Verbal sentence to mathematical sentence translation IN mathematical expressions, we usually use variables like x, y, z to represent numbers or quantities that are not known to us. They are always assigned values later on, which will give us a meaningful solution.Variables are fundamental in mathematics.
They are used to represent values that are not known in the problem being addressed. They are used in a wide range of fields, from solving equations to scientific experiments, computer programs, and even art, for example in plotting a graph.Learning Task 1: Translate the Verbal Sentence to Mathematical Sentence using Variable x to represent Number."Use variable x to represent number," as required in the problem.
Let us assume that the verbal sentence is, "The sum of a number and 12 is 25."
We will first find out what this verbal sentence implies.The sum of means addition A number is represented by x12 is added to the number to get the sum as 25.
With this information, we can write the mathematical sentence to represent this verbal sentence as:
x + 12 = 25
This mathematical sentence is the solution to the problem. We can solve this equation to find the value of x and prove it to be correct.
A mathematical sentence can be simple or complex, depending on its purpose and application. The use of variables in mathematical expressions makes it easier to solve complex problems. The translation of verbal sentences to mathematical sentences helps to ensure that we have a clear understanding of the problem and are addressing the right question.
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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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Adrienne invested a total of $2800.00 in two simple-interest money markét accounts. Account A paid 39 annual interest and account B paid 5% annual interest. The total amount of interest she earned after ont year was $128.00. If a represents the amount invested in dollars in account A and b represents the amount invested in dollars in account B, the system of equations a + b= 2800.00 can be used [0.03a +0.056 = 128.00 to represent this situation. How much did Adrienne invest in each account? Adrienne invested $ in account A and $ in account B.
Adrienne invested $1200 in account A and $1600 in account B.
Let's set up a system of equations to represent the given information. We are given that the total amount invested is $2800, so we have the equation a + b = 2800.
The interest earned from account A is given as 39% of the amount invested in account A, which can be represented as 0.39a.
Similarly, the interest earned from account B is 5% of the amount invested in account B, represented as 0.05b. The total interest earned is $128, so we have the equation 0.39a + 0.05b = 128.
Solving this system of equations can be done using various methods, such as substitution or elimination. One way to solve is by substitution.
From the first equation, we can solve for a in terms of b: a = 2800 - b. Substituting this into the second equation, we get 0.39(2800 - b) + 0.05b = 128.
Simplifying and solving for b, we find b = $1600. Substituting this value back into the first equation, we get a = $1200.
Therefore, Adrienne invested $1200 in account A and $1600 in account B.
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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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HW IS DUE SOON PLS HELP
Each day you do HW for "m" minutes and watch TV for 30 minutes. Write an expression that you can use to find out how many minutes you do both activities in 5 days. (pls use like terms to complete the equation thank you)
The expression for the time for which a person does both activities in 5 days is 5(m+30) minutes.
We have to write an expression that can help to find out the minutes for which a person does both the activities (homework and TV) each day. Let the time for which the person does homework each day be m minutes.
Therefore, the expression for time for which a person does both the activities each day is (m+30) minutes.To find out the time for which a person does both the activities for 5 days, we need to multiply the time for which the person does both the activities each day by 5.
Hence, the expression for the time for which a person does both activities in 5 days is:5(m+30) minutes
We have been given that each day, a person does homework for m minutes and watches TV for 30 minutes. We have to find an expression that can help to find out the minutes for which the person does both the activities each day.
Let us begin by defining variables. Let the time for which a person does homework each day be m minutes. Therefore, the expression for time for which a person does both the activities each day is (m+30) minutes.
Now we need to find the time for which the person does both activities in 5 days. To do so, we need to multiply the time for which the person does both the activities each day by 5.
Hence, the expression for the time for which a person does both activities in 5 days is:5(m+30) minutes.Now let’s consider an example to understand this better.Suppose the time for which a person does homework each day is 60 minutes.
Therefore, the expression for time for which a person does both the activities each day is (60+30) minutes = 90 minutes.
In this case, the time for which the person does both activities in 5 days is:
5(60+30) minutes = 5 x 90 minutes = 450 Minutes Therefore, in 5 days, a person will do both activities for 450 minutes.
The expression to find the minutes for which a person does both activities each day is (m+30) minutes. The expression for the time for which a person does both activities in 5 days is 5(m+30) minutes.
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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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The average height of nosiku,naza,john and tom is 1. 4m. If johns height is 1. 25m what is the total height of the other three children?
The average height is 1.4m and the total height of the other three children is given by T = 2.95 m
Given data,
To find the total height of the other three children, we first need to determine the combined height of Nosiku, Naza, and Tom.
