Given that a telephone pole casts a shadow of 20 feet when the angle of elevation of the sun is directly away from the pole, the task is to determine the length of the pole to the nearest tenth of a foot.
We can use the concept of similar triangles to solve this problem. The telephone pole, the shadow, and the sun form two right triangles that are similar to each other. Let's assume the height of the pole is h feet. The length of the shadow is given as 20 feet. Since the angle of elevation of the sun is directly away from the pole, the angle between the shadow and the height of the pole is 90 degrees.
By considering the two similar triangles, we can set up a proportion: the length of the shadow / the height of the pole = the length of the adjacent side / the length of the opposite side. This can be written as 20 / h = tan(angle of elevation).To solve for h, we can rearrange the equation: h = 20 / tan(angle of elevation).
Since the angle of elevation is not given in the problem, we cannot calculate the exact length of the pole. However, if the angle of elevation is provided, we can substitute it into the equation to find the length of the pole to the nearest tenth of a foot.
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Create a relative frequency table that could be used to show the percentages of belt wearers who wear a watch or not, as well as the percentages of people without belts who wear a watch or not
Percentage of belt wearers who wear watch or not = 65% & 34% respectively.
Percentage of non belt wearers, wearing watch or not = 60% & 40% respectively.
Given,
Accessory choices of 143 people,
Now in tabular manner,
Absolute Frequency Table :
Watch No Watch Total
Belt 62 32 94
No Belt 29 20 49
Total 91 52 143
Relative Frequency Table
Watch No Watch Total
Belt 62/94 = 0.66 32/94 = 0.34 94
No Belt 29/49 = 0.60 20/49 = 0.40 49
Total 91/143 = 0.63 52/143 = 0.36 143
Hence,
Percentage of belt wearers who wear watch or not = 65% & 34% respectively.
Percentage of non belt wearers, wearing watch or not = 60% & 40% respectively.
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True or False :President Franklin D. Roosevelt felt that creating jobs was a better solution to the hardships of the Depression than government handouts of money.
True. President Franklin D. Roosevelt believed that creating jobs was a more effective approach to address the challenges of the Great Depression than relying solely on government handouts of money.
President Franklin D. Roosevelt indeed believed that creating jobs was a preferable solution to the hardships of the Great Depression, rather than simply providing government handouts of money. During his presidency, he implemented various policies and programs aimed at stimulating economic growth and increasing employment opportunities for the American people.
One of the most significant initiatives introduced by President Roosevelt was the New Deal, a series of programs and reforms enacted between 1933 and 1938. The New Deal included a wide range of measures such as the Civilian Conservation Corps (CCC), the Works Progress Administration (WPA), and the Tennessee Valley Authority (TVA). These programs aimed to create jobs and stimulate the economy by investing in infrastructure projects, public works, and conservation efforts. By providing employment opportunities to millions of Americans, these initiatives sought to alleviate the immediate hardships caused by the Great Depression.
Roosevelt's emphasis on job creation was based on the belief that work not only provided individuals with financial stability but also instilled a sense of dignity, self-worth, and purpose. He believed that government handouts, while necessary in some cases, could create dependency and erode the motivation and self-reliance of the American people. By focusing on job creation, Roosevelt aimed to restore confidence in the economy, encourage productivity, and foster a sense of national unity and resilience during a time of great hardship.
In conclusion, President Franklin D. Roosevelt strongly believed that creating jobs was a superior solution to the challenges of the Great Depression compared to government handouts of money. His policies and programs, such as the New Deal, reflected this belief by prioritizing job creation, economic stimulation, and the restoration of individual dignity and self-reliance.
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The volume of helium in a blimp is 6. 28 × 109 milliliters. The density of helium in the blimp is 0. 1786. Find the mass of the helium in the blimp. (Hint: 1,000 L = 1 cubic meter. ).
To calculate the mass of the helium in the blimp, we have to use the formula;m=ρvWhere m is the mass of the helium, ρ is the density of helium in the blimp, and v is the volume of helium in the blimp.To find the mass of the helium:
The given density is 0.1786 and volume is 6.28×109 milliliters. We have to convert the volume in liters because the given density is in liters. We know that 1,000 L = 1 cubic meter.To convert the volume in liters, we have to divide the volume by 1,000. We will get;
V = 6.28 × 109 mL/ 1,000 = 6.28 × 106 L
We have got the volume of the helium in liters. We can use this volume and the given density to find the mass of the helium in the blimp.
m = ρv = 0.1786 kg/L × 6.28 × 106 L
m= 1123310 g
We have found the mass of helium in grams. We can convert it into kilograms by dividing it by 1,000.
m=1123310 g / 1000
m= 1123.31 kg
The mass of helium in the blimp is 1123.31 kg.
