To determine the range within which the length of the third side of a triangle must fall, we can use the Triangle Inequality Theorem. According to the theorem, the sum of the lengths of any two sides of a triangle must be greater than the length of the third side.
1) For the sides 8 and 13, the inequality would be:
8 + 13 > x, where x represents the length of the third side.
2) For the sides 5 and 23, the inequality would be:
5 + 23 > x.
3) For the sides 6 and 22, the inequality would be:
6 + 22 > x.
4) For the sides 15 and 22, the inequality would be:
15 + 22 > x.
These inequalities indicate that the length of the third side must be less than the sum of the given two sides.
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The length of a rectangle is represented by 2n+8, and its width is represented by n-7. Write the polynomial for the perimeter of the rectangle. Write your answer in standard form.
The polynomial for the perimeter of the rectangle can be expressed as P(n) = 2(2n+8) + 2(n-7), which simplifies to P(n) = 4n + 16 + 2n - 14.
Combining like terms, we get P(n) = 6n + 2. Therefore, the polynomial in standard form for the perimeter of the rectangle is P(n) = 6n + 2.
To find the perimeter of the rectangle, we need to add up the lengths of all four sides. The length of the rectangle is represented by 2n+8, so we have 2 sides of length (2n+8). The width of the rectangle is represented by n-7, so we have 2 sides of length (n-7). To calculate the perimeter, we add up the lengths of all four sides: (2n+8) + (2n+8) + (n-7) + (n-7). Simplifying this expression, we get 6n + 2, which is the polynomial in standard form for the perimeter of the rectangle.
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John flipped a coin 9 times and recorded 5 heads. What is the ratio of heads to tails John recorded?
John recorded 5 heads and flipped a coin 9 times. The ratio of heads to tails recorded by John is 5:4.
John flipped a coin 9 times and recorded 5 heads. To determine the ratio of heads to tails, we need to compare the number of heads to the number of tails. Since John recorded 5 heads, the remaining flips would be tails.
Therefore, the number of tails recorded would be 9 - 5 = 4. The ratio of heads to tails recorded by John is thus 5:4, which means for every 5 heads, there were 4 tails. This ratio represents the relative frequency of heads and tails in John's coin flips.
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A cash withdrawal of R5 000. 00 was made at Signet Blue on the
20/05/2019. Calculate what percentage the withdrawal fee is of the
transaction amount. Calculate the percentage of R5000. 00
The withdrawal fee of R100.00 is 2% of the transaction amount of R5,000.00.
To calculate the percentage that the withdrawal fee is of the transaction amount, we need to determine the fee amount and then express it as a percentage of the transaction amount.
Let's assume that the withdrawal fee is 2% of the transaction amount. To calculate the fee amount, we multiply the transaction amount by the fee percentage:
Fee Amount = 2% of R5,000.00
= 0.02 * R5,000.00
= R100.00
Therefore, the withdrawal fee is R100.00.
To calculate the percentage of R5000.00, we can divide the fee amount by the transaction amount and then multiply by 100 to express it as a percentage:
Percentage = (Fee Amount / Transaction Amount) * 100
= (R100.00 / R5000.00) * 100
= 2%
Hence, the withdrawal fee of R100.00 is 2% of the transaction amount of R5,000.00.
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Shirley has already jogged 5 miles. She continues to jog at an average rate of 3. 5 miles per hour. This situation is modeled by the function y=3. 5x+5 where y is the total miles jogged and x is the number of hours Shirley continues to jog. Identify the rate of change and the initial value of the function. Express your answers as decimals if necessary
The rate of change and the initial value of the function can be identified based on the given situation and the function y = 3.5x + 5.
The rate of change represents the constant rate at which the miles jogged increase per hour, while the initial value indicates the starting point or the number of miles jogged before any additional hours.
In the given function y = 3.5x + 5, the coefficient of x, which is 3.5, represents the rate of change. It indicates that for every hour Shirley continues to jog, she will add 3.5 miles to the total distance already jogged.
The constant term, 5, represents the initial value of the function. In this case, it signifies that Shirley has already jogged 5 miles before she starts jogging at an average rate of 3.5 miles per hour.
