating the length of an arc intercepted by a central angle is L=, where L is the arc's length, is the circle's radius, and is the central angle in radians. The length of the arc to the nearest tenth is 35.8 units. Given, In a circle with radius r = 6.5, an angle measuring = 5.5 radians intercepts an arc. We know that the formula for calculating the length of an arc intercepted by a central angle is L=, where L is the arc's length, is the circle's radius, and is the central angle in radians. Substituting the values in the formula, we get:
L = rL = 6.5(5.5)L = 35.75 ≈ 35.8 (to the nearest 10th)
Therefore, the length of the arc to the nearest tenth is 35.8 units.
In a circle, the length of an arc intercepted by a central angle is determined by the central angle's size and the circle's radius. This is known as the arc's length formula. L=where L is the arc length, is the radius of the circle, and is the central angle in radians. We can use this formula to find the length of an arc intercepted by a central angle in a circle. Let's consider the following illustration to understand the concept better. In a circle with a radius of 6.5, an angle of 5.5 radians intercepts an arc. We'll use the arc length formula to find the arc's length, L.L= (Length of arc formula)Substitute the given value of r and in the formula. L = 6.5 × 5.5L = 35.75The length of the arc is 35.75 units. We'll round this answer to the nearest tenth to get the final answer. L ≈ 35.8Therefore, the length of the arc to the nearest tenth is 35.8 units.
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Consider the reduction of the triangle
Round to the nearest tenth what is the value of x
The value of the variable x in the given figure is given by 19.1 ft.
Here in the given picture the given two triangles are similar triangles.
For the similar triangles, the ratios of the similar sides are equal.
So here the side with 9.3 ft of first triangle is similar with the side with x ft and the side of 1.7 ft of first triangle is similar with the side with 3.5 ft.
By the condition then,
x/9.3 = 3.5/1.7
x = 9.3 * (3.5 / 1.7) = 19.1 [rounding off to the nearest first decimal place]
Hence the value of x in the given figure is 19.1 ft.
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The question is incomplete. The complete question will be -
Explain why it makes no sense to consider the limit of a function at an isolated point of the domain of the function
When talking about a limit of a function at a particular point, it's significant to note that this means evaluating the function as the input approaches that point. It's worth noting that the point in question must be a limit point of the domain of the function for the function to have a limit.
An isolated point is one that doesn't have any other points near it in the domain of the function. Because of this, it makes no sense to consider the limit of a function at an isolated point of the domain of the function.
A limit is defined as the value that a function approaches as the input (x) approaches a certain point (c). This definition is simple enough, but it necessitates the function having values near that point in the domain. That is to say, there must be a sufficient number of points near the point c in the domain such that we can talk about the input approaching c without going out of the domain.
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What is the exact value of Tangent (StartFraction 19 pi Over 12 EndFraction)?
A. StartFraction 1 minus StartRoot 3 EndRoot Over 1 + StartRoot 3 EndRoot EndFraction
B. StartFraction 1 + StartRoot 3 EndRoot Over 1 minus StartRoot 3 EndRoot EndFraction
C. StartFraction 3 minus StartRoot 3 EndRoot Over 3 + StartRoot 3 EndRoot EndFraction
D. StartFraction 3 + StartRoot 3 EndRoot Over 3 minus StartRoot 3 EndRoot EndFraction
The exact value of tangent (19π/12) is option C: StartFraction 3 minus StartRoot 3 EndRoot Over 3 + StartRoot 3 EndRoot EndFraction.
To find the exact value of tangent (19π/12), we can use the trigonometric identity:
tangent (θ) = sin (θ) / cos (θ).
First, let's find the values of sin (19π/12) and cos (19π/12).
Using the unit circle, we can determine that sin (19π/12) = -1/2 and cos (19π/12) = -√3/2.
Now we can substitute these values into the tangent formula:
tangent (19π/12) = sin (19π/12) / cos (19π/12) = (-1/2) / (-√3/2).
Simplifying the expression by multiplying the numerator and denominator by 2/√3:
tangent (19π/12) = (-1/2) * (2/√3) / (-√3/2) = (1/√3).
To rationalize the denominator, we multiply the numerator and denominator by √3:
tangent (19π/12) = (1/√3) * (√3/√3) = √3/3.
Therefore, the exact value of tangent (19π/12) is option C: StartFraction 3 minus StartRoot 3 EndRoot Over 3 + StartRoot 3 EndRoot EndFraction.
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X to the power of 3 is equal to y to the power of 5
The equation x^3 = y^5 represents a relationship between two variables, x and y, raised to different exponents. This equation states that the cube of x is equal to the fifth power of y.