Given that the average height of Nosiku, Naza, John, and Tom is 1.4m, and John's height is 1.25m, we can calculate the total height of the other three children as follows:
Total height of the other three children = Average height * Number of children - John's height
Total height of the other three children = ( 1.4m x 3 ) - 1.25m
T = 4.2m - 1.25m
T = 2.95m
Hence , the total height of the other three children (Nosiku, Naza, and Tom) is 2.95 meters.
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A 2 ¾-pound bag of frozen Scandinavian vegetable mix costs $0.88 per pound. How much does a 5-ounce serving cost?$_______________a.0.48b.0.28c.8.80d.2.42
Answer: To find out how much a 5-ounce serving of the frozen Scandinavian vegetable mix costs, we need to calculate the cost per ounce first.
Given that a 2 ¾-pound bag costs $0.88 per pound, we can calculate the cost per pound as follows:
Cost per pound = $0.88
Since there are 16 ounces in a pound, we can calculate the cost per ounce by dividing the cost per pound by 16:
Cost per ounce = Cost per pound / 16
Cost per ounce = $0.88 / 16
Cost per ounce ≈ $0.055
Now, to find the cost of a 5-ounce serving, we can multiply the cost per ounce by 5:
Cost of a 5-ounce serving = Cost per ounce * 5
Cost of a 5-ounce serving ≈ $0.055 * 5
Cost of a 5-ounce serving ≈ $0.275
Therefore, the cost of a 5-ounce serving of the frozen Scandinavian vegetable mix is approximately $0.275, which is closest to option (b) $0.28.
A municipality has budgeted R 80 000 for putting up new street name boards. The street name boards cost R 134 each. How many new street name boards can be put up,and how much money will be left in the budget?
With a budget of R 80,000 and each street name board costing R 134, the municipality can afford to put up approximately 597 new street name boards. After purchasing these boards, there will be R 9,998 remaining in the budget.
To find out how many new street name boards can be put up, we divide the total budget of R 80,000 by the cost of each board, which is R 134. This calculation gives us 597. So, the municipality can put up approximately 597 new street name boards.
To determine how much money will be left in the budget, we subtract the total cost of the boards from the initial budget. The total cost of 597 boards can be calculated by multiplying the cost of each board (R 134) by the number of boards (597), resulting in R 80,098. Subtracting this amount from the initial budget of R 80,000 leaves us with R 9,998 remaining in the budget.
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A supplement of an angle is six times as large as a complement of the angle. What is the measure of the angel?
A supplement of an angle is six times as large as a complement of the angle. the measure of the angle is 72°.
To find the measure of the angle, we can use the concept of the supplementary angle and the complementary angle. So, Let's consider the angle as "x"∴ Complement of the angle = 90° - x Supplement of the angle = 180° - x According to the given statement,180° - x = 6(90° - x) ⇒ 180° - x = 540° - 6x⇒ 5x = 540° - 180°⇒ 5x = 360°⇒ x = 360°/5⇒ x = 72°.
We are given that, a supplement of an angle is six times as large as a complement of the angle. We need to find the measure of the angle. Let's consider the angle as "x".∴ Complement of the angle = 90° - x Supplement of the angle = 180° - x According to the given statement, we can write,180° - x = 6(90° - x)⇒ 180° - x = 540° - 6x.
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Six times the smaller of two numbers minus the larger number is –15. Thirteen more than twice the smaller number is three times the larger number.
The equations smaller number is -2 and the larger number is 3.
The smaller number as "x" and the larger number as "y". Based on the given information the following equations:
Six times the smaller number minus the larger number is -15:
6x - y = -15
Thirteen more than twice the smaller number is three times the larger number:
2x + 13 = 3y
A system of two equations use various methods, such as substitution or elimination.
use the substitution method to solve the system:
From equation 2),
2x - 3y = -13
express 6x from equation 1) in terms of y:
6x = -15 + y
x = (-15 + y) / 6
Substituting this value of x into equation 2)
2((-15 + y) / 6) - 3y = -13
Simplifying and solving this equation
(-30 + 2y) - 18y = -78
-16y = -48
y = 3
Substituting the value of y back into equation 1), find the value of x:
6x - 3 = -15
6x = -12
x = -2
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2 Calculo la capacidad en litros de pipa
cilindrica de un trailer que mide 0. 70m de radio
y 6. 50m de largo
The capacity of the cylindrical pipe in the trailer is approximately 10,009 liters
What is the capacity?To calculate the capacity of a cylindrical pipe, one need to know the height or length of the pipe as well as the radius.