We found the mass of helium in a blimp using the formula m=ρv. The given volume was in milliliters, and the given density was in liters. Therefore, we converted the volume in liters and used the formula to find the mass. The mass of the helium in the blimp is 1123.31 kg.
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Someone and someone were comparing the two functions f(x)=25x^2 and g(x)=60(5)^x
Answer:
Step-by-step explanation:
When comparing the two functions f(x) = 25x^2 and g(x) = 60(5)^x, we can analyze their properties and behavior.
Growth rate: The function g(x) = 60(5)^x grows exponentially, meaning it increases rapidly as x increases. On the other hand, the function f(x) = 25x^2 grows at a quadratic rate, which is slower than exponential growth. x-intercept: The function f(x) = 25x^2 has an x-intercept at x = 0, indicating that the graph passes through the origin. The function g(x) = 60(5)^x, being an exponential function, does not have an x-intercept. Symmetry: The function f(x) = 25x^2 is symmetric about the y-axis, while the function g(x) = 60(5)^x does not exhibit any symmetry.
In summary, the functions f(x) = 25x^2 and g(x) = 60(5)^x have different growth rates, x-intercepts, and symmetry properties. Function g(x) grows exponentially, while function f(x) has a quadratic growth pattern.
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Find A5 for the geometric series in which S6 = 63 and the common ratio r = 2.
A5, the fifth term of the geometric series, is equal to -16. S6 is equal to 63, and the common ratio (r) is 2.
To find A5, we need to determine the fifth term of the geometric series. We are given that S6 is equal to 63, and the common ratio (r) is 2.
The formula to calculate the sum of a geometric series is:
S_n = A * (1 - r^n) / (1 - r),
where S_n represents the sum of the series up to the nth term, A is the first term, r is the common ratio, and n is the number of terms.
In this case, we have S6 = 63, so n = 6 and S_n = 63. We also know that r = 2.
Using the formula, we can rearrange it to solve for A:
S_n = A * (1 - r^n) / (1 - r)
63 = A * (1 - 2^6) / (1 - 2).
Simplifying the equation:
63 = A * (1 - 64) / (-1)
63 = -63A.
Now we can solve for A by dividing both sides of the equation by -63:
A = 63 / -63
A = -1.
So, the first term of the geometric series is A = -1.
To find A5, we can use the formula for the nth term of a geometric series:
A_n = A * r^(n-1),
where A_n represents the nth term, A is the first term, r is the common ratio, and n is the term number.
Plugging in the values, we have:
A5 = (-1) * 2^(5-1)
A5 = (-1) * 2^4
A5 = (-1) * 16
A5 = -16.
Therefore, A5, the fifth term of the geometric series, is equal to -16.
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Bridget is planting a pepper garden. She has enough space to plant 4 rows. She decides to plant
1
2
of a row of each type of pepper. How many different types of peppers is she going to plant?
Bridget is planting a pepper garden and she has space to plant four rows. She decides to plant 1/2 of a row of each type of pepper. We need to find how many different types of peppers she is going to plant.
To find the solution to this problem, we first need to determine the total number of rows Bridget will plant. Bridget has space to plant four rows and she is planting 1/2 of a row of each type of pepper. So, the total number of rows she is going to plant = 4 * 1/2= 2 rows. Next, we need to find how many different types of peppers Bridget is going to plant. As she is planting 1/2 of a row of each type of pepper, we can assume that each type of pepper occupies 1/2 of a row. So, the total number of different types of peppers she is going to plant = Total number of rows / Number of rows occupied by one type of pepper= 2 / 1/2 = 2 * 2/1= 4Thus, Bridget is going to plant four different types of peppers.
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Ahmed invested $1,500 at an interest rate of 4%, compounded quarterly. How much is the investment worth at the end of 6 years?
Ahmed's investment would be worth approximately $1,902.36 at the end of 6 years, compounded quarterly.To calculate the investment worth at the end of 6 years, we can use the formula for compound interest:
A = P(1 + r/n)^(nt)
Where:
A = Final amount (investment worth)
P = Principal amount (initial investment)
r = Annual interest rate (as a decimal)
n = Number of times interest is compounded per year
t = Number of years
In this case, Ahmed invested $1,500 at an interest rate of 4% (0.04 as a decimal), compounded quarterly (n = 4), for 6 years (t = 6).