To better understand this relationship, we can take the cube root of both sides to isolate x: x = y^(5/3). This equation shows that x is equal to the fifth root of y raised to the power of 5/3.
In simpler terms, it means that if we raise y to the power of 5/3 and then take the cube root of that result, we will obtain x.
This equation allows us to relate x and y and determine the value of one variable based on the value of the other.
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The number of crimes that occurred in a certain city per 1000 people had decreased from 45.3 in 1920 to 44.3 in 1970. Find the average rate of change in the number of crimes per 1000 people that occurred from 1920 to 1970.
The average rate of change in the number of crimes per 1000 people in a certain city from 1920 to 1970 was a decrease of 0.1 crimes per 1000 people per year.
To find the average rate of change, we can use the formula:
Average rate of change = (final value - initial value) / (final year - initial year)
In this case, the initial value is 45.3 crimes per 1000 people in 1920, and the final value is 44.3 crimes per 1000 people in 1970. The initial year is 1920, and the final year is 1970.
Substituting the values into the formula, we get:
Average rate of change = (44.3 - 45.3) / (1970 - 1920)
= (-1) / 50
= -0.02 crimes per 1000 people per year
Therefore, the average rate of change in the number of crimes per 1000 people from 1920 to 1970 is a decrease of 0.02 crimes per 1000 people per year. This means that, on average, the number of crimes per 1000 people decreased by 0.02 every year during that period.
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There are 3 roads leading from York to Castle, 5 roads leading from Castle to Oakville, and 7 roads leading from Oakville to Sunfield. How many ways are there to get from York to Sunfield?
The number of ways to get from York to Sunfield is 105. To calculate the total number of ways, we multiply the number of choices at each step along the way.
We start at York and need to reach Sunfield. We have 3 options for the first step, as there are 3 roads leading from York to Castle. After reaching Castle, we have 5 options for the second step, as there are 5 roads leading from Castle to Oakville. Finally, from Oakville to Sunfield, we have 7 options for the third step.
To determine the total number of ways to get from York to Sunfield, we multiply the number of choices at each step. Multiplying 3 options for the first step, 5 options for the second step, and 7 options for the third step gives us: 3 * 5 * 7 = 105.
Therefore, there are 105 ways to travel from York to Sunfield, considering all the possible combinations of roads.
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slove the linear equation x+4+3x=72.state the property that justiflies your first step and why you chose it
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The solution to the equation is x = 9.71 (rounded to two decimal places). To solve the equation x + 4 + 3x = 72, we will combine like terms and then isolate the variable x.
To solve the linear equation x + 4 + 3x = 72, we'll combine like terms on the left side of the equation. The property that justifies this step is the distributive property. We distribute the coefficient 3 to both x terms, which results in 4x + 3x = 7x.
So, rewriting the equation with the combined like terms, we have 4x + 3x + 4 = 72.
The reason we chose to apply the distributive property is to simplify the equation by adding the coefficients of the x terms together. This allows us to work with a simpler equation and proceed with solving for x.
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Felipe just started collecting stamps he has 36 times so far his uncle Carlo has 1890 stamps in his collection to the number of stamps Carlo has how many times the number Felipe has?
The number of times Felipe's stamp collection is contained within his uncle Carlo's collection is 52.5 times.
Felipe has 36 stamps in his collection, and his uncle Carlo has 1890 stamps in his collection. To determine how many times Felipe's collection fits into Carlo's collection, we can divide the number of stamps Carlo has by the number of stamps Felipe has.
1890 / 36 = 52.5
Therefore, Felipe's stamp collection is contained within his uncle Carlo's collection approximately 52.5 times.
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B. Directions: Make a real-life situation to represent the given integer.
Example: -25----- Joe owes Martin Php25
1. -18
2. +5
3. -38
4. 90
5. +7
3. -38: Sarah's bank account balance is -$38, indicating that she has overdrafted and owes the bank money.
The integer -38 can be represented in a real-life situation where Sarah's bank account balance is negative, indicating an overdraft.
In this scenario, the negative integer -38 represents a negative bank account balance. When Sarah checks her bank account, she sees that her balance is -$38. This means that she has overdrafted her account and owes the bank $38. The negative sign indicates a deficit or debt in this real-life situation. Sarah will need to deposit funds into her account to bring her balance back to positive and clear her debt to the bank.
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describe the fully transformation that maps triangle a to b
The fully transformation that maps triangle A to triangle B involves a combination of translation, rotation, and scaling operations.
To map triangle A to triangle B, we can apply a series of transformations. First, we can perform a translation to move triangle A to the desired position. Translation involves shifting the entire triangle in a specific direction. Once the translation is applied, the vertices of triangle A will be in the correct position relative to triangle B.