Given:
Radius (r) = 0.70 mHeight (h) = 6.50 mSo to calculate the capacity (volume) of a cylindrical pipe, one can:
Volume = π * r² * h,
So to calculate the capacity:
Volume = π x (0.70 m)^2 * 6.50 m
= π * 0.49 m² x 6.50 m
= 3.14 * 0.49 m² x 6.50 m
≈ 10.009 m³
Since the volume is in cubic meters, to convert it to liters, we multiply it by 1000 (1 cubic meter = 1000 liters):
Capacity = 10.009 m³ x 1000
= 10,009 liters
Therefore, the capacity of the cylindrical pipe in the trailer is approximately 10,009 liters
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Araceli had 20 minutes to a three problem quiz, She spent 11 7/10 minutes on question A and 3 2/5 on question B, what did she get for question C
Araceli had 20 minutes for a 3-problem quiz. She spent 11 7/10 minutes on question A and 3 2/5 minutes on question B, leaving her 5 1/5 minutes for question C. Effective time management is important during tests.
Araceli had 20 minutes to complete a three-problem quiz, and she spent 11 7/10 minutes on question A and 3 2/5 minutes on question B. To find out how much time she spent on question C, we can subtract the time she spent on question A and question B from the total time of 20 minutes:
20 minutes - 11 7/10 minutes - 3 2/5 minutes = 5 1/5 minutes
Therefore, Araceli spent 5 1/5 minutes on question C.
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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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A diver begins at sea level and dives down 200 feet. He ascends at a steady rate of 121/3 feet per minute for 4. 5 minutes. This depth is represented by the numerical expression: -200 121 3 (4. 5) Simplify the expression using the order of operations. What is the diver’s depth? -200 37 3 (4. 5) -200 55. 5 feet.
The numerical expression, -200 121 3 (4.5), represents the depth of the diver. The expression is to be simplified using the order of operations.
According to the given expression, the diver begins at sea level and dives down 200 feet. Then he ascends at a steady rate of 121/3 feet per minute for 4.5 minutes. The depth is represented by the numerical expression: -200 121/3 (4.5). Here, the expression has to be simplified using the order of operations as follows:
First, we need to simplify 121/3 * 4.5 which is equal to 363/2. Next, we have to multiply -200 with 363/2 to get -72600/2. Finally, -72600/2 can be simplified to -36300. Now, it is evident that the result of the simplified expression in feet is -36300/12 which is equal to -3025/4 or -7550/8 or -1895/2 or -947.5. Therefore, the diver's depth is -255.5 feet.
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Which hyperbola has one focus in common with the hyperbola ? A. B. C. D.
The correct option is D, which has the equation (y+13)²/144 - (x+5)²/25 = 1.
The hyperbola x²/16 - y²/9 = 1 has its center at (0, 0), its transverse axis along the x-axis, and its foci at (-c, 0) and (c, 0),
Where c is the distance from the center to the foci.
The formula for the distance from the center to the foci is c = √(a² + b²), Where a is the distance from the center to a vertex on the transverse axis, and b is the distance from the center to a vertex on the conjugate axis.
In this case,
a² = 16, so a = 4, and b² = 9, so b = 3.
Therefore, c = √(16 + 9) = 5.
So, we are looking for a hyperbola with one focus at (-5, 0) or (5, 0).
Option A has a focus at (13, 5) and a focus at (13, -5), so it does not have a focus in common with the given hyperbola.
Option B has a focus at (13, 5) and (13, -5), so it does not have a focus in common with the given hyperbola.
Option C has a focus at (13, 5) and (13, -5), so it does not have a focus in common with the given hyperbola.
Option D has a focus at (-5, -13) and (-5, 13), so it has a focus in common with the given hyperbola. Therefore, the correct answer is D.
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The complete question is:
Which hyperbola has one focus in common with the hyperbola x²/16 - y²/9 = 1.
A certain game involves tossing 3 fair coins, and it pays 12 cents for 3 heads, 7 cents for 2 heads, and 4 cents for 1 head. Is 7 cents a fair price to pay to play this game? That is, does the 7 cents cost to play make the game fair?
The expected payout is 5.625 cents, and the cost to play the game is 7 cents, it can be concluded that paying 7 cents to play this game is not fair. The expected payout is lower than the cost, resulting in a disadvantage for the player.
In this game, tossing 3 fair coins results in different payouts for the number of heads obtained. The payouts are 12 cents for 3 heads, 7 cents for 2 heads, and 4 cents for 1 head. The question is whether paying 7 cents to play this game is fair.