Using the formula, we can calculate the investment worth:
A = 1500(1 + 0.04/4)^(4*6)
A = 1500(1 + 0.01)^24
A = 1500(1.01)^24
A ≈ 1500(1.268242)
A ≈ $1,902.36
Therefore, Ahmed's investment would be worth approximately $1,902.36 at the end of 6 years, compounded quarterly.
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If (2x+3y direct proportional (x+5y) or x direct proportional y
The given expression, (2x + 3y), is directly proportional to (x + 5y) if and only if x is directly proportional to y.
To determine if (2x + 3y) is directly proportional to (x + 5y), we need to analyze the relationship between the variables x and y. If x is directly proportional to y, it means that as x increases or decreases, y will increase or decrease in the same ratio.
Let's assume that x is directly proportional to y. In this case, we can write x = ky, where k is the constant of proportionality. Now we substitute this expression into the given equation:
2(ky) + 3y = (ky) + 5y
Simplifying this equation, we get:
2ky + 3y = ky + 5y
Next, we combine like terms:
(2k + 3)y = (k + 5)y
For this equation to hold true for all values of y, the coefficients of y on both sides of the equation must be equal. Therefore, we can conclude that 2k + 3 = k + 5.
Solving this equation, we find:
2k + 3 = k + 5
k = 2
So, x = 2y, which confirms that x is directly proportional to y.
In summary, the expression (2x + 3y) is directly proportional to (x + 5y) if and only if x is directly proportional to y. This relationship holds true when x can be expressed as a constant multiple of y, with the constant of proportionality equal to 2.
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In Adams, the school is 16 kilometers due south of the library and 12 kilometers due west of the firehouse. What is the distance between the library and the firehouse?
Enter the correct answer in the box
kilometers
To find the distance between the library and the firehouse in Adams, we can use the Pythagorean theorem, which states that in a right triangle, the square of the hypotenuse (the side opposite the right angle) is equal to the sum of the squares of the other two sides.
In this case, the library and the firehouse form the two sides of a right triangle, with the school being the right angle. The distance between the library and the school is 16 kilometers (south) and the distance between the firehouse and the school is 12 kilometers (west).
Using the Pythagorean theorem, we can calculate the distance between the library and the firehouse:
[tex]Distance^2 = (Library-School Distance)^2 + (School-Firehouse Distance)^2[/tex]
[tex]Distance^2 = 16^2 + 12^2[/tex]
[tex]Distance^2 = 256 + 144[/tex]
[tex]Distance^2 = 400[/tex]
Taking the square root of both sides, we find:
Distance = √400
Distance = 20 kilometers
Therefore, the distance between the library and the firehouse in Adams is 20 kilometers.
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Use the situation to answer questions 7a-7c: Jackson’s car was making a rumbling noise for two weeks. He decided to take it to the mechanic to get it checked out. To diagnose the problem, the mechanic tells Jackson that he charges an initial fee of $60 and $35 for each hour he spends trying to identify the problem.7b. How much would it cost Jackson if it took the mechanic 3 hours to diagnose the problem? Explain your reasoning.7c. Does this situation represent a proportional relationship? Why or why not?
If it took the mechanic 3 hours to diagnose the problem with Jackson's car, it would cost him $165. The situation does not represent a proportional relationship because the cost depends on the number of hours spent, which is not directly proportional to the initial fee.
7b. To calculate the cost if it took the mechanic 3 hours to diagnose the problem, we need to consider the initial fee of $60 and the additional cost per hour of $35.
- The initial fee is $60.
- The cost per hour is $35.
- The number of hours spent by the mechanic is 3.
To find the total cost, we multiply the number of hours by the cost per hour and add the initial fee:
Total cost = (Number of hours * Cost per hour) + Initial fee
= (3 * $35) + $60
= $105 + $60
= $165.
Therefore, if it took the mechanic 3 hours to diagnose the problem, it would cost Jackson $165.
7c. This situation does not represent a proportional relationship because the cost does not vary directly with the number of hours. In a proportional relationship, the two variables would change at a constant rate or ratio. However, in this case, there is an initial fee of $60 regardless of the number of hours, and the additional cost is $35 per hour spent. The cost increases as the number of hours increases, but it is not directly proportional. If it were a proportional relationship, the cost per hour would remain constant. Here, the initial fee contributes a fixed amount to the total cost, while the hourly rate adds an additional variable component. Therefore, the situation does not exhibit a proportional relationship.