Next, we can apply a rotation transformation to align the orientation of triangle A with triangle B. Rotation involves rotating the triangle around a specific point or axis. By adjusting the rotation angle, we can ensure that the corresponding vertices of the two triangles match up.
Finally, we can apply a scaling transformation to adjust the size of triangle A to match the size of triangle B. Scaling involves uniformly expanding or shrinking the dimensions of the triangle. By scaling triangle A appropriately, we can ensure that the corresponding sides of the triangles are proportional.
By combining these three transformations—translation, rotation, and scaling—we can fully map triangle A to triangle B, ensuring that the positions, orientations, and sizes of the triangles are aligned.
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A lorry is travelling at 13.6 m/s.
The speed limit is 50 km/h.
Show that the lorry is travelling below the speed limit
To show that the lorry is traveling below the speed limit, we need to convert its speed from meters per second to kilometers per hour and compare it to the speed limit of 50 km/h.
The lorry's speed is given as 13.6 m/s. To convert this to kilometers per hour, we multiply it by the conversion factor: Speed (km/h) = Speed (m/s) * (3.6 km/h) = 13.6 * 3.6 = 48.96 km/h. Comparing the lorry's speed of 48.96 km/h to the speed limit of 50 km/h, we can see that the lorry is traveling below the speed limit.
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Find the angle of the sun above the horizon when a person 5.94 ft tall casts a shadow 9.74 ft long.
The angle of the sun above the horizon when a person 5.94 ft tall casts a shadow 9.74 ft long is approximately 34.45 degrees.
To find the angle, we can use the concept of similar triangles. The person's height, the length of the shadow, and the distance between the person and the tip of the shadow form a right triangle.
Let's denote the angle of the sun above the horizon as "θ". We can use the tangent function to find the angle:
tan(θ) = opposite/adjacent
In this case, the opposite side is the person's height (5.94 ft) and the adjacent side is the length of the shadow (9.74 ft).
tan(θ) = 5.94/9.74
To find the angle θ, we can take the inverse tangent (arctan) of both sides:
θ = arctan(5.94/9.74)
Using a calculator, we can evaluate this expression to find that θ is approximately 34.45 degrees.
Therefore, the angle of the sun above the horizon when a person 5.94 ft tall casts a shadow 9.74 ft long is approximately 34.45 degrees.
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Formula Which of the following is the total number of pennies on Rows 1-4 (the first 32 squares)? 232 – 1 232 232 1.
The total number of pennies on Rows 1-4 (the first 32 squares) is 232. The content loaded formula can be used to calculate the total number of pennies on the Rows 1-4 of the first 32 squares.
formula = 2^(n-1) + 2^(n-2) + 2^(n-3) + 2^(n-4) + 2^(n-5) + ……+ 2^1 + 2^0Where n = the number of rows The first four rows of the chessboard have 2^(4-1) = 8, 2^(4-2) = 4, 2^(4-3) = 2, and 2^(4-4) = 1 pennies respectively .The total number of pennies on the first 32 squares (Rows 1-4) is calculated using the following formula; Total = 8 + 4 + 2 + 1 = 15For the first four rows (the first 32 squares), the total number of pennies is 15. Hence, the correct option is 15.
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What is the solution to the equation? a 5 and two-thirds = 9 a 5 and two-thirds = 9. A 5 and two-thirds 5 and two-thirds = 9 minus 5 and two-thirds. A = 3 and one-third. A 5 and two-thirds = 9. A 5 and two-thirds 5 and two-thirds = 9 5 and two-thirds. A = 14 and two-thirds. A 5 and two-thirds minus 5 and two-thirds = 9 5 and two-thirds. A = 14 and two-thirds. A 5 and two-thirds minus 5 and two-thirds = 9 minus 5 and two-thirds. A = 3 and one-third.
The solution to the equation a 5 and two-thirds = 9 is A = 3 and one-third.
To solve this equation, we can subtract 5 and two-thirds from both sides of the equation.
Starting with the equation a 5 and two-thirds = 9, we can subtract 5 and two-thirds from both sides:
a 5 and two-thirds - 5 and two-thirds = 9 - 5 and two-thirds.
Simplifying the equation, we get:
a = 9 - 5 and two-thirds.
To subtract 5 and two-thirds from 9, we need to convert both numbers to the same format. 9 can be written as 8 and two-thirds, so the equation becomes:
a = 8 and two-thirds - 5 and two-thirds.
Subtracting the fractions, we have:
a = 3 and one-third.
Therefore, the solution to the equation a 5 and two-thirds = 9 is A = 3 and one-third.
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