Therefore, the rate of change of the function is 3.5 miles per hour, indicating the increase in miles jogged per hour, and the initial value is 5 miles, representing the distance already jogged by Shirley before any additional hours of jogging.
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At Lyft drivers charge $2.7 per mile driven and a booking fee of $2.5 when a customer rides with them. At Uber drivers charge $2.5 per mile and a $3.7 booking fee. After how many miles do the two services cost the same?
After 6 miles, the cost of using Lyft and Uber becomes the same. To find the number of miles at which the cost of using Lyft and Uber becomes the same, we can set up an equation based on the given information.
This is a problem based on solving equation with one variable. Let's denote the number of miles as "x". The cost of using Lyft can be expressed as:
Cost of Lyft = 2.7x + 2.5
The cost of using Uber can be expressed as:
Cost of Uber = 2.5x + 3.7
To find the number of miles at which the costs are equal, we can set the two equations equal to each other and solve for x:
2.7x + 2.5 = 2.5x + 3.7
Simplifying the equation:
0.2x = 1.2
x = 1.2 / 0.2
x = 6
Therefore, after 6 miles, the cost of using Lyft and Uber becomes the same.
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12. Zoë had 3 times as much money as her
3
brother. She spent of her money on a
new CD player. Now how many times as
much money as her brother does Zoë have?
Zoë has 2 times as much money as her brother now. Answer: Zoë has twice as much money as her brother.
Let's find out how much money Zoë had to begin with if she spent 1/3 of her money on a new CD player.Suppose Zoë's brother had $x. Since Zoë had 3 times as much money as her brother, she had $3x to begin with.She spent 1/3 of her money on a new CD player.1/3 of $3x = $xZoë now has $2x remaining after buying the CD player.Since $2x is twice the amount of money her brother has ($x), Zoë has twice as much money as her brother after buying the CD player.
Therefore, Zoë has 2 times as much money as her brother now. Answer: Zoë has twice as much money as her brother.
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At sea level, the air presses down on our bodies at 14.7
pounds per square inch (psi). When diving in the ocean,
the pressure increases. The equation y = 0.445x + 14.7,
where x is the number of feet a diver descends, represents
this situation.
a. Explain using the definition how you know the
relationship represented by the equation is a function.
We can conclude that the relationship represented by the given equation is a function. Moreover, the pressure increases as the diver descends below sea level, which is shown by the positive slope (0.445) of the equation.
The equation y = 0.445x + 14.7 represents a situation where a diver descends below sea level. This equation gives the pressure (y) of the water at a depth of x feet below sea level. Here, y is dependent on x. It means that the pressure at a given depth is dependent on that particular depth. Therefore, we can say that the given equation represents a function because for each value of x, there is only one corresponding value of y.
A function is defined as a relation that maps each input value (x) to exactly one output value (y). In other words, it is a set of ordered pairs (x, y), where each value of x is paired with a unique value of y. The equation given above satisfies this definition of a function because it represents a one-to-one relationship between the depth (x) and the pressure (y) of the water.
Therefore, we can conclude that the relationship represented by the given equation is a function. Moreover, the pressure increases as the diver descends below sea level, which is shown by the positive slope (0.445) of the equation.
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The spheres cost $2 per square foot and Selim can spend $20 per sphere. What is the maximum diameter of the spheres he can purchase?
The surface area of a sphere is 4πr2, where r is the radius of the sphere. The cost of a sphere is 2 per square foot, so the cost of a sphere with radius r is 8πr2. Selim can spend 20 per sphere, so he can purchase a sphere with radius r such that 8πr2≤20. This inequality can be solved for r to get r≤8π20=2π5. The diameter of a sphere is 2r, so the maximum diameter of the spheres Selim can purchase is 22π5=10π≈3.162 feet.
A conservationist determines that a particular beach is eroding at a rate of 1. 1% each year. When writing an explicit formula to represent the amount of beach remaining each year, which value should she use as the common ratio?.
The conservationist should use a common ratio of 0.989 to represent the erosion rate of 1.1% each year. Explicit formula- P * (0.989)^n.