To determine if the game is fair, we need to compare the expected payout with the cost to play. Let's calculate the probabilities and payouts for each outcome. There are a total of 8 possible outcomes when tossing 3 coins: HHH, HHT, HTH, THH, TTH, THT, HTT, and TTT (H denotes a head, and T denotes a tail).
The probability of getting 3 heads is 1/8, so the payout for this outcome is 12 cents. The probability of getting 2 heads is 3/8 (HHH, HHT, HTH), so the payout for this outcome is 7 cents. The probability of getting 1 head is also 3/8 (TTH, THT, HTT), resulting in a payout of 4 cents. The probability of getting 0 heads (3 tails) is 1/8, resulting in a payout of 0 cents.
Now, let's calculate the expected payout by multiplying each outcome's probability with its corresponding payout and summing them up:
Expected payout = (1/8 * 12) + (3/8 * 7) + (3/8 * 4) + (1/8 * 0) = 1.5 + 2.625 + 1.5 + 0 = 5.625 cents.
Since the expected payout is 5.625 cents, and the cost to play the game is 7 cents, it can be concluded that paying 7 cents to play this game is not fair. The expected payout is lower than the cost, resulting in a disadvantage for the player.
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Say that Australia has a working population of 11,565,470 people, and that the average salary is $26,450 annually. How much tax revenue would Australia generate each year by instituting a 31. 4% income tax? a. $81,528,467,671 b. $90,224,333,274 c. $96,054,697,991 d. $209,851,983,509.
The tax revenue that Australia generate each year by instituting a income tax is $96,054,697,991. The Option C.
How much tax revenue would Australia generate each year by instituting a 31.4% income tax?
Tax revenue is the income that is collected by governments through taxation. To know the tax revenue, we will multiply the working population by the average salary and then multiply that by the tax rate.
Tax Revenue = (Working population) * (Average salary) * (Tax rate)
Tax Revenue = 11,565,470 * $26,450 * 0.314
Tax Revenue = $96,054,697,991
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How can 100. Ml of sodium hydroxide solution with a ph of 13. 00 be converted to a sodium hydroxide solution with a ph of 12. 00 ?
Answer:
Precise measurements and calculations are necessary to achieve the desired pH of 12.00.
Step-by-step explanation:
To convert a sodium hydroxide solution with a pH of 13.00 to a pH of 12.00, you would need to decrease the concentration of hydroxide ions (OH-) in the solution. One way to achieve this is by diluting the solution with a neutral solvent, such as water.
Here's a step-by-step process:
Determine the volume of the sodium hydroxide solution you want to prepare with a pH of 12.00. Let's assume you want to prepare 100 mL of the new solution.
Calculate the amount of water needed to dilute the solution. Since you want to decrease the concentration of hydroxide ions, you need to add water. The amount of water needed depends on the desired concentration and the initial concentration.
pH is a logarithmic scale, so the difference in pH values represents a 10-fold difference in concentration. Since the pH is decreasing from 13.00 to 12.00, you need to dilute the solution by a factor of 10.
Therefore, to dilute 100 mL of the sodium hydroxide solution by a factor of 10, you would need to add 900 mL of water.
Mix the sodium hydroxide solution with the calculated amount of water. Ensure thorough mixing to obtain a homogeneous solution.
By diluting the sodium hydroxide solution with water, you decrease the concentration of hydroxide ions, resulting in a lower pH value. However, it's important to note that pH is a logarithmic scale, so small changes in concentration can result in significant changes in pH.
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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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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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Cynthia had a credit card with a 17% APR and a $3,265 balance. She had budgeted to have the credit card paid off in 24 months. But after missing a single monthly payment, Cynthia’s credit card company has increased her interest rate to 21%. How much extra will Cynthia have to pay in finance charges (interest) because of the increase in her APR if she still pays off the credit card in 24 months? a. $152. 16 b. $272. 08 c. $609. 32 d. $761. 48 Please select the best answer from the choices provided A B C D.
The answer is option C: $609.32.
To calculate the extra amount Cynthia will have to pay in finance charges due to the increased APR, we need to compare the interest charged at the original rate (17%) with the interest charged at the new rate (21%).
Using the formula for calculating compound interest, we can determine the interest charges for both rates over the 24-month period. The original interest charges would be 17% of the $3,265 balance, while the new interest charges would be 21% of the same balance.
By subtracting the original interest charges from the new interest charges, we find that Cynthia will have to pay an extra $609.32 in finance charges due to the increase in her APR.
Therefore, the correct answer is option C: $609.32.
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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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Paul received a coupon for 43% off one item at a clothing store. Let b be the original price of the item. Use the expression b - 0. 43bfor the new price of the item. Write an equivalent expression by combining like Terms
The equivalent expression that combines like terms for the new price of the item is b(0.57).