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The algebra tiles represent the perfect square trinomial x2+10x+c
The calculated value of c in the expression x² + 10x + c is 25
How to determine the value of cFrom the question, we have the following parameters that can be used in our computation:
x² + 10x + c
We understand that
The expression is a perfect square trinomial
So, we do the following:
Divide the coefficient of x by 2
k = 10/2
k = 5
Next, we square the result to get c
k² = 25
This means that
c = k² = 25
This means that the value of c is 25
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Question
The algebra tiles represent the perfect square trinomial x2 + 10x + c. What is the value of c?
Simplify and write the answer in exponential form
(2^6 ÷ 2^9)^5 x 2^-6
The simplified answer in exponential form is 2^(-15).
To simplify the expression (2^6 ÷ 2^9)^5 x 2^-6, we can use the properties of exponents.
First, let's simplify the division inside the parentheses by subtracting the exponents: 2^(6-9) = 2^(-3). Now, we have (2^(-3))^5 x 2^(-6).
Applying the power of a power rule, we multiply the exponents inside the parentheses: 2^(-3 x 5) x 2^(-6).
Simplifying further, we get 2^(-15 + (-6)). To multiply powers with the same base, we add the exponents: 2^(-21).
Lastly, using the rule of negative exponents, we can rewrite this as 1/2^21 or 2^(-21). However, if we want the answer in exponential form, we can express it as 2^(-15), where the exponent is simplified to its lowest form. Therefore, the simplified answer in exponential form is 2^(-15).
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A construction manager weighs a pallet that has 9 identical bricks and a 7-pound concrete block on it. The pallet weighs 25 pounds.
Given that a construction manager weighs a pallet that has 9 identical bricks and a 7-pound concrete block on it. The pallet weighs 25 pounds.
Let the weight of each brick be 'x'. As per the question, the weight of the pallet along with 9 identical bricks and a 7-pound concrete block is 25 pounds.
Therefore, the total weight of the pallet with 9 bricks and a 7-pound concrete block is: P = Weight of the pallet + (Weight of 9 bricks) + (Weight of the concrete block) P = Weight of the pallet + (9 × x) + 7P = 25
On substituting the given values,
we have 25 = Weight of the pallet + (9 × x) + 7⇒ Weight of the pallet = 25 - 9x - 7⇒ Weight of the pallet = 18 - 9x
On the other hand, we know that Weight of the pallet = (Weight of the pallet) + (Weight of the 9 bricks).
Weight of the pallet = 18 - 9x Weight of the 9 bricks = 9x
Therefore, Weight of the pallet + Weight of the 9 bricks = 25⇒ (18 - 9x) + 9x
= 25⇒ 18 - x
= 25⇒ -x
= 25 - 18 ⇒ -x
= 7⇒ x =
-7/-1⇒ x = 7
Hence, each brick weighs 7 pounds.
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On her 10-mile trip to school. Jessica's car gets 50mpg of gas. On her way home, her car gets 40 mpg. How many miles per gallon does Jessica's car get during the entire 20-mile trip?.
The number of miles per gallon Jessica's car gets during the entire 20-mile trip is 44.44. To determine the miles Jessica's car gets per gallon during the 20-mile, you must calculate the harmonic mean of the two gas mileages, 50 mpg, and 40 mpg.
The formula for the harmonic mean is given by:
H = n/(1/a + 1/b), Where H is the harmonic mean, n is the number of values, and a and b are the values whose harmonic mean is to be calculated.
So, the total number of miles traveled by Jessica during the entire trip is 20 miles, that is, 10 miles to school and 10 miles back home. Now, the harmonic mean of the two gas mileages, i.e., 50 mpg and 40 mpg, can be calculated as follows:
H = 2/(1/50 + 1/40)
= 44.44
Therefore, Jessica's car gets an average of 44.44 miles per gallon during the 20-mile trip.
Jessica's car gets 50 miles per gallon on a 10-mile trip to school, while on her way back, she gets 40 miles per gallon. So, the question seeks to know the number of miles per gallon her car gets during the 20-mile trip. To answer this question, you must calculate the harmonic mean of the two gas mileages, i.e., 50 mpg and 40 mpg. The harmonic mean is calculated using the formula:
H = n/(1/a + 1/b), Where H is the harmonic mean, n is the number of values, and a and b are the values whose harmonic mean is to be calculated. Since the total number of miles Jessica traveled during the trip is 20 miles, that is, 10 miles to school and 10 miles back home, you will have to plug in the appropriate values to get the answer. Therefore, Jessica's car gets an average of 44.44 miles per gallon during the 20-mile trip.