Since the beach is eroding, the amount of beach remaining each year will be decreasing by 1.1% of the previous year's amount. This means that the remaining beach will be 98.9% (or 0.989) of the previous year's amount.
To represent the amount of beach remaining each year, follow these steps:
Start with the initial amount of beach (let's call it "P").
Multiply P by 0.989 to find the amount of beach remaining after one year.
Multiply the result from step 2 by 0.989 to find the amount of beach remaining after two years.
Repeat this process for each subsequent year, multiplying the previous year's amount by 0.989 to find the amount of beach remaining in the next year.
The general formula for the amount of beach remaining after "n" years can be written as P * (0.989)^n, where "n" represents the number of years that have passed.
This explicit formula can be used to calculate the amount of beach remaining after any number of years, given the initial amount of beach.
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If a manufacturing company uses a single, weight-losing raw material to manufacture its finished product, then most likely the company will:_________.
i. Choose to outsource its labor component.
ii. Locate its manufacturing plant at the raw material site.
iii. Locate several manufacturing plants close to consumers.
iv. Use a ubiquitous raw material.
v. Agglomerate close to similar factories
Option B : Locate its manufacturing plant at the raw material site.
Given,
Weight losing raw material to manufacture its finished products .
Here,
Weight loss raw materials are those which loses their weight while production sugar, iron and steel, and aluminum that lose weight during production.
For example we can take the industries that require minerals for their production works .
Another example is of sugar industry which require weight losing raw material .
Thus the correct option will be B .
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For the circle: (x+3)^2 + (y-4)^2 = 100, find the length of the diameter
The length of the diameter of the circle in this problem is given as follows:
20 units.
What is the equation of a circle?The equation of a circle of center [tex](x_0, y_0)[/tex] and radius r is given by:
[tex](x - x_0)^2 + (y - y_0)^2 = r^2[/tex]
The equation for this problem is given as follows:
(x + 3)² + (y - 4)² = 100.
Hence the measure of the radius is given as follows:
r = 10 units.
The diameter has a measure which is twice the radius, hence:
d = 2 x 10
d = 20 units.
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a blueprint of a house is drawn using a scale of 1/4 in = 3ft. If the bedroom of the actual house is 16 by 12 in, what are the dimensions of the bedroom of the blueprint
The dimensions of the bedroom in the blueprint are approximately 1/9 ft by 1/12 ft.
To find the dimensions of the bedroom in the blueprint, we can use the given scale of 1/4 in = 3 ft.
First, let's convert the dimensions of the actual bedroom into feet:
Length of the actual bedroom = 16 in * (1 ft / 12 in) = 16/12 ft = 4/3 ft
Width of the actual bedroom = 12 in * (1 ft / 12 in) = 12/12 ft = 1 ft
Now, let's use the scale to find the dimensions of the bedroom in the blueprint:
Length of the bedroom in the blueprint = Length of the actual bedroom * Scale
Length of the bedroom in the blueprint = (4/3 ft) * (1/4 in / 3 ft)
Length of the bedroom in the blueprint = 4/3 * 1/12
Length of the bedroom in the blueprint = 4/36
Length of the bedroom in the blueprint = 1/9 ft
Width of the bedroom in the blueprint = Width of the actual bedroom * Scale
Width of the bedroom in the blueprint = (1 ft) * (1/4 in / 3 ft)
Width of the bedroom in the blueprint = 1 * 1/12
Width of the bedroom in the blueprint = 1/12 ft
Therefore, the dimensions of the bedroom in the blueprint are approximately 1/9 ft by 1/12 ft.
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2 dot plots. The highlands have a mean rainfall of 15. 27 millimeters, and the Lowlands have a mean rainfall of 12. 05 millimeters. The dot plots show rainfall totals for several spring storms in highland areas and lowland areas. What is the mean rainfall for the highland storms? What is the mean rainfall for the lowland storms?.
The mean rainfall for the highland storms is 15.27 millimeters, and the mean rainfall for the lowland storms is 12.05 millimeters.
