Shape C, a complicated shape, needs to be divided into simpler shapes in order to calculate its area. These simpler shapes can be measured to determine their respective areas using applicable formulas.
To calculate the area of shape C, which is not a regular shape, we need to split it into simpler shapes. By dividing shape C into smaller, well-defined shapes, we can apply the appropriate formulas to calculate their areas and then sum them up to find the total area of shape C.
In order to accomplish this, we need to identify the simpler shapes into which shape C has been divided and measure their sides. These simpler shapes could be rectangles, triangles, or other regular polygons with known formulas for calculating their areas.
Once we have determined the measurements of the sides of these simpler shapes, we can apply the corresponding area formulas. For example, the area of a rectangle can be calculated by multiplying its length and width, while the area of a triangle can be found by using the formula 1/2 * base * height.
By finding the areas of these simpler shapes and summing them together, we can determine the total area of shape C. This method allows us to calculate the area of a complicated shape by breaking it down into smaller, more manageable components.
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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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the 9th and 1st term of an arithmetic progress are 50 and 65 respectively find the sum of its first two terms
The function between the given functions f(x) = x² + 5x and
g(x) = 8x² - 1 can be found by adding the two functions together.
The function between f(x) and g(x) is,
f(x) + g(x) = x² + 5x + 8x² - 1
= 8x² + x² + 5x - 1
= 9x² + 5x - 1
Given,
f(x) = x² + 5x
and
g(x) = 8x² - 1
We need to find the function between the given functions.
Since f(x) and g(x) are polynomials, we can find their greatest common factor.
f(x) can be written as x(x + 5), and g(x) can be written as (2x)²- 1.
The greatest common factor of the two polynomials is,
x(x + 5) + (2x - 1)(2x + 1)
= x² + 5x + 4x - 1
= x² + 9x - 1
Therefore, the function between f(x) and g(x) is,
f(x) + g(x) = x² + 5x + 8x² - 1
= 8x² + x² + 5x - 1
= 9x² + 5x - 1
In conclusion, the function between the given functions f(x) = x² + 5x
and g(x) = 8x² - 1 is represented by the equation
f(x) + g(x) = 9x² + 5x - 1
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A recipe has a ratio of 1 1/2 cups of cheese to 6 ounces of pasta based on this recipe which statement is true
The statement that holds true is that for every 1 1/2 cups of cheese used, there should be 6 ounces of pasta.
Based on the given ratio of 1 1/2 cups of cheese to 6 ounces of pasta in the recipe, the following statement is true:
For every 1 1/2 cups of cheese used, there should be 6 ounces of pasta.
The ratio indicates the proportion or relationship between the amounts of cheese and pasta in the recipe. In this case, for each 1 1/2 cups of cheese, the recipe calls for 6 ounces of pasta. This means that the quantities of cheese and pasta are in a consistent and proportional relationship.
To illustrate this further, if you were to double the amount of cheese used in the recipe, you would also need to double the amount of pasta. For example, if you use 3 cups of cheese, you would need 12 ounces of pasta (2 times 6 ounces).
Therefore, based on the given ratio, the statement that holds true is that for every 1 1/2 cups of cheese used, there should be 6 ounces of pasta.
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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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Susie spent $4. 57 on color and black-and-white copies for her project. She made 7 more
black-and-white copies than color copies. If color copies cost $0. 44 per page and black-and-
white copies cost $0. 07 per page, how many color copies did she make?
If Susie spent $4. 57 on color and "black-white" copies for her project, then she made 8 color-copies.
Let us assume that Susie made "x" "color-copies",
The cost of each color copy is $0.44, so, total cost of color copies would be = 0.44x,
She made 7 more black-and-white copies than color copies, which means she made (x + 7) black-and-white copies.
The cost of each black-and-white copy is $0.07, so the total cost of black-and-white copies would be = 0.07(x + 7).
According to the information, Susie spent a total-amount of $4.57 on both color and black-and-white copies, which can be represented in equation form as :
So, 0.44x + 0.07(x + 7) = 4.57
0.44x + 0.07x + 0.49 = 4.57
0.51x + 0.49 = 4.57
0.51x = 4.57 - 0.49
0.51x = 4.08
x = 4.08 / 0.51
x = 8
Therefore, Susie made 8 color-copies for her project.
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Tell whether or not f(x)= pi(sin) 3x - 4x sin 2x is a sinusoid.
a.
Yes
b. No
No, the function f(x) = πsin(3x) - 4xsin(2x) is not a sinusoid. A sinusoid is a function that can be represented by a sine or cosine function with certain characteristics.
In the given function f(x) = πsin(3x) - 4xsin(2x), we can see that there are two sine terms with different frequencies, 3x and 2x. This indicates that the function does not have a constant frequency, which is a requirement for a sinusoid. Additionally, the presence of the term -4x introduces a linear term, which further deviates from the sinusoidal form.