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A landscaper is constructing a rectangular garden with an area of 108 square feet. He draws the garden on paper and represents the length as
and the width as
. Find the length and the width of the garden.
The length of the garden could be 12 feet, and the width could be 9 feet, or vice versa, in order to achieve an area of 108 square feet.
Let's represent the length of the garden as 'L' and the width as 'W'. The area of a rectangle is given by the formula A = L * W. In this case, the area is 108 square feet. Therefore, we have the equation:
L * W = 108.
To find the length and width of the garden, we need to determine the factors of 108 that could represent its dimensions. The factors of 108 are 1, 2, 3, 4, 6, 9, 12, 18, 27, 36, 54, and 108.
By examining these factors, we look for pairs of values that multiply to 108. For example, L = 12 and W = 9 would satisfy the equation L * W = 108. Similarly, L = 9 and W = 12 would also work.
Therefore, the length of the garden could be 12 feet and the width could be 9 feet, or vice versa. Both combinations result in an area of 108 square feet, fulfilling the given conditions.
In conclusion, the length of the garden could be 12 feet, and the width could be 9 feet, or vice versa, in order to achieve an area of 108 square feet.
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A cylindrical garbage can of depth 3 ft and radius 1 ft fillswith rainwater up to a depth of 2 ft. Howmuch work would be done in pumping the water up to the top edge of the can
The amount of work that would be done by pumping water up to the top edge of the can would be 784.14 ft-lbs.
How to find the work done ?The work done to pump water depends on both the weight of the water and the distance it's moved. The weight of the water is its volume times its density, and the density of water is about 62.4 lbs/ft³.
To find the total work, we add up (integrate) the work done on each piece of water, from the top of the water (x=1 ft) to the bottom of the water (x=3 ft):
W = ∫ (from x = 1 to x = 3) of 62. 4π xdx = 62.4π x [1/2x²] (from x=1 to x=3)
= 62.4π x (1/23² - 1/21²)
= 62.4π x (1/2*9 - 1/2)
= 62.4π x (4.5 - 0.5)
= 62.4π x 4
= 249.6π ft-lbs
= 784.14 ft-lbs
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A coordinate grid is placed over a map. City A is located at (3,8) and a city B is located at (-3,20). If city C is halfway between city A and city B, find the distance between city A and city C to the nearest 2 decimal digits.
To find the distance between City A and City C, we need to calculate the midpoint between the coordinates of City A and City B.
Given:
City A: (3, 8)
City B: (-3, 20)
To find the midpoint between City A and City B, we can use the midpoint formula:
Midpoint = [(x1 + x2) / 2, (y1 + y2) / 2]
Applying the formula:
Midpoint = [(3 + (-3)) / 2, (8 + 20) / 2]
Midpoint = [0 / 2, 28 / 2]
Midpoint = [0, 14]
So, the coordinates of City C are (0, 14).
Now, to calculate the distance between City A and City C, we can use the distance formula:
Distance = √[(x2 - x1)^2 + (y2 - y1)^2]
Applying the formula:
Distance = √[(0 - 3)^2 + (14 - 8)^2]
Distance = √[(-3)^2 + 6^2]
Distance = √[9 + 36]
Distance = √45
Distance ≈ 6.71 (rounded to two decimal places)
Therefore, the distance between City A and City C is approximately 6.71 units.
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A group of 8 friends each buy 1 ticket and 1 small popcorn at the movie theater. Each ticket costs $7.50. The group
of friends spends a total of $83.60.
Enter the cost of 1 small popcorn.
t
x
1
2
3
4
5
6
7
8
9
0
US 10:
The cost of one small popcorn is $23.60. The total amount spent by the group of friends is $83.60, and each ticket costs $7.50.
To find the cost of one small popcorn, we can subtract the total cost of the tickets from the total amount spent by the group of friends.
The total amount spent by the group of friends is $83.60, and each ticket costs $7.50. Let's calculate the cost of one small popcorn:
Cost of one small popcorn = Total amount spent - (Number of tickets * Cost per ticket)
Cost of one small popcorn = $83.60 - (8 * $7.50)
Calculating further:
Cost of one small popcorn = $83.60 - $60
Cost of one small popcorn = $23.60
Therefore, the cost of one small popcorn is $23.60.