In the dot plots, each dot represents the rainfall total for a spring storm in either the highland or lowland areas. To find the mean rainfall, we calculate the average of all the rainfall values in each plot.
For the highland storms, the mean is 15.27 millimeters, which indicates that, on average, the rainfall for the spring storms in the highland areas is 15.27 millimeters.
For the lowland storms, the mean is 12.05 millimeters, suggesting that the average rainfall for the spring storms in the lowland areas is 12.05 millimeters.
These values provide a measure of the central tendency or average rainfall for the respective areas and can help in comparing the rainfall patterns between the highlands and lowlands.
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The leg of a right triangle is 8 and the hypotenuse is 17. What is the other leg?
b is the length of a side of a triangle, it cannot be negative. The length of the other leg of the right triangle is 15.
A right triangle is a triangle that has one of its angles exactly 90°. The leg of a right triangle is 8 and the hypotenuse is 17. To find the length of the other leg of the right triangle, we can use the Pythagorean theorem.
This theorem states that for any right triangle, the sum of the squares of the lengths of the legs is equal to the square of the length of the hypotenuse. In equation form, this can be written as: a² + b² = c²where a and b are the lengths of the legs of the right triangle, and c is the length of the hypotenuse. Substituting the given values into this equation, we have: 8² + b² = 17²
Simplifying the left-hand side of the equation, we get:
64 + b² = 289
Subtracting 64 from both sides, we get:
b² = 225
Taking the square root of both sides, we get:
b = ±15
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6:2:3 last month 24 pairs of boots were sold how many boots all the together were sold last month
Last month, a total of 72 boots were sold. To calculate the total number of boots sold last month, we need to multiply the number of pairs of boots sold (24) by the ratio 6:2:3. In this ratio, each part represents a fraction of the total number of boots.
In the given ratio, the first part represents 6 out of 11 parts. So, we can calculate the fraction of boots sold by multiplying the first part of the ratio (6) by the total number of parts (11): 6/11 * 24 = 72/11.
Therefore, a total of 72 boots were sold last month.
The ratio 6:2:3 indicates that for every 6 parts of boots sold, there are 2 parts of another type of boots and 3 parts of yet another type. In this case, since we only have information about the first part (24 pairs of boots), we need to find the fraction of the total number of boots that the first part represents.
To calculate this fraction, we multiply the first part (6) by the total number of parts in the ratio (11). This gives us the fraction 6/11, which represents the proportion of boots sold out of the total. Multiplying this fraction by the total number of pairs of boots sold (24) gives us the total number of boots sold last month, which is 72.
Therefore, using the given ratio and the number of pairs of boots sold, we can determine the total number of boots sold by considering the proportion of each type of boots in the ratio.
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4) Emily can walk 3/4 of a mile in 1/4 of an hour. At
this same rate, how long does it take Emily to walk 1
mile?
A.1/2 of an hour
B. 2/5 of an hour
C. 1/3 of an hour
D. 2/3 of an hour
Emily can walk 3/4 of a mile in 1/4 of an hour. At the same rate, time taken to walk 1 mile =1/3 of an hour.
Mathematical representation
We know that, Emily can walk 3/4 of a mile in 1/4 of an hour.
Meaning,
Time taken to walk 3/4 of a mile = 1/4 of an hour
Distance covered = 3/4 mile
We need to find the time taken by Emily to walk 1 mile.
The rate is defined as the distance covered in unit time. So,
Rate = Distance / Time
We know that Rate of Emily = 3/4 ÷ 1/4
= 3/4 × 4/1
= 3 miles/hour
The rate of walking is 3 miles/hour.
Now we can find the time taken to walk 1 mile using rate formula.
Distance = Rate × Time
We have to walk 1 mile and the rate of walking is 3 miles/hour.
Time = Distance / Rate
Time taken to walk 1 mile = 1 / 3 = 1/3 hour.
So, the answer is option C.
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Calvin wants to sell a basic badminton kit to his friends. In that kit, he puts two rackets worth ₹140₹140₹, 140 each and a shuttlecock worth ₹80₹80₹, 80. He wants to have a profit of 25\%25%25, percent?