To write an equivalent expression by combining like terms for the new price of the item with a 43% discount, we can simplify the expression b - 0.43b.
First, let's understand the given expression: b represents the original price of the item, and 0.43b represents the amount of the discount (43% of the original price).
To combine like terms, we can factor out the common term 'b' from both terms in the expression:
b - 0.43b = b(1 - 0.43).
Next, we can simplify the expression within the parentheses:
1 - 0.43 = 0.57.
Finally, substituting the simplified expression back into the original equation, we get:
b - 0.43b = b(0.57).
Therefore, the equivalent expression that combines like terms for the new price of the item is b(0.57).
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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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Which of the following shows 2x3y − 3x2 7y2x − 12y written in standard form? 2x3y 7y2x − 3x2 − 12y −12y 7y2x − 3x2 2x3y 7y2x − 12y 2x3y − 3x2 −12y − 3x2 7y2x 2x3y.
This is the expression written in standard form, where the terms are ordered in descending order of the variables' exponents: 2x^3y - 7y^2x - 3x^2 + 12y
To write the expression 2x^3y - 3x^2 - 7y^2x + 12y in standard form, we rearrange the terms in descending order of the variables' exponents.
The standard form of a polynomial is written as follows:
ax^n + bx^m + ... + cx^2 + dx + e
where a, b, c, d, and e are coefficients, and n, m, and so on represent the exponents of the variables.
Applying this to the given expression:
2x^3y - 3x^2 - 7y^2x + 12y
Rearranging the terms, we get:
2x^3y - 7y^2x - 3x^2 + 12y
This is the expression written in standard form, where the terms are ordered in descending order of the variables' exponents:
2x^3y - 7y^2x - 3x^2 + 12y
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Aleka and Helene both opened savings accounts that earn 2. 5% interest a year. Aleka puts $2,500 into her account. Helene put $1,500 into her account and also saves $200 cash a year. X = number of years Aleka: f(x) = 2500(1. 025)x Helene: g(x) = 1500(1. 025)x 200x Which function represents the difference, h(x) = f(x) – g(x), between the value of Aleka’s and Helene’s total savings after x years? h(x) = –1000(1. 025)x 200x h(x) = 1000(1. 025)x 200x h(x) = 1000(1. 025)x – 200x h(x) = 4000(1. 025)x 200x.
The function that represents the difference between the value of Aleka's and Helene's total savings after x years is h(x) = 1000(1.025)^x - 200x.
To determine the function that represents the difference between the value of Aleka's and Helene's total savings after x years, we need to subtract Helene's total savings from Aleka's total savings.
1: The function for Aleka's total savings after x years is f(x) = 2500(1.025)^x.
2: The function for Helene's total savings after x years is g(x) = 1500(1.025)^x + 200x.
3: To find the difference, subtract g(x) from f(x): h(x) = f(x) - g(x).
4: Substitute the expressions for f(x) and g(x) into the equation for h(x):
h(x) = 2500(1.025)^x - (1500(1.025)^x + 200x).
5: Simplify the expression by distributing the negative sign:
h(x) = 2500(1.025)^x - 1500(1.025)^x - 200x.
6: Combine like terms to simplify further:
h(x) = (2500 - 1500)(1.025)^x - 200x.
7: Simplify the coefficients:
h(x) = 1000(1.025)^x - 200x.
Therefore, the function that represents the difference between the value of Aleka's and Helene's total savings after x years is h(x) = 1000(1.025)^x - 200x.
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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 -
A badminton tournament begins with 128 teams. After the first round, 64 teams remain. After the second round, 32 teams remain. A. Write a sequence that represents the number of teams that have been eliminated in round n of the badminton tournament in Exercise 33
In each round, half of the remaining teams are eliminated.7th round: 2 - 1 = 1 team eliminated The sequence shows the progressive elimination of teams as the tournament progresses.
The sequence that represents the number of teams that have been eliminated in round n of the badminton tournament. This pattern continues until there is only one team left, which becomes the winner of the tournament.
It can be written as follows:
1st round: 128 - 64 = 64 teams eliminated
2nd round: 64 - 32 = 32 teams eliminated
3rd round: 32 - 16 = 16 teams eliminated
4th round: 16 - 8 = 8 teams eliminated
5th round: 8 - 4 = 4 teams eliminated
6th round: 4 - 2 = 2 teams eliminated
7th round: 2 - 1 = 1 team eliminated
In each round, half of the remaining teams are eliminated. This pattern continues until there is only one team left, which becomes the winner of the tournament. The sequence shows the progressive elimination of teams as the tournament progresses.
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