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Petra is making donuts by stamping circles in dough using a pastry stamp with a radius of 1. 5 inches. For the donut hole, she stamps out a circle of dough using a pastry stamp with a radius of 0. 5 inches
The difference between the radii of the two pastry stamps represents the thickness of the donut. In this case, the thickness would be (1.5 - 0.5) inches, which is 1 inch.
Petra's method of using pastry stamps with different radii to create donuts with specific thickness and distinct ring shape. A radius of 1.5 inches for outer circle, another with radius of 0.5 inches for donut hole.
Petra is using two different pastry stamps to make donuts, one with a radius of 1.5 inches for the outer circle and another with a radius of 0.5 inches for the donut hole.
Outer Circle: The pastry stamp with a radius of 1.5 inches is used to stamp out the outer circle of the donut. The outer circle represents the main body of the donut.
Donut Hole: The pastry stamp with a radius of 0.5 inches is used to stamp out the donut hole in the center of the donut. The donut hole is the circular space left in the middle of the donut.
Difference: The difference between the radii of the two pastry stamps represents the thickness of the donut. In this case, the thickness would be (1.5 - 0.5) inches, which is 1 inch.
Overall Shape: The combination of the outer circle and the donut hole creates the characteristic ring shape of a donut, with the thickness determined by the difference in radii.
Therefore, Petra's method of using pastry stamps with different radii allows her to create donuts with a specific thickness and a distinct ring shape.
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What is 277777777778/100000000000 simplified? (please help)
The expression 277777777778/100000000000 when simplified is 2.78
How to simplify the expressionFrom the question, we have the following parameters that can be used in our computation:
277777777778/100000000000
When the quotient is evaluated, we have
277777777778/100000000000 = 2.77777777778
Approximate
So, we have
277777777778/100000000000 = 2.78
Hence, the expression when simplified is 2.78
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Evaluate S5 for 400 200 100 … and select the correct answer below. 25 775 1,125 500.
The value of S5 for the given sequence is 500.
To evaluate S5, we need to find the sum of the first five terms of the sequence: 400, 200, 100, ...
We can observe that the sequence follows a pattern where each term is half of the previous term. Starting with 400, the next term is 200, then 100, and so on.
Using this pattern, we can calculate the sum by adding the terms:
S5 = 400 + 200 + 100 + 50 + 25 = 775.
However, none of the provided options match this result. Therefore, there seems to be an error in the options. Based on the given sequence, the correct answer for S5 should be 500.
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Mr Reyan made an agreement with his son Smith who is studying in grade12 as follows.Smith will get pocket money after he finishes all his homework everyday.He will start first day with R1.He can use this saving for his matric dance
1.write the information as a sequence
2.write the formula for the nth term of above sequence
3.write the formula for the sum of n terms of the above series
R1, R2, R3, R4, R5, ... The formula for the nth term: Rn = R1 + (n - 1) The formula for the sum of n terms: Sn = (n/2) * (2R1 + (n - 1))The information can be represented as a sequence,
where each term represents the amount of pocket money Smith receives after finishing his homework each day. The sequence starts with R1 and continues with R2, R3, R4, R5, and so on. The sequence can be extended indefinitely, representing the daily accumulation of pocket money. The formula for the nth term of the sequence can be derived by observing that the amount of pocket money Smith receives increases by one unit each day. Therefore, the formula for the nth term is Rn = R1 + (n - 1), where R1 represents the initial amount of pocket money (R1) and (n - 1) represents the number of days Smith has completed his homework. The formula for the sum of n terms in the sequence can be obtained using the formula for the sum of an arithmetic series. In this case, the sequence represents an arithmetic progression with a common difference of 1. The sum of n terms in an arithmetic series is given by the formula Sn = (n/2) * (2a + (n - 1)d), where a represents the first term (R1), n represents the number of terms, and d represents the common difference
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Write a fraction for each statement 2 copies of 1/6 is
2 copies of 1/6 can be represented as the simplified fraction 1/3. In conclusion, the fraction that represents 2 copies of 1/6 is 1/3.
To represent the statement "2 copies of 1/6," we can multiply the fraction 1/6 by 2.
When we multiply a fraction by a whole number, we simply multiply the numerator (the top number) by the whole number while keeping the denominator (the bottom number) the same. In this case, we have:
2 * (1/6) = 2/1 * 1/6 = (2 * 1) / (1 * 6) = 2/6.
So, 2 copies of 1/6 is equal to the fraction 2/6.