The selling price for Calvin's badminton kit, with a desired profit of 25%, is ₹450.
To determine the selling price for Calvin's badminton kit, including a desired profit of 25%, we need to calculate the cost price and add the profit margin.
The cost price of the badminton kit consists of two rackets worth ₹140 each and a shuttlecock worth ₹80. Let's calculate the total cost price:
Cost Price = (2 * ₹140) + ₹80 = ₹280 + ₹80 = ₹360
To find the selling price with a 25% profit margin, we need to add 25% of the cost price to the cost price:
Profit = 25% of ₹360 = (25/100) * ₹360 = ₹90
Selling Price = Cost Price + Profit = ₹360 + ₹90 = ₹450
Therefore, the selling price for Calvin's badminton kit, with a desired profit of 25%, is ₹450.
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2 cyclists leave town 86 kilometers apart at the same time and travel toward each other. one cyclist travel 7 km/h faster than the other.
Two cyclists leave a town 86 kilometers apart at the same time and travel towards each other. One cyclist is traveling 7 km/h faster than the other. The task is to find their speeds.
Let's assume the speed of the slower cyclist is x km/h. Since the other cyclist is traveling 7 km/h faster, their speed would be x + 7 km/h.
The total distance between the two cyclists is 86 kilometers, and they are traveling towards each other. This means that the sum of the distances covered by both cyclists will equal the total distance of 86 kilometers.
Using the formula Distance = Speed × Time, we can set up the equation:
Distance covered by the slower cyclist + Distance covered by the faster cyclist = 86
The time taken by both cyclists will be the same since they start at the same time. So, we can rewrite the equation as:
(x km/h) × (t hours) + (x + 7 km/h) × (t hours) = 86
Simplifying the equation, we get:
xt + (x + 7)t = 86
xt + xt + 7t = 86
2xt + 7t = 86
Since we have two variables (x and t), we need another equation to solve the system. Without additional information, it is not possible to determine the exact values of x and t.
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There are 640 acres in a square mile, and 5280 feet in 1. 00 mile. What is the length in feet (to the nearest foot) of the side of a square having an area of 1. 00 acre?
The side lengt of the square is approximately 1839 feet.
How to find the side length?To find the length in feet of the side of a square with an area of 1.00 acre, we need to convert the acreage to square feet.
Given:
1 acre = 640 acres/mile² (640 acres in a square mile)
1 mile = 5280 feet (conversion factor from miles to feet)
To convert acres to square feet, we can multiply by the conversion factor:
1 acre = 640 acres/mile² * 1 mile² * 5280 feet
Simplifying the units:
1 acre = 640 * 5280 square feet
Now, to find the length of the side of the square, we can take the square root of the area:
Side length = √(1 acre * 640 * 5280 square feet)
Calculating:
Side length ≈ √(1 * 640 * 5280) ≈ √3379200 ≈ 1839.29 feet
Rounding to the nearest foot, the length of the side of the square with an area of 1.00 acre is approximately 1839 feet.
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Divide x^3 – 3x² - 10x+ 24 by x-2
Step 1 - Fill in the missing number:
k | 1 -3 -10 24
k=
The result of dividing [tex]x^3 - 3x^2 - 10x + 24[/tex] by [tex]x - 2[/tex] is [tex]x^2 + 2x - 6[/tex] with a remainder of 12.
To divide the polynomial [tex]x^3 -3x^2 - 10x + 24[/tex] by x - 2, we can use polynomial long division.
Write the polynomial in descending order of powers of x, filling in missing terms with zeros.
[tex]x^3 - 3x^2 - 10x + 24[/tex] becomes[tex]x^3 + 0x^2 - 3x^2 - 10x + 24[/tex].
Divide the first term of the dividend (x^3) by the first term of the divisor (x) to get the quotient.
The quotient is x^2.
Multiply the divisor [tex](x - 2)[/tex] by the quotient [tex](x^2)[/tex] and write the result below the dividend.
[tex](x - 2) \times (x^2) = x^3 - 2x^2[/tex].
Subtract the result from the dividend.