Therefore, due to the varying frequencies and the inclusion of a linear term, the function f(x) = πsin(3x) - 4xsin(2x) does not meet the criteria to be classified as a sinusoid.
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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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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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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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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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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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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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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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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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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?
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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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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Triangle ABC has the coordinates A(8,4) B(12,4) C(16,12) if the triangle is dilated with a scale factor of 1/4 what are the new coordinates
After dilating Triangle ABC with a scale factor of 1/4, the new coordinates of A', B', and C' are A'(2,1), B'(3,1), and C'(4,3), respectively.
To dilate Triangle ABC with a scale factor of 1/4, we need to multiply the coordinates of each vertex by the scale factor.
Let's apply the scale factor to each coordinate:
A' = (8 * 1/4, 4 * 1/4)
= (2, 1)
B' = (12 * 1/4, 4 * 1/4)
= (3, 1)
C' = (16 * 1/4, 12 * 1/4)
= (4, 3)
Therefore, after dilating Triangle ABC with a scale factor of 1/4, the new coordinates of A', B', and C' are (2,1), (3,1), and (4,3) respectively. The scale factor of 1/4 shrinks the original triangle by a factor of 1/4 in both the x and y directions, resulting in a smaller triangle with the new coordinates.
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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 -
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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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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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 value of a polynomial is 0 when x=5 which expression must be a factor of the polynomial
If the value of a polynomial is 0 when x=5, then (x-5) must be a factor of the polynomial.
A polynomial is a mathematical expression consisting of variables (or indeterminates) and coefficients, combined using addition, subtraction, and multiplication operations.
Polynomials are widely used in mathematics and various fields such as physics, engineering, computer science, and economics. They play a crucial role in solving equations, interpolation, approximation, and modeling various phenomena. Polynomial equations are also studied extensively in algebra, and techniques like factoring, long division, synthetic division, and the quadratic formula are used to analyze and solve them.
Given that the value of a polynomial is 0 when x=5.
To find the expression which must be a factor of the polynomial we can use the factor theorem which states that:
If x-a is a factor of polynomial f(x), then f(a) = 0.So, if the value of a polynomial is 0 when x=5, then (x-5) must be a factor of the polynomial.
Hence, the required expression which must be a factor of the polynomial is (x - 5).
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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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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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A 2. 0 kg box is released from rest at a height yo = 0. 25 m on a frictionless ramp. The box slides from the
ramp onto a rough horizontal surface with a friction coefficient puse = 0. 50.
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How far does the box slide along the rough surface?
The box slides along the rough surface for a distance of d meters. At the bottom of the ramp, the box has zero potential energy and maximum kinetic energy.
To determine the distance the box slides along the rough surface, we need to consider the conservation of energy and the effects of friction.
Initially, the box is at a height of 0.25 m and has potential energy given by mgyo, where m is the mass of the box (2.0 kg) and yo is the initial height (0.25 m). As the box slides down the frictionless ramp, the potential energy is converted into kinetic energy. At the bottom of the ramp, the box has zero potential energy and maximum kinetic energy.
Upon reaching the rough horizontal surface, the box encounters friction. The work done by friction results in the conversion of kinetic energy into thermal energy, reducing the box's speed.
To calculate the distance the box slides on the rough surface, we need to determine the work done by friction. The work done by friction is given by the equation work = force × distance. The force of friction can be calculated using the equation force = friction coefficient × normal force, where the normal force is equal to the weight of the box (mg).
Using the given friction coefficient (μ = 0.50) and the mass of the box (m = 2.0 kg), we can calculate the force of friction. Once we have the force of friction, we can calculate the work done by friction.
The work done by friction is equal to the change in kinetic energy of the box. We can equate this work to the initial kinetic energy and solve for the distance traveled (d). The initial kinetic energy is given by (1/2)mv², where v is the velocity of the box at the bottom of the ramp.
By solving the equation for the work done by friction and equating it to the initial kinetic energy, we can determine the distance the box slides along the rough surface (d).
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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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Does the equation y-250x=500 represent the same relationship between the distance from the start of the trail and the elevation? Explain your reasoning pls
Yes, the equation y - 250x = 500 represents the same relationship between the distance from the start of the trail and the elevation.
The given equation is y - 250x = 500.
The above equation is of the form y = mx + c, where m = slope of the line and c = y-intercept of the line.
Let us convert the given equation into the form y = mx + c, y - 250x = 500, y = 250x + 500. Now, we can see that this equation is of the form y = mx + c, where m = 250, which means that the slope of the line is 250 and the value of y-intercept is 500.
Thus, the equation y - 250x = 500 represents the relationship between the distance from the start of the trail and the elevation.
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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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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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