However, we can simplify the fraction 2/6 further. Simplifying a fraction means dividing the numerator and denominator by their greatest common divisor (GCD). In this case, the GCD of 2 and 6 is 2. By dividing both the numerator and denominator by 2, we get 1/3
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QRST is a parallelogram. Determine the measure of ∠Q. Parallelogram Q R S T. Angle Q has measure (4 x + 10) degrees, angle R is (9 x + 1) degrees, angle S is (5 x minus 3) degrees.
The measure of ∠Q is 62 degrees.
Given that, QRST is a parallelogram.
Angle Q has measure (4x + 10) degrees, angle R is (9x + 1) degrees, angle S is (5x − 3) degrees.
We have to find the measure of angle Q.
In parallelogram opposite angles are equal, and adjacent angles are supplementary.
Therefore, we can say that,
Angle T = Angle R
= 9x + 1°
Angle Q = Angle S
= 5x - 3°
Also,
Angle Q + Angle R
= 180°(4x + 10) + (9x + 1) = 180°
Solving the above equation,
4x + 10 + 9x + 1
= 18013x + 11
= 18013x
= 180 - 11
= 169x
= 169/13
Therefore, x = 13
Now, we can calculate the measure of angle Q, Angle Q = 5x - 3°= 5 × 13 - 3°= 65 - 3°= 62°
Hence, the measure of ∠Q is 62 degrees.
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. Mallory took two trips to the pizzeria to purchase food for her party. On her first trip, she bought 5 pizza pies and 3 bottles of soda, which cost her $50.50 without tax. On her second trip, she bought 2 pizza pies and 6 bottles of soda, which cost her $31.00 without tax. How much did each pizza pie cost?
Each pizza pie costs $8.75. The cost of each bottle of soda is represented by "y" dollars.
Let's assume the cost of each pizza pie is represented by "x" dollars, and the cost of each bottle of soda is represented by "y" dollars.
Based on the given information, we can set up the following system of equations:
Equation 1: 5x + 3y = 50.50 (First trip cost without tax)
Equation 2: 2x + 6y = 31.00 (Second trip cost without tax)
To solve this system of equations, we can use the method of elimination.
Multiply Equation 1 by 2 and Equation 2 by 5 to create coefficients of "x" that will cancel each other out:
2(5x + 3y) = 2(50.50)
5(2x + 6y) = 5(31.00)
Simplifying:
10x + 6y = 101
10x + 30y = 155
Now, subtract Equation 1 from Equation 2:
(10x + 30y) - (10x + 6y) = 155 - 101
24y = 54
y = 54/24
y = 2.25
Now substitute the value of "y" back into Equation 1 to solve for "x":
5x + 3(2.25) = 50.50
5x + 6.75 = 50.50
5x = 43.75
x = 43.75/5
x = 8.75
Therefore, each pizza pie costs $8.75.
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Mr. Kushner's class is selling candles for a class trip. There are 18 students in his class in all. 3 students sell 5 candles. The number of students who sell 6 candles is 2 more than the number who sell 5 candles. 3 students sell 8 candles. 1 student sells 12 candles. The rest of the students sell 9 candles. Part AThe students make a line plot named "Candles Sold. " Which of the following is a good scale for their line plot?
The line plot is also known as a dot plot.
The given information can be organized as follows:3 students sold 5 candles2 more students sold 6 candles than those who sold 5 candles3 students sold 8 candles1 student sold 12 candles Remaining students sold 9 candles.To create a line plot of candles sold, they will mark an X on the number line for each student's number of candles sold. The number line should go from 0 to the largest number of candles sold. The largest number of candles sold in this case is 12.The number of students selling the same number of candles is used to determine the height of each X mark. For example, 3 students sold 5 candles, so their mark should be placed at the number 5 on the number line with the height of the mark as 3.
A good scale for their line plot is to count by ones (1). This is because the highest number of candles sold is 12, and counting by ones will make it easy to mark an X on the number line for each student's number of candles sold.
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Tony goes into Dave's Army-Navy store and buys a hat for $14. He gives Dave a $20 bill. Dave doesn't have any change, so he takes the $20 bill across the street to Laura, the clerk in Watson's Hardware store. Laura trades Dave's $20 bill for twenty $1 bills. Dave comes back and gives Tony $6 in change. Tony takes the hat and the $6 and leaves town forever. Half an hour later Laura comes over to Dave's store, just furious. She has discovered that the $20 bill he gave her is counterfeit. Dave, of course, makes it good, giving Laura a genuine $20 bill he has in the till from earlier.