[tex]x^3 + 0x^2 - 3x^2 - 10x + 24 - (x^3 - 2x^2) = 2x^2 - 10x + 24[/tex].
Bring down the next term from the dividend, which is -10x.
Repeat steps 2-5 with the new dividend [tex](2x^2 - 10x + 24)[/tex].
Divide the first term of the new dividend [tex](2x^2)[/tex] by the first term of the divisor (x) to get the next term of the quotient.
The next term of the quotient is 2x.
Multiply the divisor (x - 2) by the new term of the quotient (2x) and write the result below the new dividend.
[tex](x - 2) \times (2x) = 2x^2 - 4x[/tex]
Subtract the result from the new dividend.
[tex]2x^2 - 10x + 24 - (2x^2 - 4x) = -6x + 24[/tex].
Bring down the last term from the new dividend, which is 24.
Repeat steps 2-5 with the new dividend [tex](-6x + 24)[/tex].
Divide the first term of the new dividend (-6x) by the first term of the divisor (x) to get the final term of the quotient.
The final term of the quotient is -6.
Multiply the divisor [tex](x - 2)[/tex] by the final term of the quotient (-6) and write the result below the new dividend.
[tex](x - 2) \times (-6) = -6x + 12[/tex].
Subtract the result from the new dividend.
[tex]-6x + 24 - (-6x + 12) = 12[/tex].
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Luis created a spreadsheet of his expenses for three months. Which of Luis's expenses are variable expenses?
Expenses
rent
utility bill
car loan payment
insurance payment
Jan Feb Mar
$1,250. 00 $1,250. 00 $1,250. 00
$124. 11 $108. 72
$121. 69
$384. 00 $384. 00 $384. 00
$97. 18
$97. 18
$97. 18
$315,43 $367. 25 $341. 04
$72. 18 $152. 74 $0. 00
$108. 71 $117. 46 $127. 34
groceries
clothing
fuel
the variable expensive in Luis's spreadsheet are groceries and fuel.Variable expenses are those that can change from month to month based on usage or consumption.
Looking at the given expenses, the variable expenses in Luis's spreadsheet would be:
1. Groceries: The amounts for groceries vary from month to month. In January, the expense is $315.43, in February it is $367.25, and in March it is $341.04. These amounts indicate that the grocery expenses are not fixed and can fluctuate.
2. Fuel: The amounts for fuel also differ for each month. In January, the expense is $72.18, in February it is $152.74, and in March it is $0.00. The varying amounts suggest that fuel expenses are dependent on usage and can vary.
On the other hand, the following expenses appear to be fixed or consistent:
1. Rent: The rent expense remains the same throughout the three months at $1,250.00.
2. Utility bill: The utility bill expenses also remain consistent in each month at $124.11, $108.72, and $121.69.
3. Car loan payment: The car loan payment remains unchanged at $384.00 for each month.
4. Insurance payment: The insurance payment is also consistent in each month at $97.18.
Therefore, the variable expensive in Luis's spreadsheet are groceries and fuel.
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Rome has a lower temperature than Toronto because 10. 8°C is closer to 0°C than –24. 9°C. True or false
The statement "Rome has a lower temperature than Toronto because 10.8°C is closer to 0°C than –24.9°C" is false.
To determine which location has a lower temperature, we need to compare the actual temperature values, not their distances from 0°C. In this case, the temperatures given are 10.8°C and -24.9°C. Comparing these temperatures directly, we can see that -24.9°C is significantly lower than 10.8°C.
The negative sign indicates that -24.9°C is below the freezing point of water, while 10.8°C is above it. The statement mistakenly focuses on the distance of the temperatures from 0°C. While it is true that 10.8°C is closer to 0°C in absolute value than -24.9°C, it does not determine which location has a lower temperature.
The actual values of the temperatures indicate that -24.9°C is colder than 10.8°C. Therefore, the statement is false. Rome does not necessarily have a lower temperature than Toronto based on the given comparison.
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Find the volume of a right circular cone that that that has a height of 13.8ft and a base with a radius of 7.8ft
The volume of the right circular cone with a height of 13.8ft and a base radius of 7.8ft is approximately 672.59 cubic feet.
1. The formula for the volume of a right circular cone is V = (1/3)πr²h, where V represents the volume, π is a mathematical constant (approximately 3.14159), r is the radius of the base, and h is the height of the cone.
2. Plug in the given values into the formula: V = (1/3)π(7.8ft)²(13.8ft).
3. Calculate the volume: V = (1/3)π(60.84ft²)(13.8ft).
4. Simplify the expression: V ≈ 7.484π(13.8ft).
5. Use the approximation π ≈ 3.14159: V ≈ 7.484(3.14159)(13.8ft).
6. Calculate the volume: V ≈ 293.48ft³.
7. Round the result to two decimal places: V ≈ 672.59 cubic feet.
Therefore, the volume of the given right circular cone is approximately 672.59 cubic feet.
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Consider the field above. It has 5 sides. The total perimeter is LaTeX: 16x^2+21x+1616 x 2 + 21 x + 16. The lengths of the four shortest sides are LaTeX: 3x+8,\:2x^2+4x,\:2x^2+2x,\:and\:5x^2+3x+23 x + 8 , 2 x 2 + 4 x , 2 x 2 + 2 x , a n d 5 x 2 + 3 x + 2. Find the length of the longest side.
The answer is "The length of the longest side is 6x² - 12x + 16. Here, the total perimeter is given as LaTeX: 16x² + 21x + 16.
As there are five sides, we can express the total perimeter as the sum of all the five sides. Let the length of the longest side be 'l'.
So, the total perimeter is equal to the sum of all five sides, which can be expressed as:
3x + 8 + 2x² + 4x + 2x² + 2x + 5x² + 3x + 2 + l16x + 21x + 16
= 10x + 9x + l.
Now, we can find the length of the longest side by simplifying the above equation and solving for 'l'.
16x² + 21x + 16 = 10x² + 9x + l
l = 6x² - 12x + 16
Therefore, the length of the longest side is 6x² - 12x + 16.
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Jessie tried to solve an equation step by step. 1. 5b+9=111. 5b=3Step 1b=2Step 2\qquad\begin{aligned} 1. 5b+9&=11\\\\ \\ 1. 5b&=3&\green{\text{Step } 1}\\\\ \\ b&=2&\blue{\text{Step } 2}\\\\ \end{aligned}1. 5b+91. 5bb=11=3=2Step 1Step 2Find Jessie's mistake. Choose 1 answer:Choose 1 answer:(Choice A)AStep 1\green{\text{Step }1}Step 1start color #28ae7b, start text, S, t, e, p, space, end text, 1, end color #28ae7b(Choice B)BStep 2\blue{\text{Step }2}Step 2start color #6495ed, start text, S, t, e, p, space, end text, 2, end color #6495ed(Choice C)CJessie did not make a mistake
Jessie made a mistake in Step 1 of solving the equation. The correct equation should be 5b + 9 = 111 instead of 5b + 9 = 11.
In Step 1, Jessie mistakenly wrote the right-hand side of the equation as 11 instead of 111. The correct equation should be 5b + 9 = 111, not 5b + 9 = 11. This error occurred in the process of trying to isolate the variable b by subtracting 9 from both sides of the equation.
Step 2, where Jessie obtained 5b = 3, is correct. However, the mistake in Step 1 led to an incorrect starting point, which affected the subsequent steps.
Therefore, the correct answer is Choice A: Jessie made a mistake in Step 1.
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Why was the fifth grader looking foward to being 11 years old
The fifth grader was looking forward to being 11 years old for a few reasons. For starters, 11 is a prime number and prime numbers are fascinating.
Secondly, 11 is a transitional age as it marks the end of childhood and the beginning of the preteen years. This age group is usually associated with new responsibilities, such as being able to stay home alone and taking on new challenges. The fifth-grader might have also been looking forward to having more independence and control over their life at this age. 11 is also an age where you start to develop your own interests and hobbies, which can be exciting for a child who is eager to explore and learn.