Question: Now that it is all over, who came out behind? And by how much? Explain
In this scenario, Tony is the one who comes out behind, and by $14. Tony's loss of $14 is smaller than Dave's loss of $20, making Tony the one who comes out behind by a smaller amount.
Tony initially purchases a hat for $14 and gives Dave a $20 bill. Since Dave doesn't have any change, he goes to Laura at Watson's Hardware store and exchanges the $20 bill for twenty $1 bills. Dave gives Tony $6 in change, which means Tony effectively paid $8 for the hat ($14 - $6).
However, it is later discovered that the $20 bill given to Laura by Dave was counterfeit. As a result, Dave compensates Laura by giving her a genuine $20 bill from the store's till. This means that Dave essentially lost $20 in the process.
So, in total, Tony ends up $14 behind because he paid $8 for the hat and received $6 in change, while Dave ends up $20 behind due to the counterfeit $20 bill. Tony's loss of $14 is smaller than Dave's loss of $20, making Tony the one who comes out behind by a smaller amount.
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Suppose you measure the temperature of milk in a vat. ther thermemter says 28*R. What is the temperature in degrees Celsius? Fill in the black to complete the statement.
The temperature in degrees Celsius, when the thermometer reads 28 R, is approximately -257.59 °C.
To convert the temperature from degrees Rankine (R) to degrees Celsius (°C), we can use the formula:
°C = (°R - 491.67) × 5/9
Given that the temperature reading on the thermometer is 28 R, we can substitute this value into the formula to find the temperature in degrees Celsius:
°C = (28 - 491.67) × 5/9
Simplifying the calculation:
°C ≈ (-463.67) × 5/9
°C ≈ -257.59
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Celia wants to evaluate (6.7*10^-16)-(8.2*10^-17). what steps should Celia take to find the difference?
To evaluate (6.7 * 10⁻¹⁶) - (8.2 * 10⁻¹⁷), Celia should Subtract the numbers to get the difference.
Step 1: Make the powers of 10 the same To make the powers of 10 the same, adjust the second number, which is 8.2 × 10⁻¹⁷, to have the same power of 10 as the first number, which is 6.7 × 10⁻¹⁶.
Since 10⁻¹⁷ is a smaller power of 10 than 10⁻¹⁶, we must multiply the numerator and denominator of 8.2 × 10⁻¹⁷ by 10 to obtain an equivalent value that has the same power of 10 as the first number. Therefore, we get;8.2 × 10⁻¹⁷ = (8.2 × 10⁻¹⁷) × (10 / 10)
= 82 × 10⁻¹⁸.
Step 2: Subtract the numbers Now that we have the same power of 10 in both numbers, we can subtract them. 6.7 × 10⁻¹⁶ - 82 × 10⁻¹⁸ = 6.7 × 10⁻¹⁶ - 0.0082 × 10⁻¹⁶ = 6.6918 × 10⁻¹⁶.
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Shania bought a $1,455 drum set on the installment plan. The installment agreement included a 15% down payment and 18 monthly payments of $80. 78 each.
a. How much is the down payment?
b. What is the total amount of the monthly payments?
c. How much will Shania pay for the drum set on the installment plan?
d. What is the finance charge?
The answers are: a. The down payment is $218.25. b. The total amount of the monthly payments is $1,455.24. c. Shania will pay $1,673.49 for the drum set on the installment plan. d. The finance charge is $218.49.
a. The down payment can be calculated by multiplying the price of the drum set by the down payment percentage. In this case, the down payment is 15% of $1,455. So, the down payment is 0.15 * $1,455 = $218.25.
b. The total amount of the monthly payments can be found by multiplying the monthly payment amount by the number of payments. In this case, Shania has 18 monthly payments of $80.78 each. So, the total amount of the monthly payments is 18 * $80.78 = $1,455.24.
c. To find the total cost of the drum set on the installment plan, we need to add the down payment to the total amount of the monthly payments. The total cost is $218.25 + $1,455.24 = $1,673.49.
d. The finance charge can be calculated by subtracting the price of the drum set from the total cost. In this case, the finance charge is $1,673.49 - $1,455 = $218.49.
Therefore, the answers are:
a. The down payment is $218.25.
b. The total amount of the monthly payments is $1,455.24.
c. Shania will pay $1,673.49 for the drum set on the installment plan.
d. The finance charge is $218.49.
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