Additionally, at 11, you are closer to becoming a teenager, which can be an exciting prospect for some kids. Lastly, the fifth-grader might have been looking forward to being able to participate in more activities and events that are designed for older kids. In conclusion, turning 11 years old represents a significant milestone in a child's life, and there are many reasons why the fifth-grader was excited about it.
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In preparation for the homecoming football game, members of the student body are painting the school rock. If Angela works alone, it will take
her 5 and one-half hours. If Brandon works alone it will take him 7 hours. If they work together, approximately how long will it take?
4
3
6. 25
125
When working together, it will take Angela and Brandon about 3 hours and 12 minutes to paint the school rock.
The answer is 3
Let's first assume that Angela can paint the school rock in x hours, then Brandon would be able to paint the school rock in y hours.Angela’s work rate: \frac{1}{x} of the rock per hour .
So, Angela’s work rate = [tex]$\frac{1}{5.5}$[/tex]and Brandon’s work rate = \frac{1}{7} Working together, Angela and Brandon’s work rate will be: \frac{1}{5.5} + \frac{1}{7} of the rock per hour [tex]$\frac{1}{5.5} + \frac{1}{7}$ = $\frac{0.1818 + 0.1429}{1}$ = $\frac{0.3247}{1}$[/tex] Working together, they will paint the rock in \frac{1}{0.3247} hours = 3.08 hours. Rounding off to the nearest minute, it will take them about 3 hours and 12 minutes .
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Give the equations of the asymptotic of f(x),g(x) and h(x)
The equation of the asymptote for function f(x) is y = 0.
The equation of the asymptote for function g(x) is x = a, where a is a constant.
The equation of the asymptote for function h(x) is y = mx + b, where m and b are constants.
For function f(x), the asymptote is y = 0 since the function approaches zero as x approaches positive or negative infinity.
For function g(x), the asymptote is a vertical line at x = a. This occurs when the function approaches a specific x-value but does not cross it.
For function h(x), the asymptote is a straight line represented by y = mx + b. This occurs when the function approaches a linear relationship as x approaches positive or negative infinity. The values of m and b depend on the slope and y-intercept of the asymptote, respectively.
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In a sale, normal prices are reduced by 20%The normal price for a coat is reduced by £15Work out the normal price of a coat
The normal price of a coat is £75.
In a sale, normal prices are reduced by 20%.
The normal price for a coat is reduced by £15.
Lets find the normal price of a coat.
Step 1
Let the normal price of the coat be x.
Then, the price of coat after reducing 20% from the normal price will be `(x - (20/100)x)`.
Therefore, the price of coat is
`(x - (20/100)x) = 0.8x`.
Step 2
It is given that the normal price for a coat is reduced by £15.
Hence, 0.8x = x - 15
Solving this equation for x:
x - 0.8x = 150.2x = 15x = `15/0.2`x = 75
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Suppose a chemist combines a 25% acid solution and a 50% acid solution to make 40 L of 45% acid solution. How many liters of each solution did she use? Use the blanks below to fill in your numerical answers.
__________ L of 50% solution; __________ L of 25% solution
To create a 40 L solution with a 45% acid concentration, a chemist combines a 25% acid solution and a 50% acid solution. Therefore, the chemist used 32 L of the 50% acid solution and (40 - 32) = 8 L of the 25% acid solution to create the 40 L solution with a 45% acid concentration.
Let's assume the chemist uses "x" liters of the 50% acid solution. Since the total volume of the mixture is 40 L, the remaining volume will be (40 - x) liters of the 25% acid solution.
The acid content in the 50% solution is 0.5x, while the acid content in the 25% solution is 0.25(40 - x).
To find the acid content in the final 45% solution, we multiply the acid concentration (0.45) by the total volume (40):
0.45 * 40 = 0.5x + 0.25(40 - x)
Simplifying the equation:
18 = 0.5x + 10 - 0.25x
Combining like terms:
0.25x = 8
Dividing both sides by 0.25:
x = 32
Therefore, the chemist used 32 L of the 50% acid solution and (40 - 32) = 8 L of the 25% acid solution to create the 40 L solution with a 45% acid concentration.
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